Condensed Matter Theories

The following sections are included:

• PREFACE

• CONTENTS

The 2D Fully Frustrated XY(FFXY) class of models is shown to contain a new ground-state in addition to the checkerboard groundstate of the standard 2D XY model. The spin configuration of this additional groundstate is obtained and its connection to a broken Z₂-symmetry explained. This means that the class of 2D FFXY models belongs within a U(1) ⊗ Z₂ ⊗ Z₂-symmetry phase-transition representation. The phase diagram is reviewed and the central charges of the four multicritical points described. The implications for the standard 2D FFXY-model are discussed and elucidated, in particular with respect to the long standing controversy concerning the phase transitions of the standard 2D FFXY-model.

We study the two-dimensional Ising model with competing nearest-neighbour and diagonal interactions and investigate the phase diagram of this model. We show that the ground state at low temperatures is ordered either as stripes or as the Néel antiferromagnet. However, we also demonstrate that the energy of defects and dislocations in the lattice is close to the ground state of the system. Therefore, many locally stable (or metastable) states associated with local energy minima separated by energy barriers may appear forming a glass-like state.

We discuss the results in connection with two physically different systems. First, we deal with planar clusters of loops including a Josephson π-junction (a π-rings). Each π-ring carries a persistent current and behaves as a classical orbital moment. The type of particular state associated with the orientation of orbital moments in the cluster depends on the interaction between these orbital moments and can be easily controlled, i.e. by a bias current or by other means. Second, we apply the model to the analysis of the structure of the newly discovered two-dimensional form of carbon, graphene. Carbon atoms in graphene form a planar honeycomb lattice. Actually, the graphene plane is not ideal but corrugated. The displacement of carbon atoms up and down from the plane can be also described in terms of Ising spins, the interaction of which determines the complicated shape of the corrugated graphene plane.

The obtained results may be verified in experiments and are also applicable to adiabatic quantum computing where the states are switched adiabatically with the slow change of coupling constant.

I will discuss the expansion of various thermodynamic quantities about the ideal gas in powers of the electric charge, and I will discuss some cellular models. The first type of cellular model is appropriate for hydrogen. The second type is for Z > 1. It has the independent electron approximation within the atoms. These models are cross compared and minimal regions of validity are determined. The actual region of validity is expected to be larger. In the cellular models, the phase boundaries for liquid-gas transitions are found. For the second type of cellular model, in the part of the low-temperature, low-density region where there is not much expectation of validity of these methods, a non-thermodynamic region is found. I have devised a construction, similar in spirit to the Maxwell construction, to bridge this region so as to leave a thermodynamically valid equation of state. The non-thermodynamic region does not occur in hydrogen and it seems to be due to the inadequacy of the aforementioned approximation in that region.

A quasiclassical expression for the kinetic energy of interacting quantum many-body systems is derived from the full quantum expression for the kinetic energy as derived by means of the Fourier path integral representation of the canonical many-body density matrix of such systems. This quasiclassical form of the kinetic energy may be cast in the shape of thermodynamic expectation values w.r.t. to the classical Boltzmann distribution of the many-body system, which involves only the many-body interaction in contrast to the full Fourier path integral quantum distribution, which carries contributions also from the many-body kinetic energy operator. The quasiclassical quantum correction terms to the classical Boltzmann equipartition value are valid when the product of temperature and particle mass is large and then lead to significant technical simplifications and increase of speed of Monte Carlo computations of the quantum kinetic energy. The formal findings are tested numerically in quantum Fourier path integral versus classical Monte Carlo simulations.

In recent years the term ergodicity has come into scientific vogue in various physical problems. In particular when a system exibits chaotic behavior, it is often said to be ergodic. Is it a correct usage of the term ergodicity? Does it not mean that the time and ensemble averages of a variable are equal? Are they really related one to one? We examine this issue via simple models of harmonic oscilators by means of the theorems of Birkhoff and Khinchin and also by our own physical theory of ergometry. This study also considers the chaotic behavior in the logistic map.

