arXiv subjects

V. I. Yukalov

Publications and source records attributed to V. I. Yukalov.

At least 217 records · Page 12Linked to original sources

arXiv2007

Bose-Einstein-condensed systems in random potentials

The properties of systems with Bose-Einstein condensate in external time-independent random potentials are investigated in the frame of a self-consistent stochastic mean-field approximation. General considerations are presented, which are valid for finite temperatures, arbitrary strengths of the interaction potential, and for arbitrarily strong disorder potentials. The special case of a spatially uncorrelated random field is then treated in more detail. It is shown that the system consists of three components, condensed particles, uncondensed particles and a glassy density fraction, but that the pure Bose glass phase with only a glassy density does not appear. The theory predicts a first-order phase transition for increasing disorder parameter, where the condensate fraction and the superfluid fraction simultaneously jump to zero. The influence of disorder on the ground-state energy, the stability conditions, the compressibility, the structure factor, and the sound velocity are analyzed. The uniform ideal condensed gas is shown to be always stochastically unstable, in the sense that an infinitesimally weak disorder destroys the Bose-Einstein condensate, returning the system to the normal state. But the uniform Bose-condensed system with finite repulsive interactions becomes stochastically stable and exists in a finite interval of the disorder parameter.

cond-mat.stat-mech↗

arXiv2007

Bose-Einstein-condensed gases with arbitrary strong interactions

Bose-condensed gases are considered with an effective interaction strength varying in the whole range of the values between zero and infinity. The consideration is based on the usage of a representative statistical ensemble for Bose systems with broken global gauge symmetry. Practical calculations are illustrated for a uniform Bose gas at zero temperature, employing a self-consistent mean-field theory, which is both conserving and gapless.

cond-mat.stat-mech↗

arXiv2007

Nonlinear Dynamical Model of Regime Switching Between Conventions and Business Cycles

We introduce and study a non-equilibrium continuous-time dynamical model of the price of a single asset traded by a population of heterogeneous interacting agents in the presence of uncertainty and regulatory constraints. The model takes into account (i) the price formation delay between decision and investment by the second-order nature of the dynamical equations, (ii) the linear and nonlinear mean-reversal or their contrarian in the form of speculative price trading, (iii) market friction, (iv) uncertainty in the fundamental value which controls the amplitude of mispricing, (v) nonlinear speculative momentum effects and (vi) market regulations that may limit large mispricing drifts. We find markets with coexisting equilibrium, conventions and business cycles, which depend on (a) the relative strength of value-investing versus momentum-investing, (b) the level of uncertainty on the fundamental value and (c) the degree of market regulation. The stochastic dynamics is characterized by nonlinear geometric random walk-like processes with spontaneous regime shifts between different conventions or business cycles. This model provides a natural dynamical framework to model regime shifts between different market phases that may result from the interplay between the effects (i-vi).

nlin.AO↗

arXiv2006

Self-Consistent Theory of Bose-Condensed Systems

In the theory of Bose-condensed systems, there exists the well known problem, the Hohenberg-Martin dilemma of conserving versus gapless approximations. This dilemma is analysed and it is shown that it arises because of the internal inconsistency of the standard grand ensemble, as applied to Bose-systems with broken global gauge symmetry. A solution of the problem is proposed, based on the notion of representative statistical ensembles, taking into account all constraints imposed on the system. A general approach for constructing representative ensembles is formulated. Applying a representative ensemble to Bose-condensed systems results in a completely self-consistent theory, both conserving and gapless in any approximation.

cond-mat.stat-mech↗

arXiv2006

Nonequilibrium Bose systems and nonground-state Bose-Einstein condensates

The theory of resonant generation of nonground-state Bose-Einstein condensates is extended to Bose-condensed systems at finite temperature. The generalization is based on the notion of representative statistical ensembles for Bose systems with broken global gauge symmetry. Self-consistent equations are derived describing an arbitrary nonequilibrium nonuniform Bose system. The notion of finite-temperature topological coherent modes, coexisting with a cloud of noncondensed atoms, is introduced. It is shown that resonant generation of these modes is feasible for a gas of trapped Bose atoms at finite temperature.

cond-mat.stat-mech↗

arXiv2006

Gapless Hartree-Fock-Bogoliubov Approximation for Bose Gases

A dilute Bose system with Bose-Einstein condensate is considered. It is shown that the Hartree-Fock-Bogolubov approximation can be made both conserving as well as gapless. This is achieved by taking into account all physical normalization conditions, that is, the normalization condition for the condensed particles and that for the total number of particles. Two Lagrange multipliers, introduced for preserving these normalization conditions, make the consideration completely self-consistent.

