arXiv subjects

V. I. Yukalov

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

At least 271 records · Page 15Linked to original sources

arXiv2002

Nonlinear Coherent Modes of Trapped Bose-Einstein Condensates

Nonlinear coherent modes are the collective states of trapped Bose atoms, corresponding to different energy levels. These modes can be created starting from the ground state condensate that can be excited by means of a resonant alternating field. A thorough theory for the resonant excitation of the coherent modes is presented. The necessary and sufficient conditions for the feasibility of this process are found. Temporal behaviour of fractional populations and of relative phases exhibits dynamic critical phenomena on a critical line of the parametric manifold. The origin of these critical phenomena is elucidated by analyzing the structure of the phase space. An atomic cloud, containing the coherent modes, possesses several interesting features, such as interference patterns, interference current, spin squeezing, and massive entanglement. The developed theory suggests a generalization of resonant effects in optics to nonlinear systems of Bose-condensed atoms.

cond-mat↗

arXiv2002

Self-Similar Approximations for a Trapped Bose-Einstein Condensate

An approximate solution to the Gross-Pitaevskii equation for Bose-Einstein condensate in a spherical harmonic trap is suggested, which is valid in the whole interval of the coupling parameter, correctly interpolating between weak-coupling and strong-coupling limits. This solution is shown to be more accurate than the optimized Gaussian approximation as well as the Thomas-Fermi approximation. The derivation of the solution is based on the self-similar approximation theory. The possibility of obtaining interpolation formulas in the case of nonspherical traps is discussed.

cond-mat↗

arXiv2002

Processing Information by Punctuated Spin Superradiance

The possibility of realizing the regime of punctuated spin superradiance is advanced. In this regime, the number of superradiant pulses and the temporal intervals between them can be regulated. This makes it feasible to compose a kind of the Morse Code alphabet and, hence, to develop a technique of processing information.

cond-mat↗

arXiv2002

Spectrum of Coherent Modes for Trapped Bose Gas

The spectrum of coherent modes for dilute atomic Bose gas, confined in a cylindrical trap, is calculated by applying optimized perturbation theory and the technique of self-similar root approximants. The latter technique makes it possible to derive accurate analytical formulas. The obtained expressions are valid for arbitrary energy levels of all excited nonlinear coherent modes and for different traps, spherical, sigar-shape, and disk-shape.

cond-mat↗

arXiv2002

Matrix Order Indices in Statistical Mechanics

A new notion is introduced of matrix order indices which relate the matrix norm and its trace. These indices can be defined for any given matrix. They are especially important for matrices describing many-body systems, equilibrium as well as nonequilibrium, for which the indices present a quantitative measure of the level of ordering. They characterize not only the long-range order, but also mid-range order. In the latter case, when order parameters do not exist, the matrix indices are well defined, providing an explicit classification of various mid-range orders. The matrix order indices are suitable for describing phase transitions with both off-diagonal and diagonal order. Contrary to order parameters whose correct definition requires the thermodynamic limit, the matrix indices do not necessarily need the latter. Because of this, such indices can distinguish between different phases of finite systems, thus, allowing for the classification of crossover phase transitions.

cond-mat↗

arXiv2002

Superradiant Operation of Spin Masers

The theory of spin superradiance, developed earlier for nuclear magnets, is generalized to a wider class of spin systems, such as granular magnets and molecular magnets. The latter may possess strong single-site magnetocrystalline anisotropy, whose role in nonlinear spin dynamics is analysed. Transient as well as pulsing superradiant regimes are described. These coherent regimes may be employed in the operation of spin masers.

cond-mat↗

arXiv2002

Magnetic Semiconfinement of Neutral Atoms

A mechanism for creating well-collimated beams of neutral particles or atoms with spins is studied. The consideration is accomplished for a general realistic case, taking into account: (i) the finiteness of a cylindrical trap where the atoms to be shot out, are stored; (ii) the possibility of manipulating the trap magnetic fields in order to form different anisotropic field configurations; (iii) the presence of gravity curving atomic trajectories.

cond-mat↗

arXiv2002

Self-Similar Factor Approximants

The problem of reconstructing functions from their asymptotic expansions in powers of a small variable is addressed by deriving a novel type of approximants. The derivation is based on the self-similar approximation theory, which presents the passage from one approximant to another as the motion realized by a dynamical system with the property of group self-similarity. The derived approximants, because of their form, are named the self-similar factor approximants. These complement the obtained earlier self-similar exponential approximants and self-similar root approximants. The specific feature of the self-similar factor approximants is that their control functions, providing convergence of the computational algorithm, are completely defined from the accuracy-through-order conditions. These approximants contain the Pade approximants as a particular case, and in some limit they can be reduced to the self-similar exponential approximants previously introduced by two of us. It is proved that the self-similar factor approximants are able to reproduce exactly a wide class of functions which include a variety of transcendental functions. For other functions, not pertaining to this exactly reproducible class, the factor approximants provide very accurate approximations, whose accuracy surpasses significantly that of the most accurate Pade approximants. This is illustrated by a number of examples showing the generality and accuracy of the factor approximants even when conventional techniques meet serious difficulties.

cond-mat.stat-mech↗

arXiv2002

Stochastic Instability of Quasi-Isolated Systems

The stability of solutions to evolution equations with respect to small stochastic perturbations is considered. The stability of a stochastic dynamical system is characterized by the local stability index. The limit of this index with respect to infinite time describes the asymptotic stability of a stochastic dynamical system. Another limit of the stability index is given by the vanishing intensity of stochastic perturbations. A dynamical system is stochastically unstable when these two limits do not commute with each other. Several examples illustrate the thesis that there always exist such stochastic perturbations which render a given dynamical system stochastically unstable. The stochastic instability of quasi-isolated systems is responsible for the irreversibility of time arrow.

cond-mat↗

arXiv2002

Do We Understand What Is Deconfinement?