In this paper, we investigate processes associated with formation of public opinion in varies directed random, scale free and small-world social networks. The important factor of the opinion formation is the existence of contrarians which were discovered by Granovetter in various social psychology experiments^1,2,3 long ago and later introduced in sociophysics by Galam.⁴ When the density of contrarians increases the system behavior drastically changes at some critical value. At high density of contrarians the system can never arrive to a consensus state and periodically oscillates with different periods depending on specific structure of the network. At small density of the contrarians the behavior is manifold. It depends primary on the initial state of the system. If initially the majority of the population agrees with each other a state of stable majority may be easily reached. However when originally the population is divided in nearly equal parts consensus can never be reached. We model the emergence of collective decision making by considering N interacting agents, whose opinions are described by two state Ising spin variable associated with YES and NO. We show that the dynamical behaviors are very sensitive not only to the density of the contrarians but also to the network topology. We find that a phase of social chaos may arise in various dynamical processes of opinion formation in many realistic models. We compare the prediction of the theory with data describing the dynamics of the average opinion of the USA population collected on a day-by-day basis by varies media sources during the last six month before the final Obama-McCain election. The qualitative ouctome is in reasonable agreement with the prediction of our theory. In fact, the analyses of these data made within the paradigm of our theory indicates that even in this campaign there were chaotic elements where the public opinion migrated in an unpredictable chaotic way. The existence of such a phase of social chaos reflects a main feature of the human being associated with some doubts and uncertainty and especially associated with contrarians which undoubtly exist in any society.

The interaction of two magnetic particles separated by an interlayer is illustrated through the "astroid" curves that represent regions in the magnetic field plane where different numbers of minima associated with stable or metastable states may exist. For a single particle, we describe the astroid curves of the Stoner-Wohlfarth model. The case of two particles is then examined and found to be much more complicated. The energy landscape of the two-particle system contains ferromagnetic, antiferromagnetic and canting states that emerge in response to the level of applied magnetic field. Because of this, up to four energy minima can exist in the system, depending upon the strength of the magnetic field and the material properties of the particles.

The entanglement properties of correlated wave functions commonly employed in theories of strongly correlated many-body systems are studied. The variational treatment of the transverse Ising model within correlated-basis theory is reviewed, and existing calculations of the one- and two-body reduced density matrices are used to evaluate or estimate established measures of bipartite entanglement, including the Von Neumann entropy, the concurrence, and localizable entanglement, for square, cubic, and hypercubic lattice systems. The results discussed in relation to the findings of previous studies that explore the relationship of entanglement behaviors to quantum critical phenomena and quantum phase transitions. It is emphasized that Jastrow-correlated wave functions and their extensions contain multipartite entanglement to all orders.

Opportunities for topological phase transitions in strongly correlated Fermi systems near a quantum critical point are explored as an alternative to collective scenarios for experimentally observed departures from standard Fermi-liquid behavior. Attention is focused on a quantum critical point at which the effective mass is divergent due to vanishing of the quasiparticle group velocity at the Fermi surface. Working within the original Landau quasiparticle theory, it is demonstrated that the quasiparticle picture can remain meaningful beyond the quantum critical point through rearrangements of the unstable normal Fermi surface and quasiparticle spectrum. Two possibilities emerge at zero temperature, depending on whether the quasiparticle interaction is regular or singular at zero momentum transfer. In the regular case, one type of topological phase transformation leads to a state with a multiconnected Fermi surface. In the singular case, another type of topological phase transition leads to an exceptional state containing a fermion condensate – the Fermi surface swells into a volume in momentum space, within which partial occupation prevails and quasiparticle energies are pinned to the chemical potential. As the temperature increases from zero to a characteristic value T_m, a crossover can occur from the state with multiple Fermi surfaces to that containing a fermion condensate.

We describe a simple model of fermions in quasi-one dimension that features interaction-induced deconfinement (a phase transition where the effective dimensionality of the system increases as interactions are turned on) and which can be realised using dipolar fermions in an optical lattice¹. The model provides a relisation of a "soft quantum matter" phase diagram of strongly-correlated fermions, featuring meta-nematic, smectic and crystalline states, in addition to the normal Fermi liquid. In this paper we review the model and discuss in detail the mechanism behind each of these transitions on the basis of bosonization and detailed analysis of the RPA susceptibility.