cond-mat.stat-mech↗

arXiv2006

Nonequivalent operator representations for Bose-condensed systems

The necessity of accurately taking into account the existence of nonequivalent operator representations, associated with canonical transformations, is discussed. It is demonstrated that Bose systems in the presence of the Bose-Einstein condensate and without it correspond to different Fock spaces, orthogonal to each other. A composite representation for the field operators is constructed, allowing for a self-consistent description of Bose-condensed systems. Equations of motion are derived from the given Hamiltonian, which guarantees the validity of conservation laws and thermodynamic self-consistency. At the same time, the particle spectrum, obtained either from diagonalizing this Hamiltonian or from linearizing the field-operator equations of motion, has no gap. The condition of the condensate existence assures the absence of the gap in the spectrum, irrespectively to the approximation involved. The suggested self-consistent theory is both conserving and gapless.

cond-mat.stat-mech↗

arXiv2006

Self-similar power transforms in extrapolation problems

A method is suggested allowing for the improvement of accuracy of self-similar factor and root approximants, constructed from asymptotic series. The method is based on performing a power transform of the given asymptotic series, with the power of this transformation being a control function. The latter is defined by a fixed-point condition, which improves the convergence of the sequence of the resulting approximants. The method makes it possible to extrapolate the behaviour of a function, given as an expansion over a small variable, to the region of the large values of this variable. Several examples illustrate the effectiveness of the method.

cond-mat.stat-mech↗

arXiv2006

Regulating entanglement production in multitrap Bose-Einstein condensates

A system of traps is considered, each containing a large number of Bose-condensed atoms. This ensemble of traps is subject to the action of an external modulating field generating nonequilibrium nonground-state condensates. When the frequency of the modulating field is in resonance with the transition frequency between two different topological coherent modes, each trap becomes an analog of a finite-level resonant atom. Similarly to the case of atoms in an electromagnetic resonant field, one can create entanglement between atomic traps subject to a common resonant modulating field generating higher coherent modes in each of the traps. A method is suggested for regulating entanglement production in such a system of multitrap and multimode Bose-Einstein condensates coupled through a common resonant modulating field. Several regimes of evolutional entanglement production, regulated by manipulating the external field, are illustrated by numerical calculations.

cond-mat.mes-hall↗

arXiv2006

Entanglement production with multimode Bose-Einstein condensates in optical lattices

Deep optical lattices are considered, in each site of which there are many Bose-condensed atoms. By the resonant modulation of trapping potentials it is possible to transfer a macroscopic portion of atoms to the collective nonlinear states corresponding to topological coherent modes. Entanglement can be generated between these modes. By varying the resonant modulating field it is possible to effectively regulate entanglement production in this multimode multitrap system of Bose condensates.

cond-mat.mes-hall↗

arXiv2006

Kinetic energy of Bose systems and variation of statistical averages

The problem of defining the average kinetic energy of statistical systems is addressed. The conditions of applicability for the formula, relating the average kinetic energy with the mass derivative of the internal energy, are analysed. It is shown that incorrectly using this formula, outside its region of validity, leads to paradoxes. An equation is found for a parametric derivative of the average for an arbitrary operator. A special attention is paid to the mass derivative of the internal energy, for which a general formula is derived, without invoking the adiabatic approximation and taking into account the mass dependence of the potential-energy operator. The results are illustrated by the case of a low-temperature dilute Bose gas.

cond-mat.stat-mech↗

arXiv2006

Fluctuations of composite observables and stability of statistical systems

Thermodynamic stability of statistical systems requires that susceptibilities be semipositive and finite. Susceptibilities are known to be related to the fluctuations of extensive observable quantities. This relation becomes nontrivial, when the operator of an observable quantity is represented as a sum of operators corresponding to the extensive system parts. The association of the dispersions of the partial operator terms with the total dispersion is analyzed. A special attention is paid to the dependence of dispersions on the total number of particles N in the thermodynamic limit. An operator dispersion is called thermodynamically normal, if it is proportional to N at large values of the latter. While, if the dispersion is proportional to a higher power of N, it is termed thermodynamically anomalous. The following theorem is proved: The global dispersion of a composite operator, which is a sum of linearly independent self-adjoint terms, is thermodynamically anomalous if and only if at least one of the partial dispersions is anomalous, the power of N in the global dispersion being defined by the largest partial dispersion. Conversely, the global dispersion is thermodynamically normal if and only if all partial dispersions are normal. The application of the theorem is illustrated by several examples of statistical systems. The notion of representative ensembles is formulated. The relation between the stability and equivalence of statistical ensembles is discussed.

