International Journal of Modern Physics B

In the present paper, we briefly discuss the construction of mapping model of coupled oscillator systems for limit-cycle oscillators and chaotic oscillators. A comparison of the proposed mapping model and other models, i.e., the Ikeda map and the phase map model is made. Furthermore, the critical dynamics associated with the breakdown of chaotic phase synchronization based on the present mapping model is discussed.

Chaotic evolution equations sometimes display regular patterns (fronts, kinks, holes), which often correspond to closed form analytic solutions. In the dissipative-dispersive Kuramoto and Sivashinsky travelling wave reduction u(x − ct), νu‴ + bu″ + μu′ + u²/2 + A = 0, ν ≠ 0, with (ν,b,μ,A) constants, such analytic solutions are known for heteroclinic solutions, but one has also observed (Toh, 1987) homoclinic solutions without corresponding analytic solutions yet. We review the search for the most general analytic solution admissible by this chaotic differential equation. Several investigations, both analytic by the Painlevé test (Thual and Frisch, 1986) and numerical by Padé approximants (Yee, Conte, Musette, 2003) indicate its quite probable single valuedness for any (ν,b,μ,A). Moreover, Nevanlinna theory on the growth of solutions near infinity rules out (Eremenko, 2005) the possibility for the singularities of this unknown closed form single valued expression to be only poles.

We propose a qualitative closed form involving a deformed elliptic function.

Recently q-breathers - time-periodic solutions which localize in the space of normal modes and maximize the energy density for some mode vector q₀ - were obtained for finite nonlinear lattices. We scale these solutions to arbitrarily large lattices in various lattice dimensions. We study the scaling consequence for previously obtained analytical estimates of the localization length of q-breathers for β-FPU and α-FPU lattices. The first finding is that the degree of localization depends only on intensive quantities and is size independent. Secondly, a critical wave vector k_m is identified, which depends on one effective nonlinearity parameter, q-breathers minimize the localization length at k₀ = k_m and completely delocalize in the limit k₀ → 0, π.

In this talk, we argue that in a chaotic synchronization system whose driving signal is exposed to channel noise, the estimation of the drive system state can be greatly improved by applying the dynamical noise filtering to the response system states. We show that if the noise is bounded, the estimation errors can be made arbitrarily small. This property can be exploited in the design of an alternative scheme for digital communications. Further details can be found in Ref. [1].

Finite-time Lyapunov exponents of a chaotic attractor typically exhibit fluctuations about their asymptotic values. In computations or in experiments large fluctuations of these exponents are of concern, as they can lead to incorrect estimates of the actual exponents. We find that in common situations where a chaotic attractor contains two distinct dynamically connected components, such as one after crisis or arising in random dynamical systems, the extreme fluctuations of the finite-time exponents follow a universal, exponential distribution. We develop a physical analysis based on the random-matrix theory and provide numerical evidence to substantiate the finding.

We consider both static (fractal) and dynamical (intermittent) properties of large clusters of order parameter φ at critical points in thermal systems and highlight their association to q-statistics. These properties, previously obtained through the saddle-point approximation in a coarse-grained partition function, are reexamined by considering a phenomenological scheme based on sub-occupation of φ-phase space.

We present particle-based simulations for the flocking behavior of self-propelling particles. Built upon previous models, our models include realistic but simple rules for the self-propelling, drag, and inter-particle interactions. Depending on both the strength and range of the interactions, a host of stationary phases appear, including independent wandering, formation flight, swarm, and rotating vortex. Of particular interest, we determine that the rotating flock can only arise in the absence of long-range alignment. We also construct a phenomenological continuum model and obtain steady-state solutions for the rotating state.

This paper presents a review on recent investigations about the classic dynamics general features of the noninvertible and discontinuous two-dimensional maps. For concreteness we consider a system with phase space divided into two distinct but complementary regions R₁ and R₂. They are the domains of the map functions f₁(x) and f₂(x), respectively. The common features of the systems include: the stochastic web formed by image set of discontinuous borderline; phase collapse caused by the irreversibility (quasi-dissipation); fat fractal forbidden web; riddled-like attraction basin and the induced unpredictability of attractors. Several different cases where f₁(x) and f₂(x) are both area preserving; one is area preserving and another is dissipative; or both are dissipative have been studied. In all the cases the dynamics features can be displayed, however with different characteristics. The features are interesting and can be verified experimentally.

