Searcharxiv⌕ Search

arXiv subjects

A. M. Kamchatnov

Publications and source records attributed to A. M. Kamchatnov.

At least 109 records · Page 6Linked to original sources
arXiv2004

Dynamics of Bose-Einstein condensates in cigar-shaped traps

Gross-Pitaevskii equation for Bose-Einstein condensate confined in elongated cigar-shaped trap is reduced to an effective system of nonlinear equations depending on only one space coordinate along the trap axis. The radial distribution of the condensate density and its radial velocity are approximated by Gaussian functions with real and imaginary exponents, respectively, with parameters depending on the axial coordinate and time. The effective one-dimensional system is applied to description of the ground state of the condensate, to dark and bright solitons, to the sound and radial compression waves propagating in a dense condensate, and to weakly nonlinear waves in repulsive condensate. In the low density limit our results reproduce the known formulae. In the high density case our description of solitons goes beyond the standard approach based on the nonlinear Schrödinger equation. The dispersion relations for the sound and radial compression waves are obtained in a wide region of values of the condensate density. Korteweg-de Vries equation for weakly nonlinear waves is derived and existence of bright solitons on a constant background is predicted for the dense enough condensate with repulsive interaction between the atoms.

cond-mat.soft↗
arXiv2004

Theory of rapid (nonadiabatic) rotation of nonspherical nuclei

On the basis of the concept of the growing role of nonadiabatic effects of the non-conservation of the quantum number $K,$ a theory has been developed of the phenomenon which has been given the name of backbending. Above the transition point, for $J\geq J_c$, all the values $-J\leq K\leq J$ are equally probable. An investigation is made of the singularities possessed by the ordering parameter (proportional to the spectroscopic quadrupole moment of a nonspherical nucleus), the rotational angular velocity and the moment of inertia of a nucleus at the Curie point. Formulas have been derived for the intensity of quadrupole radiation in the more symmetric $n$-phase $J> J_c$. By analyzing the experimental values of the moments of inertia belonging to the $n$-phase, the radius of the mass distribution in the nucleus was determined. It agrees with the radius of the proton distribution derived from data on the scattering of electrons by nuclei. On the basis of the simplest form of the singularity of the parametric derivative of the Hamiltonian of the system a general theory of zero-temperature second-order phase transitions is developed in the Appendix.

nucl-th↗
arXiv2003

Inelastic interactions between nuclei at high energies

A theory of nucleus-nucleus collisions has been developed for kinetic energies substantially in excess of the binding energy. The very high pressure produced in the compound system as a result of the fusion of the two colliding nuclei is the reason for the subsequent hydrodynamic expansion of the nuclear medium. The energy and angular distributions of the reaction products are investigated. The charge distribution is also determined in the case where the nucleon and ion components of the reaction products are predominant. A solution is found for the expansion into vacuum of a sphere in which the initially uniformly distributed material is initially at rest and at an ultrarelativistic temperature.

nucl-th↗
arXiv2003

Thermodynamic properties of spherical nuclei

The effect of the residual interaction between the nucleons (quasiparticles) on the thermodynamic behavior of spherical nuclei is considered. Thermodynamic relations are derived for the simplest model of the residual interaction that has the necessary macroscopic structure previously established. The range of applicability of the theory is discussed.

nucl-th↗
arXiv2003

Theory of the radiative width of a highly excited nucleus

A microscopic theory of the electromagnetic radiation emitted by a highly excited nucleus is developed on the basis of the Landau theory of a Fermi liquid. Closed formulae are obtained for the mean radiative width and its mean square fluctuation from level to level. The temperatures of many nuclei are found from the observed widths. The relaxation time is estimated from the experimental data on the radiative-width fluctuations. The regions of applicability of the various types of relations between the relaxation time and the lifetime of the compound nucleus, as well as the relevant physical consequences, are discussed.

nucl-th↗
arXiv2003

Cascade emission of $γ$-quanta by highly excited nuclei

The thermodynamics of the electromagnetic radiation from heated nuclei is developed on basis of the Landau theory of a Fermi liquid [1]. The case of non-spherical nuclei is considered, in which the quasiparticle energy spectrum is not distorted by the residual interactions that affect the thermodynamic behavior of the system. The number of quanta per cascade and mean-square fluctuation are calculated; the $γ$-quantum spectrum of the whole cascade is also obtained. The formulae can be used to determine the entropy and temperature of the initial nucleus by various methods. The effective nucleon (quasiparticle) mass in nuclear matter is determined by comparison with the experimental data. The region of validity of the theory and some possibilities of its extension on the basis of new experiments are discussed.

nucl-th↗
arXiv2003

Structure of residual interaction in spherical nuclei

The effect of residual interaction between nucleons (quasiparticles) on shell oscillations of the masses of spherical nuclei is considered. The singularity of the ground state energy of the system in the vicinity of nucleon magic numbers is analyzed for various types of the dependence of residual interaction on orbital momentum of the quasiparticle. It is shown that only the perturbation band width of the Fermi distribution due to residual interaction which is proportional to the square of the angular momentum vector is consistent with the character of the magic cusps. The coupling constants between the quasiparticles are determined on the basis of the available data. The constant decreases rapidly with increase of nuclear radius. Possible consequences pertaining to the energy spectrum of infinite nuclear matter are discussed.