We work within the Density Functional Theory (DFT), in the Local Density Approximation (LDA) with Self Interaction Correction (SIC). We show that, thanks to a formulation which employs two different sets of orbitals, the equations can be written in the form of eigenvalues equations, leading to single electron interpretation. However, the resulting hamiltonian is non-local. We propose to find it's best local approximation within using the Optimized Effective Potential (OEP) method. The resulting approximate theory is denominated "Generalized Slater". We show that this new scheme cures the pathologies of the standard SIC-Slater or SIC-KLI approximations.

The microscopic quantum structure of fluid ⁴He may be clearly revealed by a proper decomposition of its spatial correlations into quantum statistical components and direct quantum correlations. This decomposition permits to elucidate the competition between the short-ranged statistical (or particle exchange) correlations and the quantum correlations brought about by the existing strong interparticle repulsion at short relative particle-particle distances. The appropriate method of choice is provided by correlated density-matrix (CDM) theory. It does not only permit a detailed formal analysis of this competition but also allows for a quantitative numerical computation of correlation functions, structure functions, and momentum and energy distributions. The theoretical CDM results for ⁴He are, so far as possible, compared with results from path-integral Monte Carlo (PIMC) calculations and with available experimental results. Reported are CDM results on relevant structure functions, correlation functions in coordinate space, kinetic energy distributions, and gross quantitities such as the exchange energy for fluid ⁴He. The calculations are performed for normal helium at various temperatures in the range T_BE = 2.17K ≤ T < 14K.

We propose a microscopic approach for a description of interaction of the ideal gas of alkali atoms with a weak electromagnetic radiation. The description is constructed in the framework of the Green functions formalism that is based on a new formulation of the second quantization method in case of the bound states (atoms) presence. For a gas in the Bose-condensed (BEC) state we study the dependencies of the propagation velocity and damping rate on the microscopic characteristics of the system. For a condensed dilute gas of sodium atoms we find the conditions of the group velocity reducing for optical pulses tuned up close to the resonant transitions. We also show that the slowing phenomenon can strongly depend on the intensity of the external static magnetic field.

A physical interpretation is given to a curious "hump" that develops in the chemical potential as a function of absolute temperature in an ideal Fermi gas for any spatial dimensionality d < 2, integer or not, in contrast with the more familiar monotonic decrease for all d ≥ 2. The hump height increases without limit as d decreases to zero. The divergence at d = 0 is shown to be a clear manifestation of the Pauli Exclusion Principle whereby two spinless fermions cannot sit on top of each other in configuration space. The hump itself is thus an obvious precursor of this manifestation, otherwise well understood in momentum space. It also constitutes an "ideal quantum dot" when d = 0.

The unusual quantum Hall effect (QHE) in graphene is often discussed in terms of Dirac fermions moving with a linear dispersion. A new theory describing the same phenomena is presented in terms of the more traditional composite bosons. The "electron" (wave packet) is shown to move easier in the direction [110] ≡ [110 c-axis] of the honeycomb lattice than perpendicular to it, while the "hole" moves easier in [001]. Since "electrons" and "holes" move in different channels, the number densities can be very high especially when the Fermi surface has "necks". The strong QHE at filling factor ν = 2 arises from the "neck" Fermi surfaces.

There is increasing evidence that DNA can support a considerable degree of charge transport along the strand by hopping of holes from one base to another, and that this charge transport may be relevant to DNA regulation, damage detection and repair. A surprisingly useful amount of insight can be gained from the construction of simple tight-binding models of charge transport, which can be investigated using the transfer-matrix method. The data thus obtained indicate a correlation between DNA charge-transport properties and the locations of cancerous mutation. We review models for DNA charge transport and their extension to include more physically realistic diagonal-hopping terms.

We discuss a recently developed embolic stroke model in relation to models of percolation. When descibing embolic stroke, it is important to know if blood flow can travel from the major arteries to the arterioles supplying the brain. In this sense, the onset of stroke bears some similarity to the central question of percolation theory. The order parameter for the percolation transition is found, and the percolation threshold is investigated. We discuss possible extensions to the model.