Our current understanding of routes to chaos is mainly based on torus bifurcation where new periods are generated, the period-doubling mechanism revealed in the logistic map, and intermittency where periodic and burst motion appear alternatively. We present a possible new route to chaos based on our geometric picture of the frequency-locking of limit-cycles in semiconductor superlattices. In the period-double route and/or its variations, the period increases exponentially with bifurcation order, whereas the period in the new route increases linearly with the order of bifurcations.

The Political Districting Problem is to partition a zone into several electoral districts subject to some constraints such as contiguity, population equality, etc. In this paper, we apply statistical physics methods to Political Districting Problem. This political problem is mapped to a q-state Potts model system, and the political constraints are written in the form of an energy function with the interactions between sites or external fields acting on the system. Districting into q voter districts is equivalent to finding the ground state of this q-state Potts model. We illustrate this problem by districting Taipei city and compare it to a computer-generated artificial system.

Planetary systems consisting of one star and n planets with equal planet masses μ and scaled orbital separation are referred as EMS systems. They represent an ideal model for planetary systems during the post-oligarchic evolution. Through the calculation of Lyapunov exponents, we study the boundary between chaotic and regular regions of EMS systems. We find that for n ≥ 3, there does not exist a transition region in the initial separation space, whereas for n = 2, a clear borderline occurs with relative separation ∼ μ^2/7 due to overlap of resonances (Wisdom, 1980). This phenomenon is caused by the slow diffusion of velocity dispersion (∼ t^1/2, t is the time) in planetary systems with n ≥ 3, which leads to chaotic motions at the time of roughly two orders of magnitude before the orbital crossing occurs. This result does not conflict with the existence of transition boundary in the full phase space of N-body systems.

A system of logistic map coupled with slowly driven items or another map is investigated in this paper. Several artificial behaviors emerge if the relation is not kept: α β < γ. Here α is number of computational precision digit, for instance, for double precision which has a unit round-off of 2 × 10⁻¹⁶. And β is parameter characterized of maximum of local dynamical expansion ability β or contraction ability 1/β. γ is attractor size of the system. β can be extracted from concept of the Lyapunov number, which is closely related to the well-known Lyapunov exponent.

We have shown that terms in the action which won't contribute to local equation of motions do contribute to globally conversed physical quantities in classical theories of gravity due to general coordinate covariance. This observation allows one to determining the Immirzi parameter in the Ashtekar variable formulation of gravitational theories even at classical level. Applying Wald's Noether charge approach and identifying the entropy on black hole horizon as the Noether charge for translation, one can demonstrate explicitly that the Immirzi parameter does make its contributions through the boundary term. Our results also shed lights in connecting the Immirzi paramter to quasi-normal modes of black holes.

The fractional diffusion equation for describing the anomalous diffusion phenomenon is derived in the spirit of Einstein's 1905 theory of Brownian motion. It is shown how naturally fractional calculus appears in the theory. Then, Einstein's theory is examined in view of quantum theory. An isolated quantum system composed of the objective system and the environment is considered, and then subdynamics of the objective system is formulated. The resulting quantum master equation is found to be of the Lindblad type.

We compare simulations performed using the Nosé-Hoover and the Langevin thermostats with the Hamiltonian dynamics of a long-range interacting system in contact with a reservoir. We find that while the statistical mechanics equilibrium properties of the system are recovered by all the different methods, the Nosé-Hoover and the Langevin nonequilibrium results differ from the Hamiltonian ones.

For the classical spin 1/2 system, a canonical ensemble theory for finite number of particles is developed to show that when the temperature approaches to 0K and in thermodynamic limit, the temperature fluctuation itself does not diverge, but the product of the particle number N and as does.

By connecting two dissimilar anharmonic lattices exemplified by Fermi-Pasta-Ulam (FPU) model and Frenkel-kontorova (FK) model, we successfully build up one dimensional thermal diode. We find the rectifying effect is closely related to asymmetric interface thermal resistance (Kapitza resistance). And the asymmetric thermal resistance depends on how the temperature gradient is applied. Moreover, a qualitative relationship between the thermal rectification and the phonon spectra is proposed.