nucl-th↗
arXiv2003

Theory of shell structure and of the "magic" effect in spherical nuclei

A consistent theory is developed of the volume energy oscillations of spherical nuclei due to sharpness of the Fermi distribution boundary for quasiparticles. The lowest value of the oscillating part of the energy corresponds to a magic nucleus. A formula is obtained for the corresponding limiting momentum of a quasiparticle and it is shown that we have here an isolated point of a temperatureless second-order phase transition. An expression for the discontinuity of the derivative of the energy of the body with respect to the number of particles is obtained in the case of a sharp (step-like) Fermi distribution limit. Comparison with experimental nuclear-mass data permits some conclusions to be drawn regarding the true structure of the boundary layer of the Fermi distribution and regarding its variation with increasing nuclear size. In the region of magic nuclei actually accessible up to the present time, apparently no signs are observed of any appreciably expressed residual phenomenon, such as the Cooper phenomenon, which would result in instability of the energy spectrum of infinite nuclear matter with an absolutely sharp Fermi limit for quasiparticles.

nucl-th↗
arXiv2003

Expansion of Bose-Einstein condensates in lower dimensions

In the hydrodynamic approximation we obtain analytic solutions to the Gross-Pitaevskii equation with positive scattering length which describe expansions of the Bose-Einstein condensates in quasi-one and quasi-two dimensional geometries. The expansion laws are expressed in terms of the initial sizes of the condensate and the trap frequencies before release, that is in terms of experimentally measurable parameters only. Three-dimensional effects are estimated with the use of variational approach. The analytical formulae show good agreement with available experimental data.

cond-mat.soft↗
arXiv2003

Dissipationless shock waves in repulsive Bose-Einstein condensates

We consider formation of dissipationless shock waves in Bose-Einstein condensates with repulsive interaction between atoms. It is shown that big enough initial inhomogeneity of density leads to wave breaking phenomenon followed by generation of a train of dark solitons. Analytical theory is confirmed by numerical simulations.

cond-mat.soft↗
arXiv2003

Formation of soliton trains in Bose-Einstein condensates as a nonlinear Fresnel diffraction of matter waves

The problem of generation of atomic soliton trains in elongated Bose-Einstein condensates is considered in framework of Whitham theory of modulations of nonlinear waves. Complete analytical solution is presented for the case when the initial density distribution has sharp enough boundaries. In this case the process of soliton train formation can be viewed as a nonlinear Fresnel diffraction of matter waves. Theoretical predictions are compared with results of numerical simulations of one- and three-dimensional Gross-Pitaevskii equation and with experimental data on formation of Bose-Einstein bright solitons in cigar-shaped traps.

cond-mat.soft↗
arXiv2003

Polariton effect in nonlinear pulse propagation

The joint influence of the polariton effect and Kerr-like nonlinearity on propagation of optical pulses is studied. The existence of different families of envelope solitary wave solutions in the vicinity of polariton gap is shown. The properties of solutions depend strongly on the carrier wave frequency. In particular, solitary waves inside and outside of the polariton gap exhibit different velocity and amplitude dependencies on their duration.

nlin.PS↗
arXiv2003

Hydrodynamic flow of expanding Bose-Einstein condensates

We study expansion of quasi-one-dimensional Bose-Einstein condensate (BEC) after switching off the confining harmonic potential. Exact solution of dynamical equations is obtained in framework of the hydrodynamic approximation and it is compared with the direct numerical simulation of the full problem showing excellent agreement at realistic values of physical parameters. We analyze the maximum of the current density and estimate the velocity of expansion. The results of the 1D analysis provides also qualitative understanding of some properties of BEC expansion observed in experiments.

cond-mat.soft↗
arXiv2003

On dissipationless shock waves in a discrete nonlinear Schrödinger equation

It is shown that the generalized discrete nonlinear Schrödinger equation can be reduced in a small amplitude approximation to the KdV, mKdV, KdV(2) or the fifth-order KdV equations, depending on values of the parameters. In dispersionless limit these equations lead to wave breaking phenomenon for general enough initial conditions, and, after taking into account small dispersion effects, result in formation of dissipationless shock waves. The Whitham theory of modulations of nonlinear waves is used for analytical description of such waves.

nlin.PS↗
arXiv2003

On Whitham theory for perturbed integrable equations

Whitham theory of modulations is developed for periodic waves described by nonlinear wave equations integrable by the inverse scattering transform method associated with $2\times2$ matrix or second order scalar spectral problems. The theory is illustrated by derivation of the Whitham equations for perturbed Korteweg-de Vries equation and nonlinear Schrödinger equation with linear damping.

nlin.SI↗
arXiv2003

On creation and evolution of dark solitons in Bose-Einstein condensates

Generation of dark solitons from large initial excitations and their evolution in a quasi-one-dimensional Bose-Einstein condensate trapped by a harmonic potential is studied analytically and numerically. In the case of a single deep soliton main characteristics of its motion such as a frequency and amplitude of oscillations are calculated by means of the perturbation theory which in the leading order results in a Newtonian dynamics, corrections to which are computed as well. It is shown that long-time dynamics of a dark soliton in a generic situation deviates substantially from outcomes of the naive application of the Ehrenfest theorem. We also consider three different techniques of controllable creation of multi-soliton structures (soliton trains) from large initial excitations and calculate their initial parameters (depths and velocities) with the use of a generalized Bohr-Sommerfeld quantization rule. Multi-soliton effects are discussed.

cond-mat.soft↗
arXiv2002

On generating functions in the AKNS hierarchy

It is shown that the self-induced transparency equations can be interpreted as a generating function for as positive so negative flows in the AKNS hierarchy. Mutual commutativity of these flows leads to other hierarchies of integrable equations. In particular, it is shown that stimulated Raman scattering equations generate the hierarchy of flows which include the Heisenberg model equations. This observation reveals some new relationships between known integrable equations and permits one to construct their new physically important combinations. Reductions of the AKNS hierarchy to ones with complex conjugate and real dependent variables are also discussed and the corresponding generating functions of positive and negative flows are found. Generating function of Whitham modulation equations in the AKNS hierarchy is obtained.

nlin.SI↗