Finite temperature scaling theory for the collapse of Bose-Einstein condensate

We show how to apply the scaling theory in an inhomogeneous system like harmonically trapped Bose condensate at finite temperature. We calculate the temperature dependence of the critical number of particles by a scaling theory within the Hartree-Fock approximation and find that there is a dramatic increase in the critical number of particles as the condensation point is approached.     

Bose-Einstein condensation and thermodynamic functions of 4He film

A monolayer of ⁴He atoms is treated as a system of hard-sphere bosons in a thin film geometry, with a finite thickness. The method of pseudopotential is used to calculate first the energy spectrum, and then the Helmholtz free energy and other thermodynamic functions of the system. It is found that Bose-Einstein condensation exists below a definite temperature. Much like a liquid-gas transition, the boson system displays a high temperature normal phase, a low temperature condensed superfluid phase and coexistence region. In the present treatment, the minimum momentum associated with the finite thickness of monolayer is used as a parameter. We find that the transition temperature is linearly proportional to the density of the ⁴He film. After performing double-tangent construction of the Helmholtz free energy curve we find for the specific heat a rounded peak at the transition temperature, in agreement with recent experiments. The ratio of the superfluid density at the transition point to the transition temperature is found to be essentially a constant.     

On the chiral transition temperature in bilocal effective QCD

The breakdown of chiral symmetry in a many-quark system at finite temperature is studied by considering a bilocal quark interaction derived from a field theoretical treatment of QCD. We find that such an approach yields a chiral transition temperature which is about 30% lower compared to the standard NJL model prediction.     

Explosive condensation in a mass transport model

We study a far-from-equilibrium system of interacting particles, hopping between sites of a 1D lattice with a rate which increases with the number of particles at interacting sites. We find that clusters of particles, which initially spontaneously form in the system, begin to move at increasing speed as they gain particles. Ultimately, they produce a moving condensate which comprises a finite fraction of the mass in the system. We show that, in contrast with previously studied models of condensation, the relaxation time to steady state decreases as an inverse power of lnL with system size L and that condensation is instantaneous for L→∞.     

Lattice bosons in a quasi-disordered environment

In this paper, we study non-interacting bosons in a quasi-disordered one-dimensional optical lattice in a harmonic potential. We consider the case of deterministic quasi-disorder produced by an Aubry–André potential. Using exact diagonalization, we investigate both the zero temperature and the finite temperature properties. We investigate the localization properties by using an entanglement measure. We find that the extreme sensitivity of the localization properties to the number of lattice sites in finite size closed chains disappear in open chains. This feature continues to be present in the presence of a harmonic confining potential. The quasi-disorder is found to strongly reduce the Bose–Einstein condensation temperature and the condensate fraction in open chains. The low temperature thermal depletion rate of the condensate fraction increases considerably with increasing quasi-disorder strength. We also find that the critical quasi-disorder strength required for localization increases with increasing strength of the harmonic potential. Further, we find that the low temperature condensate fraction undergoes a sharp drop to 0.5 in the localization transition region. The temperature dependence of the specific heat is found to be only marginally affected by the quasi-disorder.     

Bose-Einstein condensation and Casimir effect of trapped ideal Bose gas in between two slabs

We study the Bose-Einstein condensation for a 3-d system of ideal Bose gas which is harmonically trapped along two perpendicular directions and is confined in between two slabs along the other perpendicular direction. We calculate the Casimir force between the two slabs for this system of trapped Bose gas. At finite temperatures this force for thermalized photons in between two plates has a classical expression which is independent of ħ. At finite temperatures the Casimir force for our system depends on ħ. For the calculation of Casimir force we consider only the Dirichlet boundary condition. We show that below condensation temperature (T_c) the Casimir force for this non-interacting system decreases with temperature (T) and at , it is independent of temperature. We also discuss the Casimir effect on 3-d highly anisotropic harmonically trapped ideal Bose gas.     

Self-gravitating bosons at nonzero temperature

A system of charged bosons at finite temperature and chemical potential is studied in a general-relativistic framework. We assume that the boson fields interact only gravitationally. At sufficiently low temperature the system exists in two phases: the gas and the condensate. By studying the condensation process numerically we determine the critical temperature T_c at which the condensate emerges. As the temperature decreases, the system eventually settles down in the ground state of a cold boson star.     

Pion condensation in symmetric nuclear matter

Using a model which is based essentially on the chiral SU(2)×SU(2) symmetry of the pion-nucleon interaction, we examine the possibility of pion condensation in symmetric nucleon matter. We find that the pion condensation is not likely to occur in symmetric nuclear matter for any finite value of the nuclear density. Consequently, no critical opalescence phenomenom is expected to be seen in the pion-nucleus interaction.     

Bose-Einstein condensation in spin-polarized atomic hydrogen: A new superfluid

We find that in the spin-polarized hydrogen, Bose condensation occurs for certain quantized values of the magnetic field. Once the field is fixed, sweeping of the radio-frequency results in nuclear magnetic resonance so that condensation and NMR occur simultaneously. We have found that nuclear self-induced transparency occurs. A new excitation designated by the present author as superboojum, which is a discontinuity in the hydrodynamic equations in spin-polarized hydrogen having finite nuclear as well as electronic spin is discovered.     

Polariton condensation with localized excitons and propagating photons

We estimate the condensation temperature for microcavity polaritons, allowing for their internal structure. We consider polaritons formed from localized excitons in a planar microcavity, using a generalized Dicke model. At low densities, we find a condensation temperature T(c) proportional, rho, as expected for a gas of structureless polaritons. However, as T(c) becomes of the order of the Rabi splitting, the structure of the polaritons becomes relevant, and the condensation temperature is that of a BCS-like mean-field theory. We also calculate the excitation spectrum, which is related to observable quantities such as the luminescence and absorption spectra.     

