Theory of a weakly nonideal Bose gas in a magnetic field

This paper investigates Bose-Einstein condensation of an ideal gas of finite-spin bosons in an external magnetic field. We generalize Bogolyubov’s theory of a weakly nonideal Bose gas to the case where the gas of finite-spin bosons is located in an external magnetic field. We find the corresponding quasiparticle spectrum and formulate the superfluidity criterion for the boson gas. The magnetization of the weakly nonideal Bose gas is also determined. Finally, we specify a method of studying kinetic processes that take place in a weakly nonideal Bose gas. Zh. éksp. Teor. Fiz. 113, 918–929 (March 1998)     

Coherence time of the condensate of a weakly nonideal Bose gas

A system of equations for the density matrix is derived to describe the condensate and quasi-particles of a weakly nonideal spatially homogeneous Bose gas. The equations are used to find the distribution function of the number of particles and the condensate coherence time. A numerical estimate is obtained for a temperature that is significantly lower than the transition temperature. Original Text ? Astro, Ltd., 2009.     

Kinetic equation for a weakly interacting classical electron gas

A kinetic equation is derived for the two-time phase space correlation function in a dilute classical electron gas in equilibrium. The derivation is based on a density expansion of the correlation function and the resummation of the most divergent terms in each order in the density. It is formally analogous to the ring summation used in the kinetic theory of neutral fluids. The kinetic equation obtained is consistent to first order in the plasma parameter and is the generalization of the linearized Balescu-Guersey-Lenard operator to describe spatially inhomogeneous equilibrium fluctuations. The importance of consistently treating static correlations when deriving a kinetic equation for an electron gas is stressed. A systematic derivation as described here is needed for a further generalization to a kinetic equation that includes mode-coupling effects. This will be presented in a future paper.     

Degenerate slightly nonideal Bose gas in a parabolic trap

The correction to the energy and the number of particles in excited oscillator states is found in the approximation of a pair interaction between the particles at close to zero temperature. It is shown that in the case of the traps used in experiments the gas starts to differ appreciably from an ideal gas when more than N=1000 particles are trapped. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 4, 228–231 (25 August 1997)     

A nonideal Bose gas at finite temperatures

The present paper, based on an obvious generalization of the formalism of Belyaev [1,5], supplements the work of Belyaev [2] for the case T 0. The temperature dependence of the quasiparticle excitation and damping spectrum, the ground state energy, and the thermodynamic quantities is determined to second order in the gas-density parameter using the constant amplitude approximation. In the limiting case of free particles, the results are obtained for an ideal gas with T < T₀, where T₀ is the condensation temperature of the ideal Bose gas.In conclusion I wish to thank B. T. Geilikman, under whose supervision this work was performed.     

A nonideal Bose gas at high temperatures

Thermodynamic Green's functions are used to examine the properties of a Bose gas whose particles repel one another, not necessarily weakly, for finite temperatures T > T₀, in which T₀ is the phase-transition point and T/n^2/3 1. The excitation spectrum is deduced, together with the temperature dependence of the renormalized chemical potential and mass of the excitations.     

Collapse of a Bose gas: Kinetic approach

We have analytically explored the temperature dependence of critical number of particles for the collapse of a harmonically trapped attractively interacting Bose gas below the condensation point by introducing a kinetic approach within the Hartree?CFock approximation. The temperature dependence obtained by this easy approach is consistent with that obtained from the scaling theory.     

Study of weakly interacting trapped Bose gas

We have obtained expressions for single particle density and two particle density ofweakly interacting trapped quantum gases. These are valid for all temperature and in anydimension. These expressions have been simplified and expressed in terms ofnon-interacting single particle density. The ground fluctuations for T<T_cin grand canonical ensemble has been treated with care using the method of Kocharovskyet al. [Phys. Rev. A 61, 053606 (2000)]. Some numerical results are presentedin one and three dimension for isotropic harmonically trapped Bose gas with contactinteractions. It is seen that boson density decreases with increasing repulsiveinteractions. The expression for critical temperature is also shown to agree with earlierresult and is in accordance with experiments.     

