Proceedings of the Conference in Honor of C N Yang's 85th Birthday

The following sections are included:

• PREFACE

• Photographs

• CONTENTS

In this talk I discuss a range of topics on developing creativity and innovation in engineering and science: the constraints on creativity and innovation such as the necessity of a fitting into the realities of the physical world; necessary personal qualities; getting a good idea in engineering and science; the art of obsession; the technology you use; and the technology of the future.

It is a great honour and pleasure for me to participate in the conference, dedicated to 85 years celebration for Professor C. N. Yang.

The influence of C. N. Yang on my own research is very strong. Two of my directions — quantization of the Yang-Mills field and theory of solitons stem from his works. I am proud to remind, that the term "Yang-Baxter equation" was introduced by L. Takhtajan and me and now covers extensive research in integrable models and quantum groups.

In my talk I shall describe the subject, which to some extend connects solitons and Yang-Mills quantum field theory. As is reflected in the title, it is still not well established. However, I believe, that work on it will be continued in the future.

Curvature and torsion are the two tensors characterizing a general Riemannian space–time. In Einstein's general theory of gravitation, with torsion postulated to vanish and the affine connection identified to the Christoffel symbol, only the curvature tensor plays the central role. For such a purely metric geometry, two well-known topological invariants, namely the Euler class and the Pontryagin class, are useful in characterizing the topological properties of the space–time. From a gauge theory point of view, and especially in the presence of spin, torsion naturally comes into play, and the underlying space–time is no longer purely metric. We describe a torsional topological invariant, discovered in 1982, that has now found increasing usefulness in recent developments.

We present a topological classification of vacuum space-time. Viewing Einstein-Cartan theory as a gauge theory of Lorentz group and identifying the gravitational connection as the gauge potential of Lorentz group, we construct all possible vacuum gravitational connections which give a vanishing curvature tensor. With this we show that, when the space-time admits a global chart, the vacuum connection has the same topology which describes the multiple vacua of SU(2) gauge theory. This tells that the vacuum space-time can be classified by the knot topology π₃(S³) = π₃(S²). We discuss the physical implications, in particular the space-time tunneling, of our result in quantum gravity.

The cosmological QCD phase transitions may have taken place between 10^-5 and 10^-4 seconds in the early Universe offers us one of the most intriguing and fascinating questions in cosmology. In bag models, the phase transition is described by the first-order phase transition and the role played by the latent "heat" or energy released in the transition is highly nontrivial and is being classified as the first-order phase transition. In this presentation, we assume, first of all, that the cosmological QCD phase transition, which happened at a time between 10^-5 sec and 10^-4 sec or at the temperature of about 150 MeV and accounts for confinement of quarks and gluons to within hadrons, would be of first order. Of course, we may assume that the cosmological QCD phase transition may not be of the first order. To get the essence out of the first-order scenario, it is sufficient to approximate the true QCD vacuum as one of possibly degenerate vacua and when necessary we try to model it effectively via a complex scalar field with spontaneous symmetry breaking. On the other hand, we may use a real scalar field in describing the non-first-order QCD phase transition. In the first-order QCD phase transition, we could examine how and when "pasted" or "patched" domain walls are formed, how long such walls evolve in the long run, and we believe that the significant portion of dark matter could be accounted for in terms of such domain-wall structure and its remnants. Of course, the cosmological QCD phase transition happened in the way such that the false vacua associated with baryons and many other color-singlet objects did not disappear (that is, using the bag-model language, there are bags of radius 1.0 fermi for the baryons) - but the amount of the energy remained in the false vacua is negligible by comparison. The latent energy released due to the conversion of the false vacua to the true vacua, in the form of "pasted" or "patched" domain walls in the short run and their numerous evolved objects, should make the concept of the "radiation-dominated" epoch, or of the "matter-dominated" epoch to be re-examined.

By analytically continuing QCD scattering amplitudes through specific complexified momenta, one can study and learn about the nature and the consequences of factorization and unitarity. In some cases, when coupled with the largest time equation and gauge invariance requirement, this approach leads to recursion relations, which greatly simplify the construction of multi-gluon scattering amplitudes. The setting for this discussion is in the space-cone gauge.

A brief summary of the current status of neutrino oscillations will be given. Then the on-going construction of the Daya Bay Reaction Neutrino Experiment near the Daya Bay nuclear power plant is sketched. The Daya Bay experiment will measure the mixing angle θ₁₃ to the level of sin² 2θ₁₃ = 0.01.

A summary is given of some of the developments in the elastic scattering and production processes at high energies. First, Professor Yang's geometrical model of hadronic and nuclear collisions is reviewed. When there was some preliminary experimental evidence that the total cross section for proton–proton collision might not approach a constant at very high energies, theoretical studies were initiated to determine the high-energy asymptotic behavior in relativistic quantum gauge theory. With this starting point, the successive stages of development are:

I. Theoretical prediction of increasing total cross sections;

II. Development of phenomenology and quantitative predictions that were verified experimentally afterwards; and

III. Theory and phenomenology of production processes, especially that of the Higgs particle, at the Large Hadron Collider.

Since the Large Hadron Collider (LHC) is still being built, the last topic is at an early stage of development, and unexpected results may be forthcoming.

I gave a rambling talk about gravity and its many mysteries at Chen-Ning Yang's 85th Birthday Celebration held in November 2007. I do not have any answers.

All the geometric phases are shown to be topologically trivial by using the second quantized formulation. The exact hidden local symmetry in the Schrödinger equation, which was hitherto unrecognized, controls the holonomy associated with both of the adiabatic and non-adiabatic geometric phases. The second quantized formulation is located in between the first quantized formulation and the field theory, and thus it is convenient to compare the geometric phase with the chiral anomaly in field theory. It is shown that these two notions are completely different.

Many approaches at incorporating quantum effects in gravity result in a fundamental minimal length. There have been several ways of manifesting this length, notably those of Yang and Snyder. In this paper, I describe the consequences of such a possibility within the context of several simple quantum mechanical systems, and point out how these can be used to constrain the value of the minimal length. I also discuss some implications for relativistic dynamics.

