Bose-Einstein condensation in interacting gases

We study the occurrence of a Bose-Einstein transition in a dilute gas with repulsive interactions, starting from temperatures above the transition temperature. The formalism, based on the use of Ursell operators, allows us to evaluate the one-particle density operator with more flexibility than in mean-field theories, since it does not necessarily coincide with that of an ideal gas with adjustable parameters (chemical potential, etc.). In a first step, a simple approximation is used (Ursell-Dyson approximation), which allow us to recover results which are similar to those of the usual mean-field theories. In a second step, a more precise treatment of the correlations and velocity dependence of the populations in the system is elaborated. This introduces new physical effects, such as a change of the velocity profile just above the transition: the proportion of atoms with low velocities is higher than in an ideal gas. A consequence of this distortion is an increase of the critical temperature (at constant density) of the Bose gas, in agreement with those of recent path integral Monte-Carlo calculations for hard spheres. Received 13 November 1998     

Bose-Einstein condensation quantum kinetics for a gas of interacting excitons

A quantum kinetics of the Bose-Einstein condensation in the self-consistent (s.c.) Hartree-Fock-Bogoliubov (HFB) model of the interacting Bose gas is formulated and numerically solved for the example of excitons scattering with a thermal bath of acoustic phonons. The theory describes the condensation in real time starting from a nonequilibrium initial state towards the equilibrium HFB solution. The s.c. changes of the spectrum are automatically incorporated in the scattering terms.     

Difference in Bose-Einstein condensation of conserved and unconserved particles

The peculiarities in the Bose-Einstein condensation of particles and quasiparticles are discussed. The difference between the condensation of conserved and unconserved particles is analyzed. A classification of quasiparticles is given. The emphasis is made on the ability of particles and quasiparticles to condense. Illustrations include: general Bose-condensed atomic systems, such as ensembles of trapped atoms, Bose gases with conserved and unconserved number of atoms, vibrating atoms in double-well lattices, Holstein-Primakoff magnons, Schwinger bosons, slave bosons, and the condensation of singletons and triplons. The basic difference is that the system of particles, whose total number is conserved, can form equilibrium as well as nonequilibrium condensates, while unconserved particles can condense only in a nonequilibrium system subject to external pumping supporting the density of these particles sufficient for their condensation. The examples of such a nonequilibrium condensation of unconserved particles are the Bose-Einstein condensation of excitons, polaritons, and photons. Elementary collective excitations, such as bogolons and phonons, being self-consistently defined, do not condense. Magnons cannot condense in equilibrium systems. Controversies, existing in literature with regard to the Bose-Einstein condensation of some quasiparticles, are explained. Pushing a system out of equilibrium may favor the condensation of unconserved quasiparticles, but suppresses the condensate fraction of conserved particles.     

2 + 1 dimensional gravity as an exactly soluble system

By disentangling the hamiltonian constraint equations, 2 + 1 dimensional gravity (with or without a cosmological constant) is shown to be exactly soluble at the classical and quantum levels. Indeed, it is closely related to Yang-Mills theory with purely the Chern-Simons action, which recently has turned out to define a soluble quantum field theory. 2 + 1 dimensional gravity has a straightforward renormalized perturbation expansion, with vanishing beta function. 2 + 1 dimensional quantum gravity may provide a testing ground for understanding the role of classical singularities in quantum mechanics, may be related to the discrete series of Virasoro representations in 1 + 1 dimensions, and may be a useful tool in studying three-dimensional geometry.     

Quasi-spin projection in an exactly soluble model

An exactly soluble model for the study of projection techniques within the framework of the Hartree-Fock theory is presented. Properties of the exact solutions are analyzed and projections, both before and after variation, are discussed.     