Critical temperature of a trapped, weakly interacting Bose gas

We report on measurements of the critical temperature of a harmonically trapped, weakly interacting Bose gas as a function of atom number. Our results exclude ideal-gas behavior by more than two standard deviations, and agree quantitatively with mean-field theory. At our level of sensitivity, we find no additional shift due to critical fluctuations. In the course of this measurement, the onset of hydrodynamic expansion in the thermal component has been observed. Our thermometry method takes this feature into account.     

Kinetic equation for a dense soliton gas

We propose a general method to derive kinetic equations for dense soliton gases in physical systems described by integrable nonlinear wave equations. The kinetic equation describes evolution of the spectral distribution function of solitons due to soliton-soliton collisions. Owing to complete integrability of the soliton equations, only pairwise soliton interactions contribute to the solution, and the evolution reduces to a transport of the eigenvalues of the associated spectral problem with the corresponding soliton velocities modified by the collisions. The proposed general procedure of the derivation of the kinetic equation is illustrated by the examples of the Korteweg-de Vries and nonlinear Schr?dinger (NLS) equations. As a simple physical example, we construct an explicit solution for the case of interaction of two cold NLS soliton gases.     

囚禁弱相互作用玻色气体的势场优化准则

根据Thomas-Fermi近似,在基于最小动量态上玻色-爱因斯坦凝聚的前提下,研究了囚禁弱相互作用玻色气体势场的最优化问题.导出了指数吸引势阱中有效势场和粒子数极限判据,粒子数给定时,可由此判据求出所需势场强度;势场强度给定时,可由此判据求出粒子数极限.根据吸引相互作用系统的稳定性以及求出的排斥相互作用的最大粒子数极限,结合有效势场判据,分别给出了囚禁吸引和排斥相互作用玻色气体时,势场强度的最佳取值范围. 关键词： 玻色-爱因斯坦凝聚 弱相互作用 粒子数极限 势场强度     

The Bogoliubov model of weakly imperfect Bose gas

We present a systematic account of known rigorous results about the Bogoliubov model of weakly imperfect Bose gas (WIBG). This model is a basis of the celebrated Bogoliubov theory of superfluidity, although the physical phenomenon is, of course, more complicated than the model. The theory is based on two Bogoliubov's ansätze: the first truncates the full Hamiltonian of the interacting bosons to produce the WIBG, whereas the second substitutes some operators by c-numbers (the Bogoliubov approximation). After some historical remarks, and physical and mathematical motivations of this Bogoliubov treatment of the WIBG, we turn to revision of the Bogoliubov's ansätze from the point of view of rigorous quantum statistical mechanics. Since the exact calculation of the pressure and the behaviour of the Bose condensate in the WIBG are available, we review these results stressing the difference between them and the Bogliubov theory. One of the main features of the mathematical analysis of the WIBG is that it takes into account quantum fluctuations ignored by the second Bogoliubov ansatz. It is these fluctuations which are responsible for indirect attraction between bosons in the fundamental mode. The latter is the origin of a nonconventional Bose condensation in this mode, which has a dynamical nature. A (generalized) conventional Bose–Einstein condensation appears in the WIBG only in the second stage as a result of the standard mechanism of the total particle density saturation. It coexists with the nonconventional condensation. We give also a review of some models related to the WIBG and to the Bogoliubov theory, where a similar two-stage Bose condensation may take place. They indicate possibilities to go beyond the Bogoliubov theory and the Hamiltonian for the WIBG.     

Critical temperature shift in weakly interacting Bose gas

With a high-performance Monte Carlo algorithm we study the interaction-induced shift of the critical point in weakly interacting three-dimensional /psi/(4) theory (which includes quantum Bose gas). In terms of critical density, n(c), mass, m, interaction, U, and temperature, T, this shift is universal: Deltan(c)(T) = -Cm(3)T(2)U, the constant C found to be equal to 0.0140+/-0.0005. For quantum Bose gas with the scattering length a this implies DeltaT(c)/T(c) = C(0)an(1/3), with C(0) = 1.29+/-0.05.     