We reconsider the question of the relative importance of single particle effects and correlations in the solvable interacting neutrino models introduced by Friedland and Lunardini and by Bell, Rawlinson and Sawyer. We show, by an exact calculation, that the two particle correlations are not "small", and that they dominate the time evolution in these models, in spite of indications to the contrary from the rate of equilibration. The failure of the Boltzmann single particle approximation in this model is tentatively attributed to the simplicity of the model, in particular the restriction to two flavor mixing, and the neglect of the position dependence of the interaction.

We analyze the coupled supergravity and Yang–Mills system using holomorphy, near the rigid limit where the former decouples from the latter. We find that there appears generically a new mass scale around gM_pl where g is the gauge coupling constant and M_pl is the Planck scale. This is in accord with the weak-gravity conjecture proposed recently.

It is a pleasure to dedicate this talk to Prof Yang on the occasion of his 85th birthday, especially here in my birthplace, Singapore. I still recall the year 1957 when the local Chinese newspapers broke with the story of breakdown of parity, I didn't understand the phrase 宇称不守恒, and when I checked into my high school physics text, I couldn't find any explanation. The Chinese newspapers 南阳商报,星洲日报 call this Lee–Yang breakthrough a revolution, but it was hardly noticed by the English newspapers at the time. It wasn't until I came to the U.S. in the Fall of 1957, that a true revolution occurred. I think I can speak for a whole generation of ethnic Chinese physicists who grew up in the U.S. that we personally benefitted far more from this revolution than the revolution of parity non-conservation…

The remarkable exact solution of 1D interacting fermions heralded a new era in the study of quantum many-body problems. The mathematical structure of the underlying Yang-Baxter equation led to profound advances in other fields. Recently there has been a significant revival of interest in 1D quantum many-body problems due to the striking and ongoing experimental developments in the study of cold quantum matter. In particular, through the trapping and cooling of interacting systems of atomic bosons and fermions in low dimensions. There is, e.g., already rather spectacular agreement between theory and experiment for 1D interacting bosons. This includes an experimental test of Yang-Yang thermodynamics for bosons on a chip…

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As a development step towards constructing a hard X-ray FEL in China, a soft X-ray FEL test facility (SXFEL) was proposed under C N Yangs initial suggestion. This test facility will be built on the campus of the Shanghai Synchrotron Radiation Facility and it can be converted into a user facility or a part of hard X-ray FEL in the future. This presentation describes the FEL developments in China and reports the preliminary design and status of this Chinese soft X-ray Test facility.

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The nuclear physics and particle physics researches in China have a long tradition. BEPC is a milestone of the particle physics in China. The many interesting physics results were obtained from BEPC. Beijing Synchrotron Radiation Facility based on BEPC became the major synchrotron radiation facility in China. The upgrade of BEPC, which will increase the luminosity by two orders of magnitude, is going smoothly. The non-accelerator based experiments were promoted also. Professor Yang made very important contribution to Chinese physics, especially to promote the large science facilities for the multiple discipline researches. The particle physics faces the great challenges, and meet the great opportunities in the 21^st century. The medium term plan of the particle physics in China was discussed.

We use the term "electronic matter" for electrons (charged or, hypothetically, uncharged) in their ground-state under the action of a fixed external potential (Born-Oppenheimer approximation). For a given chemical potential mu, the properties (e.g. the density)of the electrons anear a given point, say r = 0, depend primarily on the positions and nuclear charges of the nearby nuclei. This so-called "nearsightednes", its validity and limitations, will be analyzed and exemplified.

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A brief introduction and overview is given of the complexity that is possible and the challenges its study poses in many-body systems in which spatial dimension is irrelevant and naively one might have expected trivial behaviour.

Heat conduction is an old yet important problem. Since Fourier introduced the law bearing his name two hundred years ago, a first-principle derivation of this law from statistical mechanics is still lacking. Worse still, the validity of this law in low dimensions, and the necessary and sufficient conditions for its validity are still far from clear. In this talk I'll give a review of recent works done on this subject. I'll also report our latest work on asymmetric heat conduction in nonlinear systems. The study of heat condution is not only of theoretical interest but also of practical interest. The study of electric conduction has led to the invention of such important electric devices such as electric diodes and transistors. The study of heat conduction may also lead to the invention of thermal diodes and transistors in the future.

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We briefly review the spin-charge gauge approach to the 2D t-J model (prototypic doped Mott insulators) in the limit t≫J, introducing a U(1) field gauging the global charge symmetry and an SU(2) field gauging the global spin-rotational symmetry. We show that this approach can naturally explain many experimental features of transport properties for High Tc cuprates, in particular the metal-insulator crossover phenomena in the "pseudogap phase" (PG) and 1/T behavior of conductivities in the "strange metal phase" (SM) at higher T or doping concentration. Furthermore, it is able to reproduce the universality and the quadratic in T behavior (above the crossover) of in-plane resistivity in PG. A composite particle formed by binding the charge carrier (holon) and spin excitation (spinon) via the slave-particle gauge field is invoked to interpret the obtained results.

See the review: P.A. Marchetti, Z.B. Su and L. Yu, J. Phys.: Condens. Matt. 19 (2007) 125212 and references therein.

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The photon helicity may be mapped to a spin-1/2, whereby we put forward an effective interaction (a scalar) between a light beam and an electron spin current through virtual optical transitions in a direct-gap semiconductor such as GaAs. Such an effective interaction is possible since the pure spin current and the photon spin current, both keeping the time-reversal symmetry but breaking the space-inversion symmetry of the system, are of the same tensor type, namely, the rank-2 pseudo-tensor. The optical effects due to the effective coupling induces the circular birefringence, which is similar to the Faraday rotation in magneto-optics but nevertheless involve no net magnetization. Such optical birefringence effect of a pure spin current originate from the intrinsic spin-orbit coupling in valence bands but involves neither the Rashba effect from structure inversion asymmetry nor the Dresselhaus effect due to bulk inversion asymmetry of the material. This novel optical birefringence effect may be exploited for direct, non-demolition measurement of a pure spin current.