A model of a thermal transistor to control heat flow is reported. Like its electronic counterpart, the thermal transistor is a three-terminal device with the important feature that the heat current through two terminals can be switched or modulated by the temperature of the third terminal. The thermal transistor model is possible because of the negative differential thermal resistance.

We find the asymmetric heat conduction in a 1D dissimilar chain composed of Frenkel-Kontorova model and φ⁴ model. We also demonstrate that there is no reverse of asymmetric heat conduction in this case. Understanding for these behaviors is proposed.

A model describing size-dependent melting temperature and thermal conductivity of nanosemiconductors is proposed based on Lindermann's melting criterion and Debye model. By the atomic thermal vibration consideration and by introducing intrinsic size effect of phonon velocity and mean free path combined with surface scattering effect, the model predicts that the melting temperature and thermal conductivity of nanosemiconductors decrease as the size reduces. The size effect depends on such material parameters as the vibration entropy, mean free path, the characteristic crystal size and surface roughness. The predictions are in agreement with experimental results of Si nanoparticles, nanowires and thin films.

The structure and the dynamics of the gas-liquid phase interface of the three-dimensional Lennard-Jones (12-6) particle system are studied using nonequilibrium molecular dynamics simulation. Heat flux maintains the system into a gas-liquid coexisting state with a steady interface. In the steady state, the interface shows an asymmetric structure and this is well described by a free energy density model with an asymmetric double-well form. When the system approaches to the steady state, a gas of the temperature profile appears between each phase and the gap value is relaxed to that in the steady state following for large t. It is observed that heat resistance exists in gas-liquid interface in this scale.

We study the effects of networking on the extent of cooperation emerging in an evolutionary snowdrift game, which is a possible alternative to the well-known Prisoner's Dilemma game. The model is studied in the Newman-Watts network that spans the regular, small-world, and random networks through randomly added links. For a wide range of payoffs, the added links are found to suppress cooperation, when compared with a well-mixed or fully connected system. We identify extinction payoffs that characterize the emergence of a homogeneous steady state and study how these payoffs depend on the extent of addition of links to the network.

We investigate the dynamics of network minority games on Kauffman's NK networks (Kauffman nets) and growing directed networks (GDNets). We show that the dynamics and the associated phase structure of the game depend crucially on the structure of the underlying network. The dynamics on GDNets is very stable for all values of the connection number K, in contrast to the dynamics on Kauffman's NK networks, which becomes chaotic when K > K_c = 2. For Kauffman nets with K > 3, the evolutionary scheme has no effect on the dynamics (it remains chaotic) and the performance of the MG resembles that of a random choice game (RCG).

We propose a dynamical model of a competing population whose agents have a tendency to balance their decisions in time. The model is applicable to financial markets in which the agents trade with finite capital, or other multiagent systems such as routers in communication networks attempting to transmit multiclass traffic in a fair way. We find an oscillatory behavior due to the segregation of agents into two groups. Each group remains winning over epochs. The aggregation of smart agents is able to explain the lifetime distribution of epochs to 8 decades of probability. The existence of the super agents further refines the lifetime distribution of short epochs.

A novel phase transition, independent-dependent transition, is revealed in the coupling regime before the complete or generalized synchronization. The coupled chaotic behaviors will change from an approximately independent phase to a mutual correlated phase when coupling passes through the dependent transition point.

We investigate the multifractals of the first passage time on a one-dimensional small-world network with reflecting and absorbing barriers. We analyze numerically the distribution of the first passage time at which the random walker arrives for the first time at an absorbing barrier after starting from an arbitrary initial site. Our simulation is found to estimate the fractal dimension D₀ = 0.920 ∼ 0.930 for the different network sizes and random rewiring fractions. In particular, our simulation results are compared with the numerical computations for regular networks.

We introduce and study a toy model which mimics the structure formation of a typical weighted network in the real world. In particular, the organizational structures of our networks are found to be consistent with real-world networks.