We show that extraordinary magnetoresistance (EMR) arises in systems consisting of two components; a semiconducting ring with a metallic inclusion embedded. The important aspect of this discovery is that the system must have a quasi-two-dimensional character. Using the same materials and geometries for the samples as in experiments by Solin et al.^1,2, we show that, such systems indeed exhibit a huge magnetoresistance. The magnetoresistance arises due to the switching of electrical current paths passing through the metallic inclusion. Diagrams illustrating the flow of the current density within the samples are utilised in discussion of the mechanism responsible for the magnetoresistance effect. Extensions are then suggested which may be applicable to the silver chalcogenides. Our theory offers an excellent description and explanation of experiments where a huge magnetoresistance has been discovered^2,3.

We describe how the specific heat of a quantum system is related to a positive definite metric defined on the generalized phase space in which the dynamics and thermodynamics of the system take place. This relationship is given through the components of a second-rank covariant metric tensor, enhancing a topological nature of the specific heat. We also present two examples where it can be seen how the uncertainty principle imposes strong constraints on the values achieved by the specific heat showing its inherent quantum nature.

Strong electron-electron interactions in dilute two-dimensional electron systems in silicon lead to Pauli spin susceptibility growing critically at low electron densities. This effect originates from renormalization of the effective mass rather than the g-factor. The relative mass enhancement, is system- and disorder-independent, which suggests that it is determined by electron-electron interactions only.

We study properties of charge fluids with random impurities or heavy polarons using a microscopic Hamiltonian with the full many-body Coulomb interaction. At zero temperature and high enough density the bosonic fluid is superconducting, but when density decreases the Coulomb interaction will be strongly over-screened and impurities or polarons begin to trap charge carriers forming bound quasiparticle like clusters, which we call Coulomb bubbles or clumps. These bubbles are embedded inside the superconductor and form nuclei of a new insulating state. The growth of a bubble is terminated by the Coulomb force. The fluid contains two groups of charge carriers associated with free and localized states. The insulating state arises via a percolation of the insulating islands of bubbles, which cluster and prevent the flow of the electrical supercurrent through the system.

Our results are applicable to HTSC. There the Coulomb fluids discussed in the paper correspond to mobile holes located on Cu sites and heavy polarons or charged impurities located on Oxygen sites. As a result of our calculations the following two-componet picture of two competing orders in cuprates arise. The mobile and localized states are competing with each other and their balance is controlled by doping. At high doping a large Fermi surface is open. There the density of real charge carriers is significantly larger than the density of the doped ones. When doping decreases more and more carriers are localized as Coulomb clumps which are creating around heavy polarons localized on Oxygen sites and forming a regular lattice. The picture is consistent with the Gorkov and Teitelbaum (GT) analysis ^1,2 of the transport, Hall effect data and the ARPES spectra as well as with nanoscale superstructures observed in Scanning Tunneling Microscope(STM) experiments [3-8]. The scenario of the clump formation may be also applicable to pnictides, where two types of clumps may arise even at very high temperatures.

We study the noise spectra and high-frequency permeability of inhomogeneous magnetic materials consisting of single-domain magnetic nanoparticles embedded into an insulating matrix. Possible mechanisms of 1/f voltage noise in phase-separated manganites is analyzed. The material is modelled by a system of small ferromagnetic metallic droplets (magnetic polarons or ferrons) in insulating antiferromagnetic or paramagnetic matrix. The electron transport is related to tunnelling of charge carriers between droplets. One of the sources of the 1/f noise in such a system stems from fluctuations of the number of droplets with extra electron. In the case of strong magnetic anisotropy, the 1/f noise can arise also due to the fluctuations of the magnetic moments of ferrons.

The high frequency magnetic permeability of nanocomposite film with magnetic particles in insulating non-magnetic matrix is studied in detail. The case of strong magnetic dipole interaction and strong magnetic anisotropy of ferromagnetic granules is considered. The composite is modelled by a cubic regular array of ferromagnetic particles. The high-frequency permeability tensor components are found as a functions of frequency, temperature, ferromagnetic phase content, and magnetic anisotropy. The results demonstrate that magnetic dipole interaction leads to a shift of the resonance frequencies towards higher values, and nanocomposite film could have rather high value of magnetic permeability in the microwave range.