Great progress has been made in high temperature superconductivity (HTS) science, material and technology in the 20 years since its discovery. The next grand challenge will be room temperature superconductivity (RTS). Room temperature superconductivity, if achieved, can change the world both scientifically and technologically. Unfortunately, it has long been considered by some to belong to the domain of science fiction and to occur only "at an astronomical temperature and at an astronomical distance". With the advent of HTS in 1987, the outlook for RTS has become much brighter. Currently, there appears to be no reason, either theoretical or experimental, why room temperature superconductivity should be impossible. BCS theory has provided the basic framework for the occurrence and understanding of superconductivity, but, since its inception, it has failed to show where and how to find superconductivity at higher temperatures. To date, empiricism remains the most effective way to discover superconductors with high transition temperatures. In this paper based on the talk given at the Professor Yang's 85^th birthday celebration on October 31, 2007 in Singapore, I shall summarize the search for superconductors of higher T_c prior to and after the discovery of HTS, list the common features of HTS and describe some approaches toward RTS that we are currently pursuing.

We give an elementary construction of the Fibonacci model, a unitary braid group representation that is universal for quantum computation. This paper is dedicated to Professor C. N. Yang, on his 85-th birthday.

We review old and recent results on periodic quantum Toda lattice: a completely integrable system of N particles on the line with the nearest neighbors interaction with exponential potential.

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This presentation will sketch past progress and explore possible future directions in the atomic-scale structure determination of surfaces, interfaces and nanostructures. Atomic-scale structure is the basis of understanding for a wide range of phenomena in physics, chemistry, materials science and other fields, and needs to be determined from experiment, by efficient theoretical and computational interpretation.

Comparisons will be made between different available techniques for surface structure determination, in particular regarding their relative capabilities. Highlighted will be Scanning Tunneling Microscopy and Low-Energy Electron Diffraction. Both of these techniques are capable of detailed atomic-scale structure determination of nanostructures, by comparison between experiment and theoretical simulation.

Examples will be given to illustrate recent progress in structure determination of several nanostructures, including buckminsterfullerenes (C60), carbon nanotubes (CNTs) and silicon nanowires (SiNWs).

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In the early years of the last century the discreteness of matter, of electric charge, and of mechanical action became firmly established, and slowly some of the more subtle implications of the interplay of these three were worked out. Dirac showed that magnetic monopoles also had to be quantized, the importance of dislocations in solids was shown, and the quantization of circulation in neutral superfluids and of magnetic flux in superconductors was predicted and demonstrated. Such topological defects can be a sign of a symmetry broken by a phase transition, or, as Onsager suggested in his first exposition of quantized circulation, can themselves drive a phase transition. I discuss circulation in superfluids, flux in superconductors and Hall conductance in inversion layers as examples of such quantum numbers. I show why there is a topological quantum number, and ask how the mathematical quantum number is related to measurable quantities. Recently there has been interest in whether the robustness of such topological defects make them suitable for quantum manipulation.

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Professor Chen Ning Yang has made seminal and influential contributions in many different areas in theoretical physics. This talk focuses on his contributions in statistical mechanics, a field in which Professor Yang has held a continual interest for over sixty years. His Master's thesis was on a theory of binary alloys with multi-site interactions, some 30 years before others studied the problem. Likewise, his other works opened the door and led to subsequent developments in many areas of modern day statistical mechanics and mathematical physics. He made seminal contributions in a wide array of topics, ranging from the fundamental theory of phase transitions, the Ising model, Heisenberg spin chains, lattice models, and the Yang-Baxter equation, to the emergence of Yangian in quantum groups. These topics and their ramifications will be discussed in this talk.

Biology now produces huge amount of data mainly in the form of symbolic sequences. These data are noisy and incomplete so that statistics is inevitable as a first step in any analysis. However, in order to reveal the biological regularities masked by billion years of random mutations and natural selection one must invoke more or less deterministic approaches. We will draw a few simple examples from our recent bioinformatics work that make use of Poisson distribution and Markov prediction in statistics, Goulden-Jackson cluster method in enumerative combinatorics, number of Eulerian loops in graph theory, and factorizable language in formal language theory.

We investigate the spatial behavior of spin precession of traversing electrons in a two dimensional electron gas, and, also, the property of spin interference in square loop devices with Rashba and Dresselhaus spin-orbit couplings. Treating the effects due to the two coupling mechanisms by means of a spin rotation operator, we develop a convenient framework for studying the property of spin precession. We first derive analytical expressions for the spin precession which allow a more concrete description of the spatial distribution of the spin orientation. For example, the properties of spin precession, such as the rotation axis, the rotation angle and the cone angle, can be easily determined. We then extend the analytic framework to derive the spin-orbit coupling-induced phase for spin interference in square rings; this procedure makes the optimal control of the interference condition more convenient, and the spin filter more accessible experimentally.

Ludwig Boltzmann died by his own hand 101 years ago last September. He was a passionate believer in atoms: underlying thermodynamics, he felt, lay a statistical world governed by the mechanics of individual particles. His struggles against critics — "Have you ever seen an atom?" taunted Ernst Mach — left him pessimistic. Nevertheless, following Maxwell and clarified by Gibbs, he established the science of Statistical Mechanics. But today, especially granted our understanding of critical singularities and their universality, how much do atomic particles and their charged partners, ions, really matter? The answers we have also met opposition. But Boltzmann would have welcomed the insights gained and approved of applications of statistical dynamics to biology, sociology, and other enterprises.