Many agents in the real world are reluctant to change their mind. Such an “inertial” behavior may affect the dynamics and cooperation of agents. Here we study the effect of “inertia” in the framework of Minority Game by requiring agents to choose their strategies via hypothesis testing. We find both numerically and semi-analytically that the presence of “inertial” agents greatly improves global cooperation of the system.

The nodes with the largest degree are very susceptible to traffic congestion, thus an effective way to improve traffic and control congestion can be redistributing traffic load in hub nodes to others. We proposed an efficient routing strategy, which can remarkably enhance the network throughput. In addition, by using detrended fluctuation analysis, we found that the traffic rate fluctuation near the critical point exhibits the 1/f scaling in the power spectrum, which is in accordance with the empirical data.

A formal language is called factorizable if any substring of a word in it also belongs to the language. Symbolic sequences from symbolic dynamics make factorizable languages by definition. In studying avoided and under-represented strings in bacterial genomes we have defined a factorizable language for each complete genome. Recently, in studying the problem of uniqueness of reconstruction of a protein sequence from its constituent K-peptides we encounter again factorizable language which helps to build a finite state automaton to recognize the uniqueness of reconstruction. We present a brief review of these applications of factorizable languages from dynamics to biology.

We investigate the dynamical behaviour of the genetic feedback loop present in the signalling network of the transcription factor NF-κB. This transcription factor is one of the most important regulators in mammalian cells, involved in a large number of cellular responses. We find that when the external stimulus is constant, the concentration of NF-κB inside the cell nucleus is either stationary or shows spiky oscillations. If the external stimulus is time dependent, the response can be more intricate. Here, we consider the response to pulsed and periodic stimuli. In the latter case the response can be chaotic with the NF-κB concentration converging to a strange attractor. The corresponding bifurcation diagram is also presented.

To illustrate the power of the biophysical approach in solving important problems in life science, I present here one of our current research projects as example. We have developed special biophotonic techniques to study the dynamic properties of signaling proteins in a single living cell. This study allowed us to gain new insight into the signaling mechanism regulating programmed cell death.

We present a model for oscillatory behaviors of β cells in pancreatic islets and glucose regulation. With attention to the noise induced by channel-gating stochasticity and coupling via gap junctions, we obtain via extensive numerical simulations complex oscillations including clusters of bursting action potentials, slow and fast oscillations of calcium and insulin secretion, and so on.

The growth of connections in a quasi two-dimensional neuronal network in vitro is probed by the synchronized bursting frequency of the system. A model of an early stage of active search growth followed by a later stage of diffusive search mode is proposed. Our model can explain quantitatively the variation of the critical age(for synchronized firing) of the culture as a function of cell density. The later stage of growth implies a probability of connection that is exponentially decay in the mean connectivity. The biological significance of the model is discussed in the light of homeostatic feedback and plasticity.

Synchronization of cortical neural cultures is studied as a function of the effective network connectivity in the phenomenon of synchronized firing(SF). The synchronized bursting frequency (during SF) of the network is found to be much slower than the characteristic time scale of a neuron and increases with the network connectivity. The synchronized bursting frequency f is characterized by a critical age (t_c) as: . Furthermore, t_c is found to scale with the cell plating density ρ as t_c ~ ρ^−β with β ≃ 0.44 ± 0.08. Although some aspects of the observed SF is similar to the array enhanced synchronization, detailed comparison of measured spike statistics from synchronized and non-synchronized cultures suggests that the nature of synchronization during SF is different from that of the array-enhanced synchronization. In particular, electrophysiological measurements using double patch technique revel that even though the bursting frequencies are synchronized, the intra-burst spikes are not.

We study the emergent functional neural network organized by synaptic reorganization by the spike timing dependent synaptic plasticity (STDP). We show that small-world and scale-free functional structures organized by STDP, in the case of synaptic balance, exhibit hierarchial modularity.