We present a new type of sonic crystal technology offering a novel method of achieving broad acoustic band gaps. The proposed design of a locally resonating sonic crystal (LRSC) is constructed from "C"-shaped Helmholtz resonators as opposed to traditional solid scattering units. This unique construction enables a two band gap system to be generated in which the first — a Bragg type band gap, arises due to the periodic nature of the crystal, whilst the second gap results from resonance of the air column within the resonators. The position of this secondary band gap is found to be dependent upon the dimensions of the resonating cavity.

The band gap formation is investigated theoretically using finite element methods, and confirmed through experimental testing. It is noted that the resonance band gaps detected cover a much broader frequency range (in the order of kHz) than has been achieved to date. In addition the possibility of overlapping such a wide band gap with the characteristic Bragg gap generated by the structure itself could yield gaps of even greater range.

A design of sonic crystal is proposed, that comprises of several resonators with differing cavity sizes. Such a structure generates multiple resonance gaps corresponding to the various resonator sizes, which may be overlapped to form yet larger band gaps.

This multiple resonance gap system can occur in two configurations. Firstly a simple mixed array can be created by alternating resonator sizes in the array and secondly using a System coined the Matryoshka (Russian doll) array in which the resonators are distributed inside one another.

The proposed designs of LRSC's offer a real potential for acoustic shielding using sonic crystals, as both the size and position of the band gaps generated can be controlled. This is an application which has been suggested and investigated for several years with little progress. Furthermore the frequency region attenuated by resonance is unrelated to the crystals lattice constant, providing yet more flexibility in the design of such devices.

The effect of random on-site disorder on s-wave (BCS) superconductors described by a two dimensional negative-U Hubbard model is studied using Bogoliubov-de Gennes (BdG) method. The mean field pairing amplitudes become spatially inhomogeneous at large values of disorder where the system breaks up into superconducting islands with large pairing amplitudes, separated by insulating strips. The amplitude fluctuations are correctly accounted for via BdG calculations, however it misses phase fluctuations which are inherent to low dimensions. The phase fluctuations affect superconducting properties strongly, and the effect is more pronounced in the limit of large disorder. We provide a close estimate of the actual transition temperature, T_c by incorporating phase fluctuations about the inhomogeneous BdG state. This is obtained by relating the jump in renormalized D_s (obtained from a self consistent Harmonic approximation on a phase-only Hamiltonian) at the Kosterlitz-Thouless (KT) transition and the KT transition temperature, T_KT obtained from D_s(T) = (2/π)T_KT as temperature tends to T_KT from below. This yields opening of a large region sandwiched between (obtained by the vanishing of ) and T_KT where there is no phase coherence between the pairs, however amplitude correlations continue to exist, reminiscent of a pseudogap phase in high-T_c superconductors which is marked by short ranged preformed pairs without any definite phase relation between them. Further, the appearance of the superconducting islands from a homogeneous phase indicates the evolution of a system consisting of large and overlapping pairs to one that contains short and tightly bound pairs - a scenario termed as BCS-BEC crossover. We have investigated in details the crossover phenomenon as a function of disorder and confirmed it's existence at small values of electron concentration, however, absent at larger densities.

We study the effect of electron confinement on the superconducting-to-normal phase transition driven by a magnetic field and/or on the current-carrying state of the superconducting condensate in nanowires. Our investigation is based on a self-consistent numerical solution of the Bogoliubov-de Gennes equations. We show that in a parallel magnetic field and/or in the presence of supercurrent the transition from superconducting to normal phase occurs as a cascade of discontinuous jumps in the superconducting order parameter for diameters D < 10 ÷ 15 nm at T = 0. The critical magnetic field exhibits quantum-size oscillations with pronounced resonant enhancements.

New boundary condition for the order parameter in the Ginzburg-Landau theory is applied to the case of CuO₂ planes which are the main structural elements responsible for superconductivity in high-T_c superconductors. It was found that the order parameter in these superconductors is significantly depressed in the CuO₂ planes. As a result, this boundary condition to the GL equations is found to limit the critical temperature of high-T_c superconductors. Thus, in order to increase T_c of cuprate superconductors, the number of CuO₂ planes that are within a short distance of each other in unit cell or insulating properties of the layers located in the vicinity to the CuO₂ planes should be increased.