Dynamical structure factor and spin-density separation for a weakly interacting two-component Bose gas

We show that spin-density separation in a Bose gas is not restricted to 1D but also occurs in higher dimensions. The ratio (alpha) of the intraspecies atom-atom interaction strength to the interspecies interaction strength strongly influences the dynamics of spin-density separation and the elementary excitations. The density wave is phononlike for all values of alpha. For alpha < 1, the spin wave is also phononlike. The spin waves have a quadratic dispersion in the alpha=1 coupling regime, while in the phase separated regime (alpha > 1) the spin waves are found to be damped. The dynamical structure factor reveals two distinct peaks corresponding to the density and spin waves for alpha < or =1. For alpha > 1 there is only one dynamical structure factor peak corresponding to the density wave.     

Superfluidity and Anderson localisation for a weakly interacting Bose gas in a quasiperiodic potential

Using exact diagonalisation and Density Matrix Renormalisation group (DMRG) approach we analyse the transition to a localised state of a weakly interacting quasi-1D Bose gas subjected to a quasiperiodic potential. The analysis is performed by calculating the superfluid fraction, density profile, momentum distribution and visibility for different periodicities of the second lattice and in the presence (or not) of a weak repulsive interaction. It is shown that the transition is sharper towards the maximally incommensurate ratio between the two lattice periodicities, and shifted to higher values of the second lattice strength by weak repulsive interactions. We also relate our results to recent experiments.     

A converging equation of state of a weakly nonideal hydrogen plasma without mystery

A detailed independent derivation of the equation of state of a weakly nonideal hydrogen plasma is presented. The impetus for this work was the demand for high accuracy of the equation of state of the solar plasma in relation to the problems of modern helioseismology, accuracy sufficient for reproducing the velocity of sound on the Sun from optical measurement results with errors not exceeding 10^?4. The existing equations for the second virial coefficient in the expansion of the Helmholtz thermodynamic potential for a system of electrons and protons in powers of the activities of these particles involve certain procedures for the removal of the arising divergences that provoke questions and require independent verification. The suggested equation of state is used to qualitatively estimate the accuracy of various physical and chemical models. The speed of sound and adiabatic exponent calculated along the solar trajectory are presented for a model hydrogen plasma. The calculations were performed with the inclusion of relativistic corrections, electron degeneracy effects, radiation pressure in the plasma, Coulomb interaction in the Debye-Hückel approximation with diffraction and exchange corrections, and converging contributions of bound and scattering states.     

Experimental evidence for the breakdown of a Hartree-Fock approach in a weakly interacting Bose gas

We investigate the physics underlying the presence of a quasicondensate in a nearly one dimensional, weakly interacting trapped atomic Bose gas. We show that a Hartree-Fock (mean-field) approach fails to predict the existence of the quasicondensate in the center of the cloud: the quasicondensate is generated by interaction-induced correlations between atoms and not by a saturation of the excited states. Numerical calculations based on Bogoliubov theory give an estimate of the crossover density in agreement with experimental results.     

弱磁场中弱相互作用玻色气体的热力学性质

运用外势中弱相互作用玻色体系的理论结论,研究弱磁场中弱相互作用玻色气体的高温热力学性质,给出系统总能和热容量的解析式,分析粒子之间的相互作用及磁场对系统热力学性质的影响.研究结果表明,排斥(吸引)对粒子和能量的空间分布有集中(分散)作用,并使得系统的化学势、总能、热容量都增大(减小);加强磁场既可使得粒子和能量的空间分布趋于分散又可削弱相互作用对粒子和能量空间分布的影响.相互作用对各个特征量的影响也有着不同的个性表现.     

Exact phase diagram of the Bogoliubov weakly imperfect Bose gas

We present the exact solution of the Bogoliubov truncated Hamiltonian known as the weakly imperfect Bose gas model. To that end we prove the exactness of the Bogoliubov approximation for this Hamiltonian and we find sufficient and necessary conditions for the interaction potential which ensure a nontrivial phase diagram.