While the no-slip boundary condition (no relative motion at the fluid-solid interface) has been universally accepted as a cornerstone of hydrodynamics, it was known for some time that it is incompatible with the moving contact line, defined as the motion of the line of intersection of the immiscible (two phase) fluid-fluid interface with the solid wall. By employing Onsager's principle of minimum energy dissipation, we show in this work that a continuum hydrodynamics, comprising the equations of motion as well as the relevant boundary conditions, can be obtained which resolves the moving contact line problem. Our derivation reveals that just as other dissipative system dynamics, the fluid-solid interfacial boundary condition should be consistent with the framework of linear response theory. Implications of our results are discussed.

To understand several peculiar features of d-wave superconductors such as the cuprates, we have studied a two-dimensional tight-binding (extended Hubbard) model in which the electrons interact with a potential which is attractive at nearest neighbor distance and repulsive elsewhere. Such a model is designed to produce d-wave superconductivity. It also yields antiferromagnetism and phase separation. In the two-phase region, due to vanishing compressibility the system can be easily rendered inhomogeneous by weak perturbations. Thus inhomogeneous superconductivity is a likely consequence of d-wave pairing. In addition to inhomogeneity the model also reproduces a phase diagram strikingly similar to the one observed in the cuprates. As such it throws some light on the nature of the pseudogap state.

A general procedure is presented for the multiscale analysis of atomistic models of fluctuating interfaces driven by the deposition of new material. Beginning with a lattice Langevin formulation of kinetic Monte Carlo simulations, we derive stochastic partial differential equations by regularizing the atomistic transition rules. Subsequent coarse-graining is accomplished by calculating renormalization-group trajectories from initial conditions determined by the regularized equations. We apply this methodology to the Wolf–Villain model of relaxation upon deposition and to a model for the self-organization of heteroepitaxial nanostructures.

The majority of experimental and theoretical friction studies considers translational motion, where all coarse-grained interface elements are displaced alike. An additional rotation of the slider introduces a well controlled displacement inhomogeneity across the interface. The friction response now consists of a force and a torque that are generally coupled. Recent results for a cylindrical slider are reviewed and applied to rigid objects with rotational symmetry about an axis. It is predicted that the difference between static and dynamic friction force can be suppressed, if a certain torque is applied. Moreover, we study the dynamics of the transition from sticking to sliding.

The tunnel current of a Luttinger liquid with a finite density of strong impurities is calculated using an instanton approach. For very low temperatures T or electric fields E the (nonlinear) conductivity is of variable range hopping (VRH) type as for weak pinning. For higher temperatures or fields the conductivity shows power law behavior corresponding to a crossover from multi- to single-impurity tunneling. For even higher T and not too strong pinning there is a second crossover to weak pinning. The determination of the position of the various crossover lines both for strong and weak pinning allows the construction of the global regime diagram.

Waves propagating inwardly to the wave source are called antiwaves which have negative phase velocity. In this paper the phenomenon of negative phase velocity in oscillatory systems is studied on the basis of periodically paced complex Ginzbug-Laundau equation (CGLE). We figure out a clear physical picture on the negative phase velocity of these pacing induced waves. This picture tells us that the competition between the frequency ω_out of the pacing induced waves with the natural frequency ω₀ of the oscillatory medium is the key point responsible for the emergence of negative phase velocity and the corresponding antiwaves. ω_outω₀ > 0 and |ω_out| < |ω₀| are the criterions for the waves with negative phase velocity. This criterion is general for one and high dimensional CGLE and for general oscillatory models. Our understanding of antiwaves predicts that no antispirals and waves with negative phase velocity can be observed in excitable media.

The possible effects of a large-scale mean flow, represented as a non-zero mean velocity in the shell of the largest scale, are studied using a shell model of turbulent convection. In the regime where buoyancy is dynamically important, flow reversals are not observed. On the other hand, flow reversals are found in the regime where buoyancy is not dynamically important. In both regimes, the presence of such a large-scale mean flow does not change the scaling behavior of the velocity and temperature fluctuations.

We study vibrational excitations in linearly graded materials and/or systems. Graded systems demonstrate a unique spectrum and mode profiles, resulting in a new type of localization-delocalization transition. The nature of gradients can confine certain vibrational excitations, and redistribute them spatially. These features are contrasted to the two extreme cases of inhomogeneous system, i.e., periodically modulated system and randomly disordered system, We show in detail vibrational normal modes sustained by one dimensional graded force constant and graded mass networks, in particular, a unusual kind of modes called gradons. We propose an approach to study vibrational modes in a grades elastic system with the help of a series of homogeneous systems. Using this approach, we elaborate the features of the elastic gradons and the phonon-gradon transition.