A method is proposed to measure the thermodynamic field of a superconductor; this method allows for the high-precision measurement of the first thermodynamic critical magnetic fields of the sample and its crystallites and subcrystallites. The first thermodynamic critical magnetic fields are used to estimate the critical current density of the sample, crystallites, and subcrystallites. The role of the demagnetizing fields of crystallites in HTSC samples is studied. An increase in the crystallite size is shown to suppress the intra-and intercrystalline critical currents of the sample in lower fields.

We report magnetic measurements up to 1200 K on iron-contaminated multi-walled carbon nanotube mats with a Quantum Design vibrating sample magnetometer. Extensive magnetic data consistently show a ferrromagnetic transition at about 1000 K and a ferromagnetic-like transition at about 1275 K. The ferromagnetic transition at about 1000 K is associated with an Fe impurity phase and its saturation magnetization is in quantitative agreement with the Fe concentration measured by an inductively coupled plasma mass spectrometer. On the other hand, the saturation magnetization for the ferromagnetic-like phase (at 1275 K) is about four orders of magnitude larger than that expected from the measured concentration of Co or CoFe. We show that this ultrahigh-temperature ferromagnetic-like behavior cannot be explained by ferromagnetism of any Fe-carbon phases, carbon-based phases, or magnetic impurities, but is consistent with the paramagnetic Meissner effect (orbital ferromagnetism) due to the existence of π Josephson junctions in a granular superconductor.

We review some analytical results of our studies of the charge- and spin density modulations (CDW and SDW) in a one- and two-dimensional electron systems. Self-consistent solutions of Bogoliubov- de Gennes equations for spin-charge solitonic superstructure and superconducting state are obtained in the framework of one and two-dimensional extended Hubbard models. Possible correspondence of the theory with experimental data on stripe phase in high T_c cuprates is discussed. We found various solutions for the two-dimensional self-consistent model of superconductors with d_x²-y² symmetry of the order parameter, taking into account spin and charge distributions. Analytical solutions for spin-charge density wave phases in the absence of the superconductivity ("stripe" and "checkerboard" structures) are presented. Analytical solutions for coexisting superconductivity and stripe-phase modulations in the cores of the Abrikosov's vortices are also found.

We explore the quantum-classical crossover of two coupled, identical, superconducting quantum interference device (SQUID) rings. We note that the motivation for this work is based on a study of a similar system comprising two coupled Duffing oscillators. In that work we showed that the entanglement characteristics of chaotic and periodic (entrained) solutions differed significantly and that in the classical limit entanglement was preserved only in the chaotic-like solutions. However, Duffing oscillators are a highly idealised toy model. Motivated by a wish to explore more experimentally realisable systems we now extend our work to an analysis of two coupled SQUID rings. We observe some differences in behaviour between the system that is based on SQUID rings rather than on Duffing oscillators. However, we show that the two systems share a common feature. That is, even when the SQUID ring's trajectories appear to follow (semi) classical orbits entanglement persists.

We numerically investigate the Josephson transport through ferromagnetic insulators (FIs) by taking into account its band structure. By use of the recursive Green's function method, we found the formation of the π junction in the case of the fully spin-polarized FI (FPFI), e.g., La₂BaCuO₅. Moreover, the 0-π transition is induced by increasing the thickness of FPFI. On the other hand, Josephson current through the Eu chalcogenides shows the π junction behavior in the case of the strong d-f hybridization between the conduction d and the localized f electrons of Eu. Such FI-based Josephson junctions may becomes a element in the architecture of future quantum information devices.

We theoretically study classical thermal activation (TA) and macroscopic quantum tunneling (MQT) for a YBa₂Cu₃O_7-δ(YBCO) Josephson junction coupled with an LC circuit. The TA and MQT escape rate are calculated by taking into account the two-dimensional nature of the classical and quantum phase dynamics. We find that the MQT escape rate is largely suppressed by the coupling to the LC circuit. On the other hand, this coupling leads to the slight reduction of the TA escape rate. These results are relevant for the interpretation of a recent experiment on the MQT and TA phenomena in YBCO bi-epitaxial Josephson junctions.