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Pattern formation and decay in the early stage of growth is fundamental to many materials physics and chemistry. Understanding the complex interplay between factors that influence the evolution of surface-based nanostructures can be challenging and so computer simulation can play an important role in providing insight. In this talk, I will first introduce a one-, two-, and three-dimensional Ehrlich-Schwoebel (ES) barrier in kinetics-driven growth. Within this framework, I will show how one can control the island shape, the island instability, and the film roughness efficiently. Furthermore, I will discuss a novel concept: a true upward adatom diffusion on metal surface, which is beyond the traditional Ehrlich-Schwoebel (ES) barrier model. This process offers new indications as how to use ab initio kinetic Monte Carlo simulation can uncover some of the building regulations of the evolution mechanism down to atomic-scale.

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Fifty years ago, Yang and I worked on the dilute hard-sphere Bose gas, which has been experimentally realized only relatively recently. I recount the background of that work, subsequent developments, and fresh understanding. In the original work, we had to rearrange the perturbation series, which was equivalent to the Bogoliubov transformation. A deeper reason for the rearrangement has been a puzzle. I can now explain it as a crossover from ideal gas to interacting gas behavior, a phenonmenon arising from Bose statistics. The crossover region is infinitesimally small for a macroscopic system, and thus unobservable. However, it is experimentally relevant in mesoscopic systems, such as a Bose gas trapped in an external potential, or on an optical lattice.

Quantum phenomena have become directly observable with the development of advanced techniques such as coherent field-emission electron beams, sensitive detectors, and microlithography. Examples are the single-electron build-up of an interference pattern, which contains, as R. Feynman describes in his textbook, the heart of quantum mechanics, and the Aharonov–Bohm (AB) effect, which indicates the physical significance of gauge fields. Using the AB effect, i.e., the fundamental principle behind the interaction of an electron wave with electromagnetic fields, new ways to directly observe previously unobservable microscopic quantum objects and phenomena were developed by detecting the phase of electrons.

We study dynamics of two species of fermionic atoms in optical lattices in the framework of the asymmetric Hubbard model. A common phenomenon, called phase separation is predicted to occur. We provide arguments on the existence of phase separation, accompanied by a rigorous proof that, even for a single hole case, the density wave state is unstable to the phase separation in the strong interaction limit. Using the state-of-the-art numerical techniques, we obtain the ground state phase diagram and investigate the quantum phase transition from the density wave to phase separation by studying both the corresponding charge order parameter and quantum entanglement. We also discuss experimental realization of phase separation in optical lattices.

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Our ability to control and to manipulate atomic systems has considerably increased during the last few years. Very precise measurements with ultracold atoms provide now severe new tests of fundamental theories like general relativity. The possibility to control all experimental parameters of an ultracold atomic sample, like the temperature, the density, the strength of the interactions, allows one to realize simple models of more complex systems found in other fields of physics and to get a better understanding of their behavior. A few of these developments will be briefly reviewed.

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Search for topologically non-trivial states of matter has become a prime goal for condensed matter physics. Recently, a new class of topological insulators has been proposed. These topological insulators have an insulating gap in the bulk, but have topologically protected edge states due to the time reversal symmetry. In two dimensions the edge states give rise to the quantum spin Hall (QSH) effect, in the absence of any external magnetic field. We show that the QSH state can be realized in HgTe/CdTe semiconductor quantum wells. By varying the thickness of the quantum well, the electronic state changes at a critical thickness. This is a topological quantum phase transition between a conventional insulating phase and a phase exhibiting the QSH effect with a single pair of helical edge states. This theoretical proposal has been tested in a recent experiment carried out at University of Wuerzburg, and the distinct signatures of the QSH state have been experimentally observed.

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Spin interaction Hamiltonians are obtained from the unitary Yang–Baxter Ř-matrix. Based on which, we study Berry phase and quantum criticality in the Yang–Baxter systems. We also indicate that Bogoliubov Hamiltonian is a derivative of Dirac Hamiltonian via braid relation.

Database search has wide applications and is used as a subroutine in many important algorithms. In this paper we will consider a database with a single target item. Quantum algorithm [Grover] locates the target item faster than any classical algorithm. In addition to a full [Grover] search, it frequently occurs that one is looking for a group of items [a block] containing the target item, rather than the target item itself. This problem is known as partial search. As a generalization of the full search, partial search is of particular importance in practice. Partial search trades accuracy for speed, i.e. it works faster than a full search. There exists different versions of partial search. We will study the optimized version of the algorithm discovered by Grover and Radhakrishnan and call it GRK. GRK can be applied successively [in a sequence]. First the database is partitioned into blocks and GRK is applied to find the target block. Then this target block is partitioned into sub-blocks and GRK is used again to find the target sub-block. This procedure can be repeated if the database is large enough. [This sequence of GRK's is called a hierarchy.] Another possibility is to partition the database into sub-blocks directly and use GRK to find the target sub-block once. In this paper we will prove that the latter is faster [makes less queries to the oracle].

In this paper we discuss the spin Hall effect (SHE) in cold atoms through optical coherent control means. We first briefly introduce the concepts of spin-orbit coupling and SHE in solid systems and then discuss the optical means in creating adiabatic gauge field for neutral atomic system. The optically induced SHE are then presented.

Electrons in ultrathin films are confined to form quantum well states (QWS). Photoemission provides the most direct observation of QWS in k-space. The unique capabilities now available at the Advanced Light Source (ALS) at Berkeley make it possible to measure the QW states with atomic layer resolution. In this talk, the photoemission result from the ALS on the Cu/Co(100) QW system is presented. Firstly, using a Ni monolayer to probe the Cu QWS at different positions, it is shown that the QWS in metallic thin films can be described by the envelope function of the Bloch wave. Secondly, by measuring the magnetic coupling using the magnetic dichroism, the relationship is demonstrated between the oscillatory magnetic coupling and the oscillations of the density of states at the Fermi level.