cond-mat.stat-mech↗

arXiv2006

Optimal trap shape for a Bose gas with attractive interactions

Dilute Bose gas with attractive interactions is considered at zero temperature, when practically all atoms are in Bose-Einstein condensate. The problem is addressed aiming at answering the question: What is the optimal trap shape allowing for the condensation of the maximal number of atoms with negative scattering lengths? Simple and accurate analytical formulas are derived allowing for an easy analysis of the optimal trap shapes. These analytical formulas are the main result of the paper.

cond-mat.mes-hall↗

arXiv2006

Turbulent Filamentation in Lasers with High Fresnel Numbers

The theory of turbulent photon filamentation in lasers with high Fresnel numbers is presented. A survey of experimental observations of turbulent filamentation is given. Theoretical description is based on the method of eliminating field variables, which yields the pseudospin laser equations. These are treated by the scale separation approach, including the randomization of local fields and the method of stochastic averaging. The initial, as well as the transient and final stages of radiation dynamics are carefully analysed. The characteristics of photon filaments are obtained by involving the probabilistic approach to pattern selection.

cond-mat.stat-mech↗

arXiv2006

No Anomalous Fluctuations Exist in Stable Equilibrium Systems

An equilibrium statistical system is known to be stable if the fluctuations of global observables are normal, when their dispersions are proportional to the number of particles, or to the system volume. A general theorem is rigorously proved for the case, when an observable is a sum of linearly independent terms: The dispersion of a global observable is normal if and only if all partial dispersions of its terms are normal, and it is anomalous if and only if at least one of the partial dispersions is anomalous. This theorem, in particular, rules out the possibility that in a stable system with Bose-Einstein condensate some fluctuations of either condensed or noncondensed particles could be anomalous. The conclusion is valid for arbitrary systems, whether uniform or nonuniform, interacting weakly or strongly. The origin of fictitious fluctuation anomalies, arising in some calculations, is elucidated.

cond-mat.stat-mech↗

arXiv2005

Modified semiclassical approximation for trapped Bose gases

A generalization of the semiclassical approximation is suggested allowing for an essential extension of its region of applicability. In particular, it becomes possible to describe Bose-Einstein condensation of a trapped gas in low-dimensional traps and in traps of low confining dimensions, for which the standard semiclassical approximation is not applicable. The results of the modified approach are shown to coincide with purely quantum-mechanical calculations for harmonic traps, including the one-dimensional harmonic trap. The advantage of the semiclassical approximation is in its simplicity and generality. Power-law potentials of arbitrary powers are considered. Effective thermodynamic limit is defined for any confining dimension. The behaviour of the specific heat, isothermal compressibility, and density fluctuations is analyzed, with an emphasis on low confining dimensions, where the usual semiclassical method fails. The peculiarities of the thermodynamic characteristics in the effective thermodynamic limit are discussed.

cond-mat.stat-mech↗

arXiv2005

Normal and Anomalous Averages for Systems with Bose-Einstein Condensate

The comparative behaviour of normal and anomalous averages as functions of momentum or energy, at different temperatures, is analysed for systems with Bose-Einstein condensate. Three qualitatively distinct temperature regions are revealed: The critical region, where the absolute value of the anomalous average, for the main energy range, is much smaller than the normal average. The region of intermediate temperatures, where the absolute values of the anomalous and normal averages are of the same order. And the region of low temperatures, where the absolute value of the anomalous average, for practically all energies, becomes much larger than the normal average. This shows the importance of the anomalous averages for the intermediate and, especially, for low temperatures, where these anomalous averages cannot be neglected.

cond-mat.stat-mech↗

arXiv2005

Fermi-Bose mapping for one-dimensional Bose gases

One-dimensional Bose gases are considered, interacting either through the hard-core potentials or through the contact delta potentials. Interest in these gases gained momentum because of the recent experimental realization of quasi-one-dimensional Bose gases in traps with tightly confined radial motion, achieving the Tonks-Girardeau (TG) regime of strongly interacting atoms. For such gases the Fermi-Bose mapping of wavefunctions is applicable. The aim of the present communication is to give a brief survey of the problem and to demonstrate the generality of this mapping by emphasizing that: (i) It is valid for nonequilibrium wavefunctions, described by the time-dependent Schrödinger equation, not merely for stationary wavefunctions. (ii) It gives the whole spectrum of all excited states, not merely the ground state. (iii) It applies to the Lieb-Liniger gas with the contact interaction, not merely to the TG gas of impenetrable bosons.

cond-mat.stat-mech↗