We study the nucleation of vortices in a thin mesoscopic superconducting disk and stable configurations of vortices as a function of the disk size, the applied magnetic field H and finite temperature T. We also investigate the stability of different vortex states inside the disk. Further, we compare the predictions from Ginzburg-Landau (GL) theory and London theory - the GL equations take the superconducting density into account, but the London equations do not. Our simulations from both theories show similar vortex states. As more vortices are generated, more superconducting regions will be destoryed. The GL Equations consider this effect and provide a more accurate estimate.

The propagation of single flux quanta in T-shaped Josephson junctions gives rise to the flux cloning phenomenon. We have studied numerically the dynamics of flux cloning in cases of extended Josephson junctions. The changing thicknesses of T-junctions lead to new and interesting effects in terms of their dynamics. We have found out that when an additional Josephson transmission line is larger than the main Josephson transmission line, numerical simulations do not show the cloning phenomenon and soliton is reflected when it approaches the T junction. This strange result may be happened because the soliton losses more energy in the sharp edge. Although the vortex is moving very highly and it has huge energy but it still does not give birth to a new vortex. We have investigated conditions at which flux cloning occurs when both widths, W and W₀, are changing.

Breather is an elementary excitation regarded as a bound state of a fluxon and an antifluxon in a long Josephson junction. In quantum-mechanical regime, the breather energy is quantized so that the breather can be considered as an artificial moving atom. We propose a new type of fluxon qubit that is constructed by quantum-mechanical superposition of the breather's states. We describe quantum logic gates of breather qubit required for constructing quantum computer. In addition, our qubit can move in the system so that transfer of quntum information is possible between mobile qubits as well as stationary qubits. Our talking qubits support the global information sharing in quantum information networks.

Over 10 years pass after experimental discovery Josephson plasma resonance (JPR) in high-T_c superconductors. JPR spectroscopy became the powerful tool to study vortex phase diagram and interlayer electrodynamics in Josephson coupled layered superconductors like certain of high-T_c cuprates and molecular superconductors. We describe main principles of the JPR spectroscopy for measurement longitudinal plasma oscillations at the fundamental frequency ω_p. That frequency and linewidth of resonance is directly related to the interlayer phase coherence. In this paper we report about developments and achievments in spectroscopy of JPR. The study of the vortex state of Bi₂Sr₂CaCu₂O_8+δ and c-axis electrodynamics of Bi₂Sr₂CaCu₂O_8+δ and Bi₂Sr₂CuO_6+δw in zero magnetic field by JPR.

Maxwell equations are not logical consistent. This problem is caused by the implication that the divergence and the curl of a vector are not related. Based on Chen's S-R decomposition of a rank-two tensor, this logical un-consistency is discarded and, as a consequence, the classical Maxwell equations are reformulated to deduce London equations. From boundary field point, the relations between Josephson current and outside magnetic field are established, which shows that the Josephson current is produced by vortices of boundary magnetic field. From local field point, the first London equation corresponds to the local average rotation of electric field and the second London equation corresponds to the local average rotation of magnetic field. The relation between the Josephson effects and vortices of electromagnetic fields is discussed.

A model for the analytic description of vortices in a system consisting of a long Josephson junction and a waveguide is formulated. For this system all types of elementary vortices and its chains are listed. The allowed range of velocities of an elementary vortex is found. It is established that a free vortex can be a fast one which moves with velocity much greater than the Swihart velocity of Josephson junction. The effect of the waveguide on the induced vortices motion is studied. It is shown that fast vortex can be generated by relatively small values of bias current density. The effect of vortex Cherenkov losses on the bias current is described.

We develop a semiclassical theory of the nondegenerate parametric amplification in a single miniband of superlattice. We present the formulas describing absorption and gain of signal and idler fields in superlattice and analyze the limiting cases of strong and weak dissipation. We show how the well-known Manley-Rowe relations arise in the tight-binding lattice in the weak dissipation limit. Our results can be applied to an amplification of THz signals in semiconductor superlattices and a control of nonlinear transport of cold atoms in optical lattices.