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In this talk I will describe the present situation of a young field of research: quantum information processing. In particular, I will explain how by using basic concepts coming from Quantum Mechanics it should be possible to build devices that process information in a very efficient way, and allow us to transmit information in a completely new way. Furthermore, during the last few years it has been shown that several of the ideas developed in the context of quantum information can be used to describe complicated many-body quantum systems. In particular, I will explain how new powerful algorithms can be built that should allow us to simulate important problems in the fields of atomic and condensed matter physics.

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Degradable channels are one of the very few for which the quantum capacity can be computed exactly in terms of a one-step formula. We describe several important classes of degradable channels, as well as some differences between qubits and channels on spaces of higher dimension.

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There is a photo of Prof Yang and Prof Steinberger together in May 1986, Beijing. The talk will tell the story behind the picture.

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The title is a quote from my "Yang's Pyramid" — published in the festschrift celebrating Professor Yang's 70th birthday, ≪Chen Ning Yang, a Great Physicist of the Twentieth Century≫. I likened the collection of his scientific works to a pyramid. As time goes on, hidden treasures continue to be discovered, adding to the well-known brilliant ones. This observation of mine continues to bear out in an impressive way. For the celebration of his 85th birthday, I will highlight recent developments of such remarkable achievements and make an attempt to identify the reasons for them, with the backdrop of my own perspectives.

The shape of the solid lipid monolayer domain surrounded by a fluid phase is of considerable interest from both physical and mathematical points of view. Here, we report two new results about this topic. First, we find an exact analytical solution to an approximated shape equation that we derived recently. This solution can well-describe the kidney- and boojum-like domains that abound in lipid monolayer. Second, we derive an exact domain shape equation by a direct variation of domain energy without any artificial cutoff. We find no continuous solutions that satisfy this shape equation due to the divergence of its coefficients, which is rooted in the continuous description of electrostatic dipoles.

The no-slip hydrodynamic boundary condition (NSBC) states that there can be no relative motion at the fluid-solid interface. In spite of the lack of first-principles support, either from kinetic theory or otherwise, NSBC has been regarded as a pillar of continuum hydrodynamics for more than a century. However, over the past fifty years, it has been realized that in immiscible two-phase flows, the moving contact line (MCL), defined as the intersection of the fluid-fluid interface with the solid wall, is incompatible with the NSBC. In 1988, molecular dynamic (MD) simulations for the first time explicitly demonstrated the breakdown of NSBC in the vicinity of the MCL. Since that time it was realized that without a new framework to treat the boundary condition(s), continuum hydrodynamics would be unable to accurately model nanoscale or microscale hydrodynamic behavior. This is sometimes described as an example of the "breakdown of continuum.

By applying Onsager's principle of minimum energy dissipation, we have recently derived the boundary conditions that for the first time enabled quantitative prediction of the MD simulation results from continuum hydrodyanmics, and in so doing revised the NSBC [1]. Our results indicate that the hydrodynamic boundary condition(s) should be consistent with the general statistical mechanic principle with underlie all linear response phenomena in dissipative systems. Implications of our results will be presented.

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We give a brief review of the considerable progress made recently in the field of electron-impact ionisation of atoms. Such processes require the solution of three (or more) particles interacting via the Coulomb potential. Though historically the formulation of such problems has been particularly difficult, the calculated fully differential cross sections are in remarkable agreement with experiment for both H and He from near threshold through to high energies.

The AAPPS is an umbrella organization of physical societies in the Asia Pacific region. Chen Ning Yang was the most active and important key person for the formation of the AAPPS.

The brain is considered to be the most complex system, a fertile ground for understanding the complexity of its functions through dynamical modeling. In this talk, we present some biophysical models that help to reveal the complexity of visual functions of the brain through functional self-organization processes. We also present some recent results on how the functional connectivity arises and changes in the brain, reflecting the underlying dynamics of nervous systems. The implications of our work to the brain function are discussed.

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The concept of symmetry has played a key role in the development of modern physics. For example, using symmetry, C.N. Yang and other physicists have greatly advanced our understanding of the fundamental laws of physics. Meanwhile, computer scientists have been pondering why some computational problems seem intractable, while others are easy. Just as in physics, the laws of computation sometimes can only be inferred indirectly by considerations of general principles such as symmetry. The symmetry properties of a function can indeed have a profound effect on how fast the function can be computed. In this talk, we present several elegant and surprising discoveries along this line, made by computer scientists using symmetry as their primary tool.

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In response to current energy and environmental issues the development of renewable energy sources becomes an urgent need. On the other hand, fabrication of better performance devices with much higher energy efficiency, such as LED lightings, has also become the focus of current research. Nanotechnology has been demonstrated to be a valuable and important path for the development of technologies in both the renewable energy sources and energy-saving devices. In this presentation, I shall summarize the energy related research activities in Taiwan, including our own effort on the development of high performance (high ZT value) thermoelectric materials, that supported by the national initiatives on nanotechnology.

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The time was 35 years ago. Chen-Ning Yang, my Ph.D. advisor at Stony Brook, thoughtfully led me through a career decision path that I followed, and have enjoyed since then. This is my reminiscence of that time so critical to my career.

This paper gives an introduction to some partial differential equations appeared in the study of quasicrystals. In addition the analytic solutions and weak solutions of the equations under complicated boundary conditions and initial conditions are also discussed.

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In this talk I present a simple and unified approach to both exact and quasi-exact solvabilities of the one-dimensional Schrödinger equation. It is based on the prepotential together with Bethe ansatz equations. This approach gives the potential as well as the eigenfunctions and eigenvalues simultaneously. In this approach the system is completely defined by the choice of the change of variables, and the so-called zero-th order prepotential. We illustrate the approach by several examples of Hermitian and non-Hermitian Hamiltonians with real energies. The method can be easily extended to the constructions of exactly and quasi-exactly solvable Dirac, Pauli, and Fokker-Planck equations, and to quasinormal modes.

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Some of Prof. C. N. Yang's works are related to quantum entangled states in particle physics. Quantum entanglement leads to quantum information, which has been discussed in almost all areas of physics reigned by quantum mechanics, except particle physics. Here we demonstrate that the concept of quantum information can be extended to the regime of particle physics. Specifically, we will describe a scheme of quantum teleportation using neutral kaons. We also explain an idea on how to define quantum entanglement in the setting of relativistic quantum field theory.