Bose-Einstein condensation with an entangled order parameter

We propose a practically accessible non-mean-field ground state of Bose-Einstein condensation, which occurs in an interspecies two-particle entangled state, and is thus described by an entangled order parameter. A suitably defined entanglement entropy is used as the characterization of the non-mean-field nature, and is found to persist in a wide parameter regime. The interspecies entanglement leads to novel interference terms in the dynamical equations governing the single-particle orbital wave function. Experimental feasibility and several methods of probe are discussed. We urge the study of multichannel scattering between different species of atoms.     

Critical temperature of Bose-Einstein condensation for weakly interacting bose gas in a potential trap

It has been a long history to study Bose-Einstein condensation (BEC) of weakly in-teracting Bose gas, and several theoretical models have been developed to research uni-form and weakly interacting Bose gas. Ref. [1] summarized all of these models and the corresponding results, which gave a derivation of critical temperature from ideal case 1/30Tc c n,?T = α (1) with a wide spread of parameter c from 0.7 to 2.33, where α is the scattering length of s wave and n is atom number density. Due…     

Ionic criticality: an exactly soluble model

Gas-liquid criticality in ionic fluids is studied in exactly soluble spherical models that use interlaced sublattices to represent hard-core multicomponent systems. Short-range attractions in the uncharged fluid drive criticality, but charged ions do not alter the universality class. Debye screening remains exponential at criticality in fully ion-symmetric 1:1 models. However, ionic asymmetry couples charge and density fluctuations in a direct manner: The charge correlation length then diverges precisely as the density correlation length and the Stillinger-Lovett rule is violated at criticality.     

势场中玻色-爱因斯坦凝聚的临界温度

给出了不同于文献的势场中玻色-爱因斯坦凝聚临界温度表达式.结果揭示了势场中理想玻色子气体凝聚的临界温度与势场之间的关系，表明势场中临界温度正比于无势场情况下临界温度T０ｃ，还给出了势场的有效性判据.势场的有效性是势场与玻尔兹曼常数k和无势场情况下临界温度Ｔ０ｃ乘积ｋＴ０ｃ的比较.当势场接近或大于ｋＴ０c时，临界温度会有效增加;当势场远小于ｋＴ０c时, 势场是无效的. 关键词： 玻色-爱因斯坦凝聚 临界温度 势阱     

On the Bose-Einstein condensation of an ideal gas

A mathematically precise treatment is given of the well-known Bose-Einstein condensation of an ideal gas in the grand canonical ensemble at fixed density. The method works equally well for any of the standard boundary conditions and it is shown that the finite volume activity converges and that in three dimensions condensation occurs for Dirichlet, Neumann, periodic, and repulsive walls.     

Anomalous dephasing of bosonic excitons interacting with phonons in the vicinity of the Bose-Einstein condensation

The dephasing and relaxation kinetics of bosonic excitons interacting with a thermal bath of acoustic phonons is studied after coherent pulse excitation. The kinetics of the induced excitonic polarization is calculated within Markovian equations both for subcritical and supercritical excitation with respect to a Bose-Einstein condensation (BEC). For excited densities n below the critical density , an exponential polarization decay is obtained, which is characterized by a dephasing rate . This dephasing rate due to phonon scattering shows a pronounced exciton-density dependence in the vicinity of the phase transition. It is well described by the power law that can be understood by linearization of the equations around the equilibrium solution. Above the critical density we get a non-exponential relaxation to the final condensate value p⁰ with that holds for all densities. Furthermore we include the full self-consistent Hartree-Fock-Bogoliubov (HFB) terms due to the exciton-exciton interaction and the kinetics of the anomalous functions . The collision terms are analyzed and an approximation is used which is consistent with the existence of BEC. The inclusion of the coherent exciton-exciton interaction does not change the dephasing laws. The anomalous function F_k exhibits a clear threshold behaviour at the critical density. Received 13 December 1999     

Probing anomalous longitudinal fluctuations of the interacting Bose gas via Bose-Einstein condensation of magnons