An accurate theoretical treatment of electron-electron interactions in mesoscopic systems is available in very few cases and approximation schemes are developed in most of the applications, especially for many-level quantum dots. Here we present transport calculations within the random-phase approximation for the Coulomb interaction using the Keldysh Green's functions formalism. We describe the quantum dot systems by a tight-binding Hamiltonian. Our method is similar to the one used by Faleev and Stockman [Phys. Rev. B 66 085318 (2002)] in their study of the equilibrium properties of a homogeneous 2D electron gas. The important extension at the formal level is that we combine the RPA and the Keldysh formalism for studying non-linear transport properties of open quantum dots. Within the Keldysh formalism the polarization operator becomes a contour-ordered quantity that should be computed either from the non-interacting Green functions of the coupled quantum dot (the so-called G₀W approximation) either self-consistently (GW approximation). We performed both non-selfconsistent and self-consistent calculations and compare the results. In particular we recover the Coulomb diamonds for interacting quantum dots and we discuss the charge sensing effects in parallel quantum dots.

Quantum tunneling of vortices had been found to be an important novel phenomena for description of low temperature creep in high temperature superconductors (HTSCs). We speculate that quantum tunneling may be also exhibited in mesoscopic superconductors due to vortices trapped by the Bean-Livingston barrier. The London approximation and method of images is used to estimate the shape of the potential well in superconducting HTSC quantum dot. To calculate the escape rate we use the instanton technique. We model the vortex by a quantum particle tunneling from a two-dimensional ground state under magnetic field applied in the transverse direction. The resulting decay rates obtained by the instanton approach and conventional WKB are compared revealing complete coincidence with each other.

We consider terahertz absorption and gain in a single miniband of semiconductor superlattice subject to a bichromatic electric field in the most general case of commensurate frequencies of the probe and pump fields. Using an exact solution of Boltzmann transport equation, we show that in the small-signal limit the formulas for absorption always contain two distinct terms related to the parametric and incoherent interactions of miniband electrons with the alternating pump field. It provides a theoretical background for a control of THz gain without switching to the negative differential conductivity state. For pedagogical reasons we present derivations of formulas in detail.

We theoretically consider the amplification of THz radiation in a superlattice Bloch oscillator. The main dilemma in the realization of THz Bloch oscillator is finding operational conditions which allow simultaneously to achieve gain at THz frequencies and to avoid destructive space-charge instabilities. A possible solution to this dilemma is the extended Limited Space-Charge Accumulation scheme of Kroemer (H. Kroemer, cond-mat/0009311). Within the semiclassical miniband transport approach we extend its range of applicability by considering a difference in the relaxation times for electron velocity and electron energy. The kinetics of electrons and fields establishing a stationary signal in the oscillator is also discussed.

A simple equivalent circuit of the dielectric resonator technique, using for measurement of the surface resistance of the samples of non-standard dimensions, was considered and analyzed. It was shown that the coefficient (the geometry factor) relating the surface resistance of the sample to the quality factor may be different in the cases when the inductive resistance (caused by the external inductance) of the sample exceeds significantly its active resistance and when these resistances are of the same order. It was shown too, that an anomaly in the R_S versus T dependence (i.e., a decreasing of the surface resistance with increase of the temperature) is possible in double layer structures with thin superconductor and metal films.

The electrostatic field in superconductors in the equilibrium diamagnetic state is discussed. On recent experimental data we demonstrate that the electrostatic field in superconductors is still far from being understood. Then we present the elementary ideas based on the balance of forces.

The London theory of diamagnetic currents is discussed from the magnetohydrodynamical point of view. It is argued that the motion of superconducting electrons is controlled by the electrostatic field which balances the Lorentz and the inertial forces.

In the diamagnetic Meissner state, the superconductor is in the equilibrium. The non-zero electrostatic field thus represents a minimum of the free energy. The thermodynamical formulation of the scalar potential allows us to include forces corresponding to the free energy of condensation – the so called pairing forces.

Bardeen's extension of the Ginzburg-Landau theory to low temperatures is modified so that along with magnetic properties it also covers the electrostatic field.

The theory of electrostatic fields in superconductors at equilibrium is reviewed. We start from the simple Bernoulli potential balancing the Lorentz and inertial forces. Then we add interaction of superconducting and normal electrons and forces due to gradients of the condensation energy. Nonlocal relation between perturbing forces and the induced electrostatic field is formulated within the extended Ginzburg-Landau theory.

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