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Non-Abelian gauge field approach is applied to condensed matter system with time-reversal invariance. In this article, we show its relevance to the technologically-important area of spintronics. We consider specifically the spin Hall modulation and magnetic moment dynamic and discuss the important roles they play in the physics of magnetic recording and magnetic memory.

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A two-parametric gl(2/1)-graded R-matrix satisfying the Yang-Baxter and Hecker equations is suggested. The associated quantum supergroup is a two-parametric quantum deformation of U[gl(2/1)] which by construction is a quasi-triangular Hopf superalgebra.

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A new kind of two-parametric deformations is suggested. Applying it to the superalgebra osp(1/2) we obtain a new two-parametric deformation of U[osp(1/2)] and then its grade-star representations. The latter are either finite-dimensional (for integral highest weights) or infinite-dimensional (otherwise).

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A new field was created in 1984 when, famously, Vaughan Jones discovered a new polynomial invariant of knots. In the years that immediately followed there appeared a confusing proliferation of similar constructions. The Yang-Baxter equation proved to be the essential tool that led to the systematization of these ideas within the algebraic theory of quantum groups. In this talk I want to give a taste of what has happened in the field in the twenty years since these first developments by describing a key recent result: the rationality of the Kontsevich integral.

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In 1961 Byers and Yang have discovered a theorem of periodicity of energy levels in units of a flux quantum. In superconductors, the quantum unit is hc/2e. In the semiconductors, the pairing does not occur so that the flux quantum is hc/e. We show that Byers and Yang's flux quantization is applicable to the fractional charge, experimentally observed in the quantum Hall effect. It particularly explains the observation of 1/3 charge. The flux quantization also occurs for spin other than 1/2. We find that for spin 3/2 unusual series of large charges are predicted. The charge becomes very large such as 10e, 14e,., etc. For example, for S = 3/2, (1/2)g = (1/2)+s = 2 so that g = 4, and the factor (5/2)g becomes 10 which corresponds to the effective charge of 10e. The flux quantization gives rise to plateaus and energies become independent of magnetic field. Apparently, the problem becomes independent of charge and the plateaus are then quantized in units of h²/m, the square of the Planck's constant divided by the mass of the electron.

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The Berry phases controlled by voltage in two coupled quantum dots are investigated theoretically. The coupled quantum dots are embedded in a high-Q single mode cavity and coupled to the common phonon fields. It is found that the Berry phase is different from zero even in the vacuum state of the cavity. The Berry phase can change obviously from 0 to 2π via simply tuning the gate voltage. We also show how the Berry phase depends on the environmental temperatures.

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Based on the space-time symmetry, we proposed a generalized superluminal Lorentz transformation (GSLT) of the lepton sector which leads to physics of Majorana particles. In the frame of this model, despite of proving nonzero mass in recent oscillation experiments, neutrino may conserve strictly its helicity. The space-time structure of neutrino shows that its wave function may be a dual appearance of the geodesic evolution of a material point twisting in the 3D-space. In a simplified GSLT model the geodesic cycling defines the structure of neutrino wave function. The statistical feature of the quantum wave function as well as the P-violation are commented from a point of view of the space-time symmetry and asymmetry.

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Experimental efforts to elucidate the molecular mechanism of B-Z DNA transition have often led to controversial and inconclusive results. Some experiments suggest that the nucleobases flip out of the stack before rotating about their respective glycosyl bonds while others suggest that interbase hydrogen bonds remain intact during the transition. Recent computer simulations even suggest that the DNA oligomer stretches and unwinds during the transition. To account for the myriad of mechanisms proposed, a nonlinear DNA Hamiltonian based on three conformational variables, the glycosidic bond angle, base extrusion angle and the longitudinal displacement of the nucleotide, was recently developed. In this article, we will examine some of the theoretical results derived from this Hamiltonian and explore the possibility of including helicity in the model.

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This paper is to be dedicated to Prof C N Yang's 85^th birthday celebration because the idea here was inspired by Prof Yang's public lecture in Singapore in 2006. There are many similarities between electromagnetic waves and acoustic waves. Maxwell's equations for em waves is the oldest gauge theory. We discover symmetries in the pair of wave equations in the acoustic stress field and the velocity field. We also derive a new equation in terms of the stress field for sound propagation in solids. This is different from the Christoffel's equation which is in term of the velocity field. We feel that stress field can better characterize the elastic properties of the sound waves. We also derive the acoustic gauge field condition and gauge invariance and symmetries for the acoustic fields. We also apply symmetries to study negative refraction.

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The physical properties of a macroscopic system can be well described using classical approaches in terms of the Gibbs free energy or the continuum medium mechanics, for instances, that relate the detectable quantities directly to the external stimulus such as the temperature, pressure, chemical composition, electric and magnetic field, etc, without needing consideration of atomistic origins of the property change. At the atomic scale, quantum effect becomes dominant and the physical properties of a small object can be reliably optimized in computations by solving the Schüdinger equations or Newtonian motion of equations with a sum of averaged interatomic potentials as key factors. However, for a small system at the nanometer regime, both the classical and the quantum approaches encountered some difficulties.

Recent exercises [1, 2] showed that the difficulties could be solved by considering the interatomic bond formation, dissociation, relaxation, and vibration and the associated energetic response of atoms and electrons and their consequences on the detectable quantities. It is possible to establish the functional dependence of a detectable quantity Q = Q (z_i, d_i, E_i,m) on the bonding identities such as bond order, z_i, bond length, di, bond energy, E_i, and bond nature indicator, m, and the response of the bonding identities to the external stimulus such as the coordination environment, temperature, pressure, etc. Progress made insofar is quite encouraging, which may evidence the essentiality of the approach that could describe the true situation and predict the performance of nanostructures.