The emergence of a finite staggered magnetization in quantum Heisenberg antiferromagnets subject to a uniform magnetic field can be viewed as Bose-Einstein condensation of magnons. Using nonperturbative results for the infrared behavior of the interacting Bose gas, we present exact results for the staggered spin-spin correlation functions of quantum antiferromagnets in a magnetic field at zero temperature. In particular, we show that in dimensions 1相似文献   

Theory of quasimagnetic impurity in a metal: An exactly soluble model of interacting electrons

We study an impurity atom, on which two-body forces are important, dissolved in a metal, where they are negligible. With the aid of the well-known boson excitation spectrum of the electronic Fermi sea, we predict the low-energy effects of one- and two-body potentials on the impurity, in the nonmagnetic regime. We obtain for the first time exact expressions for the cutoff independent contributions to the specific heat and paramagnetic susceptibility, the spectral amplitudes or one-electron density of states on the impurity, and the scattering cross-section. The entire spectrum of manybody eigenstates is explicitly obtained. The onset of a local magnetic moment appears as a sudden breakdown of the model Hamiltonian, and occurs when the two-body potential exceeds a critical value U_c which is O(E_F) in magnitude. A study of the renormalization of the interaction parameters terminates the paper.     

Phase transitions in an exactly soluble one-dimensional exclusion process

We consider an exclusion process with particles injected with rate at the origin and removed with rate at the right boundary of a one-dimensional chain of sites. The particles are allowed to hop onto unoccupied sites, to the right only. For the special case of = = 1 the model was solved previously by Derridaet al. Here we extend the solution to general , . The phase diagram obtained from our exact solution differs from the one predicted by the mean-field approximation.     

Bose-Einstein condensation of chromium

We report on the generation of a Bose-Einstein condensate in a gas of chromium atoms, which have an exceptionally large magnetic dipole moment and therefore underlie anisotropic long-range interactions. The preparation of the chromium condensate requires novel cooling strategies that are adapted to its special electronic and magnetic properties. The final step to reach quantum degeneracy is forced evaporative cooling of 52Cr atoms within a crossed optical dipole trap. At a critical temperature of T(c) approximately 700 nK, we observe Bose-Einstein condensation by the appearance of a two-component velocity distribution. We are able to produce almost pure condensates with more than 50,000 condensed 52Cr atoms.     

Bose-Einstein condensation of an ideal gas in a parabolic trap

The temperature-dependent velocity distribution function is found for the case of Bose-Einstein condensation of a finite number of noninteracting atoms trapped in a three-dimensional anisotropic parabolic trap. It is shown that at a temperature T of the order of the condensation temperature T ₀ the velocity distribution consists of an anisotropic part, reflecting the population of the ground state, and an isotropic part above the condensate. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 8, 559–563 (25 October 1997)     

Crossover temperature of Bose-Einstein condensation in an atomic Fermi gas

We show that in an atomic Fermi gas near a Feshbach resonance the crossover between a Bose-Einstein condensate of diatomic molecules and a Bose-Einstein condensate of Cooper pairs occurs at positive detuning, i.e., when the molecular energy level lies in the two-atom continuum. We determine the crossover temperature as a function of the applied magnetic field and find excellent agreement with the experiment of C. A. Regal et al. [Phys. Rev. Lett. 92, 040403 (2004)]] who has recently observed this crossover temperature.     

Dynamics of an interacting Bose-Einstein condensate in a three-well potential

We study the dynamics of an ultracold interacting Bose-Einstein gas confined in a one-dimensional potential composed of three symmetrical wells. We numerically solve the time-dependent Schrödinger equation of the N-particle Hamiltonian for N = 50, 150, 500, 1000. We demonstrate that the quantum phase transition from a superfluid (SF) to a Mott insulator (MI) phase in the three-well potential depends on the strength of the interactions among the particles, the total number of particles, and the confining potential in which the particles move. We discuss the appearance of population revivals as a function of time and find that, even in the case when the interaction strength among the particles is very small, its effect has the consequence that the system never returns to the initial condition. A stationary state for long times is observed in the SF phase, while the particle population in each well remains almost equal to the initial condition in the MI phase.