Bipolaron dynamics in non-degenerate polymers are discussed using the nonadiabatic dynamic method. First, charge injection process from metal electrode to a nondegenerate polymer in a metal/polymer/metal structure has been investigated. We demonstrate that the dynamical formation of a bipolaron sensitively depends on the work function of metal electrode. We also study the bipolaron dissociation process. It is found that the electric field that can dissociate the bipolaron is up to 10⁶ V/cm, which is consistent with experiments.

The effects of bond randomness on the quantum mixed-spin chain 1-1-1/2-1/2 are investigated by a quantum Monte Carlo study. We find that around the critical point of original pure system, quantum Griffiths phases appears, and its region is enlarged with increasing of bond randomness. Moreover, the critical behavior of the original quantum critical point has been changed by the randomness.

The coupling between the acoustic transverse phonons and the electron drift current, in piezoelectric semiconductors, has long been known to give rise to a negative acoustoelectric current, thereby leading to a decreased conductivity with respect to the value derived from the Ohm law. Increasing the electric field above a threshold causes the differential conductivity to become eventually negative, which triggers off an instability. The latter has been characterized experimentally by a mm-wide, high-field soliton moving at transverse sound velocity and by low-frequency current oscillations. However it is shown here to consist actually of a high-amplitude acoustoelectric microwave-packet. Because the electric permitivity is inferred to be renormalized to zero, the properties of this solution, including its vibrational frequency and amplitude, are shown to be shaped by the nonlinear piezoelectric interaction. All experimental features turn out to be accounted for satisfactorily within the framework of the present analysis. The relatively long initial transient regime, exhibiting interesting observations by Brillouin scattering, is also addressed.

The finite-size scaling functions of thermodynamic functions in anisotropic systems have been shown to be dependent on the spatial anisotropy [X.S. Chen and V. Dohm, Phys. Rev. E 70, 056136 (2004)]. Here we extend this study to the correlation length ξ_‖ of the anisotropic O(n) symmetric φ⁴ model in an L^d−1 × ∞ cylindric geometry with periodic boundary conditions. We calculate the exact finite-size scaling function of correlation length ξ_‖ for T ≥ T_c in 2 < d < 4 dimensions and in the limit n → ∞. The finite-size scaling function of ξ_‖ is dependent on a normalized symmetric (d − 1) × (d − 1) matrix defined by the anisotropy matrix of anisotropic systems.

Arrays of nanosized three dimensional islands are known to self-assemble spontaneously on strained heteroepitaxial thin films. We simulate the dynamics using kinetic Monte Carlo method based on a ball and spring lattice model. Green's function and super-particle methods which greatly enhance the computational efficiency are explained.

The quantum phase transitions of four kinds of nonuniform anisotropic XY quantum spin chains in a transverse field are studied by the Lee-Yang zeros method. It is found that the closed curves of the partition function zeros cut the positive real axis at the quantum phase transition points. The results are checked by the explicit calculations of the magnetization.

A concise variational approach is to propose to calculate the ground-state properties of none-dimensional Holstein model. The results in the weak and strong coupling limit can be easily recovered analytically. It is shown that, in the nontrivial intermediate electron-phonon coupling regime, the present results are in good agreement with those by density-matrix renormalization group and numerical exact diagonalizations. The present approach is more concise than any other analytical ones in this field, and can be easily generalized to Holstein models in higher dimensions and with more electrons.

The existence and stability of the Shapiro steps in the ac driven dissipative Frenkel-Kontorova model are studied. The particular attention has been focused on, the variations of the step width and critical depinning force with the ac amplitude. The amplitude dependence is strongly influenced by the frequency of ac force where at the higher frequencies, the oscillations have the Bessel like form.