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Applying the Jordan-Wigner transformation to spin-1/2 operators on special quasi-one dimensional paths, we show that the two-dimensional Kitaev model can be exactly mapped to a free Majorana fermion model without any redundant degrees of freedom. Via duality transformation, it can be further shown that the quantum phase transitions of the Kitaev model are described by non-local topological order parameters, which become Landau type local order parameters in the dual space. A closed relationship between conventional and topological quantum phase transitions is revealed, and the validity of conventional Landau phase transition theory with spontaneous symmetry breaking and local order parameters is also extended.

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The imaginary part of the QED effective action can be approximated by the contribution of a worldline instanton, a solution to the classical Euclidean worldline equations of motion. In this talk, I will briefly review this formalism and compute also the prefactor arising from quantum fluctuations about this classical path. I will show the excellent agreement between our semiclassical approximation, conventional WKB, and numerical results using numerical worldline loops.

I will also show the extension of the worldline instanton technique to multidimensional spatially inhomogeneous electric background fields, for which, WKB failed to apply.

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In this talk, I will describe how the ground state of a two-legged ladder of spinless fermions with infinite nearest-neighbor repulsion can be mapped onto a Fermi sea in three limiting cases: (i) very strong correlated hopping; (ii) very strong hopping along the legs; and (iii) very strong hopping along the rungs. I will then how ground-state correlations in the two-legged ladder can be computed in terms of Fermi sea correlation functions via the use of an intervening particle expansion, before discussing the asymptotic spatial dependence of Fermi-liquid-type, charge-density-wave-type, and superconducting-type correlations in each of the three limiting cases.

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The basic idea and some physical implications of nonlinear supersymmetric general relativity(NLSUSY GR) are discussed, which give new insights into the origin of mass and the mysterious relations between the cosmology and the low energy particle physics, e.g., the spontaneous SUSY breaking scale, the cosmological constant, the (dark) energy density of the universe and the neutrino mass.

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The discovery of carbon nanotubes and C-60 fullerenes has created an enormous impact on next generation nano devices. Wepropose a new generation of fullerene nano-oscillators: a single-walled carbon nanotube with one buckyball inside with an operating frequency in the tens-of-gigahertz range. A quantitative characterization of energy dissipation channels in the peapod pair has been performed via molecular dynamics simulation. Edge effects are found to be the dominant cause of dynamic friction in the carbon-peapod oscillators. A comparative study on the energy dissipation also reveals the significant impact of temperature and impulse velocity on the frictional force.

Then we apply the recently developed Reactive Force Field (ReaxFF) to study the dynamics of tubular fullerene formation process starting from C₆₀-buckyball/nanotube peapod structures. We find that the space confinement provided by the single wall nanotube encapsulating the buckyballs is of critical importance to this coalescence reaction. More importantly, we propose one effective approach to break the symmetry fortuning theenergy barrier of forming a 4-membered ring between adjacent buckyballs. This research can help the community to gain better understanding of the complicateddynamic processes in fullerene systems.

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The topological quantum effect of a magnetic string in the field-free manifold of nontrivial topology is investigated in terms of the Dirac nonintegrable phase, which is a special kind of function on a principal fibre bundle over the manifold. For the quantized string the nonintegrable phase is shown to become a gauge transformation, however, with a singularity, which we call the singular gauge transformation. The Wu-Yang singular-free monopole is obtained naturally with the singular gauge transformation.

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Large scale laser facilities mainly constructed for fusion research can be used to produce high-energy-density plasmas like the interior of stars and planets. They can be also used to reproduce the extreme phenomena of explosion and high Mach number flow in mimic scale in laboratory. With advanced diagnostic technique, we can study the physics of plasma phenomena expected to control a variety of phenomena in Universe. The subjects studied so far are reviewed, for example, in [1], [2].

The project to promote the laboratory astrophysics with Gekko XII laser facility has been initiated from April 1^st this year as a project of our institute. It consists of four sub-projects. They are

1. Physics of collisionless shock and particle acceleration,

2. Physics of Non LTE (local thermodynamic equilibrium) photo-ionized plasma,

3. Physics of planets and meteor impact,

4. Development of superconducting Terahertz device.

I will briefly explain what the laser astrophysics means and introduce what are the targets of our project. Regarding the first sub-project, we have carried out hydrodynamic and PIC simulation to design the experiments with intense laser. We clarified the physical mechanism of generation of the magnetic field in non-magnetized plasma and the collsionless shock formation caused by the ion orbit modifications by the magnetic fields generated as the result of plasma instability.

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Helicon-plasma discharge is a convenient, rather easy way to produce weakly to strongly magnetized plasmas with good effciency; helicon-plasmas have been utilized in various plasma applications. We have recently developed several different types of helicon-plasma devices for basic plasma physics experiments (mainly to simulate phenomena in space plasmas) and research on developing advanced electric propulsion systems.

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Recently radiation generation from the interaction between laser and plasma is studied. Terahertz radiation from photo-conductive antenna which is based on semiconductor technology is widely used, The power is in the order of nano-watt level so that it is hard to use for application. On the other hand, terahertz radiation from laser plasma interaction is much higher than that of semiconductor technology. In our experiments, we have studied by use DARC (dc to ac radiation converter) mechanism by using YAG laser with nano-second pulse duration. DARC is novel radiation source using the interaction between laser-created ionization front and static electric field. The frequency of radiation is determined by both plasma density of ionization front and the geometry of DARC structure. We observed radiation pulse of frequency of 1.2 THz and pulse duration of 2 ps with ZnSe crystal as media detected by EO (electro-optics) sampling technique.

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Although most of the matter in the Universe is in the state of ionized gas, the solar system remains to be the only natural laboratory for spacecraft to conduct the in-situ measurement of cosmic plasma. As revealed by many satellite observations, the velocity distribution of charged particles in the interplanetary space and Earth's space plasma environment usually exhibits non-Gaussian form. In this presentation the origin and consequence of non-Maxwellian distribution are addressed and the inter-comparison between theory and observation is illustrated.