An overview is given of different approaches to describing the process of deconfinement in quantum chromodynamics. The analysis of the known approaches demonstrates that the detailed picture of how deconfinement really occurs has not yet been understood. Therefore, one has to be rather cautious when interpreting experimental signals as attributed to deconfinement.

hep-ph↗

arXiv2002

Reconstructing Generalized Exponential Laws by Self-Similar Exponential Approximants

We apply the technique of self-similar exponential approximants based on successive truncations of continued exponentials to reconstruct functional laws of the quasi-exponential class from the knowledge of only a few terms of their power series. Comparison with the standard Padé approximants shows that, in general, the self-similar exponential approximants provide significantly better reconstructions.

cond-mat↗

arXiv2002

Photon Filamentation in Resonant Media with High Fresnel Numbers

The phenomenon of turbulent photon filamentation occurs in lasers and other active optical media at high Fresnel numbers. A description of this phenomenon is suggested. The solutions to evolution equations are presented in the form of a bunch of filaments chaotically distributed in space and having different radii. The probability distribution of patterns is defined characterizing the probabilistic weight of different filaments. The most probable filament radius and filament number are found, being in good agreement with experiment.

cond-mat↗

arXiv2002

Critical Effects in Population Dynamics of Trapped Bose-Einstein Condensates

The population dynamics of a trapped Bose-Einstein condensate, subject to the action of an external field, is studied. This field produces a spatio-temporal modulation of the trapping potential with the frequency close to the transition frequency between the ground state and a higher energy level. For the evolution equations of fractional populations, a critical line is found. It is demonstrated that there exists a direct analogy between dynamical instability at this line and critical phenomena at a critical line of an averaged system. The related critical indices are calculated. The spatio-temporal evolution of atomic density is analyzed.

cond-mat↗

arXiv2002

Optical Turbulent Structures

The problem of describing optical turbulent structures, arising in resonant media with high Fresnel numbers, is reviewed. The consideration is based on the probabilistic approach to pattern selection, ascribing a probability distribution of patterns to systems with multiple possible structures. The most probable structure corresponds to the minimal expansion exponent, or to the minimal expansion rate, characterizing the phase-space expansion of a dynamical system. Turbulent photon filamentation is studied. The most probable filament radius and the number of filaments are found, being in good agreement with experiment.

cond-mat↗

arXiv2001

Possibility of Turbulent Crystals

The possibility for the occurrence in crystals of a phenomenon, resembling turbulence, is discussed. This phenomenon, called {\it heterophase turbulence}, is manifested by the fluctuational appearance inside a crystalline sample of disordered regions randomly distributed in space. The averaged picture for such a turbulent solid is exemplified by an exactly solvable lattice-gas model. The origin of heterophase turbulence is connected with stochastic instability of quasi-isolated systems.

cond-mat↗

arXiv2001

Self-similar approach to market analysis

A novel approach to analyzing time series generated by complex systems, such as markets, is presented. The basic idea of the approach is the {\it Law of Self-Similar Evolution}, according to which any complex system develops self-similarly. There always exist some internal laws governing the evolution of a system, say of a market, so that each of such systems possesses its own character regulating its behaviour. The problem is how to discover these hidden internal laws defining the system character. This problem can be solved by employing the {\it Self-Similar Approximation Theory}, which supplies the mathematical foundation for the Law of Self-Similar Evolution. In this report, the theoretical basis of the new approach to analyzing time series is formulated, with an accurate explanation of its principal points.

cond-mat↗

arXiv2001

Principle of Pattern Selection for Nonequilibrium Phenomena

A general principle is advanced allowing the classification of nonunique solutions to nonlinear evolution equations, corresponding to different spatio-temporal patterns. This is done by defining the probability distribution of patterns, which characterizes multiple solutions as more or less probable with respect to each other. The most probable pattern is naturally defined by the maximum of the pattern distribution. This maximum is shown to be equivalent to the {\it minimum of local contraction}. The formulated principle plays for nonequilibrium dynamical systems the same ordering role as the condition of minimal free energy for equilibrium statistical systems. The generality of the principle is illustrated by several examples of different nature.

cond-mat↗

arXiv2001

Bose-Einstein Condensation of Trapped Atomic Gases

This article reviews recent investigations on the phenomenon of Bose-Einstein condensation of dilute gases. Since the experimental observation of quantum degeneracy in atomic gases, the research activity in the field of coherent matter-waves literally exploded. The present topical review aims to give an introduction into the thermodynamics of Bose-Einstein condensation, a general overview over experimental techniques and investigations, and a theoretical foundation for the description of bosonic many-body quantum systems.

cond-mat.soft↗