We sketch the major steps in a functional integral derivation of a new set of stochastic Gross-Pitaevsky equations (GPE) for a Bose-Einstein condensate (BEC) confined to a trap at zero temperature with the averaged effects of non-condensate modes incorporated as stochastic sources. The closed-time-path (CTP) coarse-grained effective action (CGEA) or the equivalent influence functional method is particularly suitable because it can account for the full back-reaction of the noncondensate modes on the condensate dynamics self-consistently. The Langevin equations derived here containing nonlocal dissipation together with colored and multiplicative noises are useful for a stochastic (as distinguished from a kinetic) description of the nonequilibrium dynamics of a BEC. This short paper contains original research results not yet published anywhere.

The superfine structure of Bose-Einstein condensate of alkali atoms due to the spin coupling have been investigated in the mean field approximation. In the limit of large number of atoms, we obtained the analytical solution for the fully condensed states and the states with one-atom excited. It was found that the energy of the one-atom excited state could be smaller than the energy of the fully condensed state, even two states have similar total spin.

In this talk we present a model to demonstrate how time-periodic potential can be used to manipulate quantum metastability of a system. We study metastability of a particle trapped in a well with a time-periodically oscillating barrier in the Floquet formalism. It is shown that the oscillating barrier causes the system to decay faster in general. However, avoided crossings of metastable states can occur with the less stable states crossing over to the more stable ones. If in the static well there exists a bound state, then it is possible to stabilize a metastable state by adiabatically increasing the oscillating frequency of the barrier so that the unstable state eventually cross-over to the stable bound state. It is also found that increasing the amplitude of the oscillating field may change a direct crossing of states into an avoided one. Hence, one can manipulate the stability of different states in a quantum potential by a combination of adiabatic changes of the frequency and the amplitude of the oscillating barrier.

We briefly review our recent work on spatial tuning of Bose-Einstein condensation (BEC). We first study spatially periodic tuning of the s-wave scattering length for controlling the propagation of a BEC matter wave, and find matter wave limiting processing and bistability. Second, we show that a stable BEC with natural attractive interaction could be formed by tuning the s-wave scattering length with a Gaussian optical field, but the condensed atom number should be less than a critical value. Further, we apply Thomas-Fermi approximation to obtain a formula for this critical value.

The proof of the no-go theorem of unconditionally secure quantum bit commitment depends crucially on the assumption that Alice knows every detail of the protocol so that no secret parameters exist. In this paper we show that, for the perfectly concealing case, it is possible to establish the no-go theorem without making this assumption.

The state of a bipartite system may be changed by a cyclic operation applied on one of its subsystem. The change is a nonlocal effect, and can be detected only by measuring the two parts jointly. By employing the Hilbert-Schmidt metric, we can quantify such nonlocal effects via measuring the distance between initial and final state. By making use of the new nonlocal effect we can measure the entanglement of bipartite system. For qubit pair, we show that this measurement is equivalent to degree of entanglement and consists with the Bell inequality.

A semiclassical theory is used for the study of fidelity. For systems with weak chaos in the classical limit, we show that the fidelity has a non-Fermi-Golden-Rule decay, which can be explained by the closeness of the distribution of action difference in the semiclassical theory to the Levy distribution. For systems with strong chaos in the classical limit, we present a semiclassical expression for fidelity decay in the Lyapunov regime, which is more general than the previously predicted Lyapunov decay and λ₁ decay of fidelity. For systems with regular motion in the classical limit, we derive the fidelity decay for initial narrow Gaussian wavepackets, which displays a quite complex behaviour, from Gaussian to power law decay t^−α with 1 ≤ α ≤ 2.

We investigate spin and charge current through a quantum dot pumped by a time-varying magnetic field. Using the density matrix method, quantum rate equations for the electronic occupation numbers in the quantum dot are obtained and solved in the stationary state limit for a wide set of parameters. Both charge and spin currents are expressed explicitly in terms of several relevant parameters and analyzed in detail. The results suggest a way of optimizing experimental parameters to obtain an maximal spin current without the charge current flow.

An overview of hypertranscendency in sciences is discussed. The theoretical framework comes to be articulated.

The Lüders postulate is reviewed and implications for the distinguishability of observables are discussed. As an example the distinguishability of two similar spin- particle observables is described and implementation issues are briefly analyzed.