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This paper discusses a novel magnetic field generation mechanism by a transport flow. The distinguishing feature of this mechanism compared with the conventional one by the convective flow lies in the intrinsic characteristics of the random motion, responsible for such transport flow, to break the line-tying effect. It is shown that anomalous plasma diffusion can induce a substantial amount of magnetic flux under certain conditions. It is also discussed that when the Bohm diffusion, typically observed in laboratory plasmas, is incorporated, the magnetic induction equation can be transformed to a type of heat equation which allows exact analytical solutions, admitting magnetic field amplification solutions.

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The dense plasma focus (DPF) device is a coaxial plasma gun that heats and compresses the plasmas to high temperatures (1–2 keV) and densities (10^25–26 m^-3). Under such extreme conditions, the plasma radiates copious X-rays and particle beams such as relativistic electrons and ion beams and also neutrons if the device is operated with deuterium gas. At Plasma Radiation Sources Laboratory (PRSL), NIE, Singapore our group has six plasma focus devices and our research efforts encompass a very wide range of topics covering various fundamental aspects of plasmas to the application of this device to lithography, soft and hard x-ray imaging, material modification and thin film deposition. In the proposed talk the details of our groups' efforts in developing dense plasma focus device for these various applications will be discussed. The proposed talk will contain details of our research work on.

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Plasma nanoscience is an emerging research area at the cutting edge of the physics of plasmas and gas discharges, nanoscience and nanotechnology, materials science and engineering, structural chemistry, and life sciences. The existing approaches to fabricating exotic nanostructures and functional nanofilms are mostly process-specific and suffer from cost-inefficient "trial and error" practices. One of the reasons is that the ability to control the generation, transport, deposition, and structural incorporation of the building units of such films and structures, still remains elusive. On the other hand, the pioneering concept of deterministic plasma nanoscience is treated with extreme caution due to inherent chaotic nature of the plasma at the microscopic level. This contribution shows how to challenge one of the previously intractable problems of bridging nine orders of magnitude between the sizes of plasma nanofabrication facilities (~0.5 m) and self-organization of building units on solid surfaces (~0.2 nm). One of the possibilities is to manipulate a variety of building blocks in the plasma sheath that separates the plasma and solid surfaces and control self-organization of nanostructure building blocks on plasma-exposed surfaces and their insertion into the nanoassemblies. The desired nanoassemblies can be engineered by using hybrid multi-scale numerical simulations and sophisticated experimentations. Recent experimental and computational results obtained within the International Research Network for Deterministic Plasma-Aided Nanofabrication suggest the possibility of deterministic synthesis of a large variety of nanostructures and their functional arrays, and are overviewed in this talk. An issue of creation of self-assembled nanodevices on plasma-exposed surfaces is discussed as well. Finally, this talk reveals how the Nature's mastery works in the assembly of nanometre-sized particles in the Universe via the astronucleosynthesis and ion-induced nucleation pathway, exotic nanoassemblies in laboratory plasmas and in possible creation of building blocks of life in primordial Earth.

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Streak photography of TEA-CO₂ laser ablation of graphite and polymers in helium and argon background gases showed two luminous fronts lifting off the ablation targets at delayed intervals. The first luminous front was driven by the plume from the immediate ablation of top surface layer of polymer, while the second front by the delayed ejection of laser-decomposed, heavy fragment of polymeric materials which lasted for more than a few hundred µs. The dynamics of these two luminous fronts were complicated by the onset of the laser-supported absorption wave at higher background gas pressure of > 50 mbar Ar, as seen in nanosecond dye-laser shadowgraphy. Optical emission spectroscopy of spatial-temporal distribution of the first plume fitted with the shifted Maxwellian-Boltzmann distribution and implied plume splitting or the presence of two-velocity components of plume specie.

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A vortex with a density cavity in its core has been observed in a magnetized cylindrical plasma. It is called "plasma hole" from the visual impression when viewed along the axis of the vortex. The flow velocity measurements revealed that the plasma hole accompanies with supersonic azimuthal flow and radial flow toward the center, on a plane perpendicular to the magnetic field. The vorticity distribution evaluated from the flow velocity field is localized near the vortex center axis. This vorticity localization is identified as a Burgers vortex, which is the first observation of Burgers vortex in a plasma. The plasma hole is divided into two regions; in the peripheral regions the Lorentz force is balanced with the electric force (ExB drift), and in the core regions the Lorentz force is balanced with the centrifugal force. Rotation driven by centrifugal force is called fast rotation, and is realized only in non-neutral plasmas so far. It is found that charge neutrality condition in the core region breaks down by three order of magnitude compared with the case without plasma hole (10^-6). The effective viscosity in the core region exhibits an anomaly as well. The detailed experimental results on the plasma hole and the implication from the viewpoint of basic plasma physics will be presented.

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In this talk, we will discuss the quantum effects of high current space charge limited (SCL) electron flows from field emission in a nangap at both steady state and ultrashort pulse conditions at 1D and 2D models. It is found the traditional models and scaling of field emission law and SCL electron flow (Child-Langmuir law) are no longer when quantum effects become important, such as limiting current density, quantum transit time, electron shot noise, quantum capacitance, etc. The extension of the models to solids with low mobility (like organic materials) will be discussed.

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This talk focus on the generation and application of steady-state, high density plasmas in two forms of low-frequency inductively coupled plasma (LF ICP) sources, namely a conventional ICP with external flat coil configuration and an internal planar unidirectional RF current driven through a specially designed internal antenna configuration. The underlying physics, results of the experimental investigation and applications of both types of LF ICP sources are discussed. The main properties of the LF ICP processed materials can be efficiently controlled by the plasma parameters and discharge operating regimes. The examples include fabrication of crystalline thin-film photovoltaic solar cells, assembly of ordered nanostructures and growth of uniform quantum dots and superlattices.

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LIST OF PARTICIPANTS