Chiral Phase Transition at Finite Isospin Density in Linear Sigma Model

Using the linear sigma model, we have introduced the pion isospin chemical potential. The chiral phase transition is studied at finite temperatures and finite isospin densities. We have studied the μ-T phase diagram for the chiral phase transition and found the transition cannot happen below a certain low temperature because of the Bose-Einstein condensation in this system. Above that temperature, the chiral phase transition is studied by the isotherms of pressure versus density. We indicate that the transition, in the chiral limit, is a first-order transition from a low-density phase to a high-density phase like a gas-liquid phase transition.     

Spin-spin correlations in ferromagnetic nanosystems

Using exact diagonalization, Monte-Carlo, and mean-field techniques, characteristic temperature scales for ferromagnetic order are discussed for the Ising and the classical anisotropic Heisenberg model on finite lattices in one and two dimensions. The interplay between nearest-neighbor exchange, anisotropy and the presence of surfaces leads, as a function of temperature, to a complex behavior of the distance-dependent spin-spin correlation function, which is very different from what is commonly expected. A finite experimental observation time is considered in addition, which is simulated within the Monte-Carlo approach by an incomplete statistical average. We find strong surface effects for small nanoparticles, which cannot be explained within a simple Landau or mean-field concept and which give rise to characteristic trends of the spin-correlation function in different temperature regimes. Unambiguous definitions of crossover temperatures for finite systems and an effective method to estimate the critical temperature of corresponding infinite systems are given.     

The Stability of the Relativistic Three-Body System and In-Medium Equations

We present a relativistic three-body equation to study the stability of the isolated three-body system and the correlations in a medium of finite temperatures and densities. Relativity is implemented utilizing the light-front form. Using a zero-range force we find the relativistic analog of the Thomas collapse and investigate the possibility that the nucleon exists as a Borromean system. Within a systematic Dyson equation approach we calculate the three-body Mott transition and the critical temperature of the color-superconducting phase.     

The phase behaviour of a fluid in a slitlike pore with permeable walls

The confinement of a lattice fluid in a set of slitlike pores separated by semipermeable walls with a finite width has been studied. The walls are modelled by a square-well repulsive potential with a finite height. The thermodynamic properties and the phase behaviour of the system are evaluated by means of Monte Carlo simulations. For some states theoretical calculations have been made using a mean-field-type theory. These investigations confirm previous findings for confined Lennard-Jones fluids, obtained from a density functional approach. For intermediate and low potential barriers that separate the pores, the isotherms exhibit two hysteresis loops and the liquid-vapour coexistence curve divides into two branches describing condensation inside the pore and inside the permeable wall. These two branches are separated by a triple point. At temperatures lower than the triple point temperature, the condensation takes place instantaneously in both the pore and inside the permeable wall. It was found that when the temperature is scaled by the bulk critical temperature, the phase diagram emerging from this simple mean-field treatment is close to the phase diagram obtained from simulation.     

三维简谐势阱中玻色-爱因斯坦凝聚的边界效应

在定义特征长度的基础上,应用Euler–MacLaurin公式,研究了理想玻色气体在三维简谐势阱中玻色-爱因斯坦凝聚的边界效应.结果表明:粒子的凝聚分数由于有限尺度和有限粒子数效应而减小,修正的凝聚分数和凝聚温度由于边界效应存在一个极大值,选择优化的最佳势阱参数,可以有效提高凝聚分数和凝聚温度;热容量的跃变存在边界效应和粒子数效应,选择合理的势阱参数时,热容量的跃变存在一个极小值.导出了简谐势阱中有限理想玻色气体的状态方程,揭示了压强的各向异性(或各向同性)取决于简谐势频率的各向异性(或各向同性).     

The Gaussian approximation for interacting charged scalar fields

The Gaussian effective-potential approach is used to explore the physics of charged theory in four space-time dimensions. We find and employ an appropriate trial system, parametrized by two effective masses, for obtaining an adequate Gaussian effective potential under conditions of the global U(1) symmetry and the finite temperature. A simple renormalization, accompanied by an explicit dimensional regularization, is employed. We find that the nontrivial approach arises from a bare coupling constant of a negative infinitesimal form, well known in the noncharged case as “precarious”. The behavior of this solution is discussed, and the symmetry breaking due to background charge density is discovered. Received: 11 January 1999 / Published online: 14 October 1999     

Bose–Einstein condensation in the three-sphere and in the infinite slab: Analytical results

We study the finite size effects on Bose–Einstein condensation (BEC) of an ideal non-relativistic Bose gas in the three-sphere (spatial section of the Einstein universe) and in a partially finite box which is infinite in two of the spatial directions (infinite slab). Using the framework of grand-canonical statistics, we consider the number of particles, the condensate fraction and the specific heat. After obtaining asymptotic expansions for large system size, which are valid throughout the BEC regime, we describe analytically how the thermodynamic limit behaviour is approached. In particular, in the critical region of the BEC transition, we express the chemical potential and the specific heat as simple explicit functions of the temperature, highlighting the effects of finite size. These effects are seen to be different for the two different geometries. We also consider the Bose gas in a one-dimensional box, a system which does not possess BEC in the sense of a phase transition even in the infinite volume limit.     

Fluctuational signals for pion Bose-Einstein condensation

We consider the Bose-Einstein condensation (BEC) in a relativistic pion gas. At high collision energy, in the samples of events with a fixed number of all pions, N, the pion system may approach the conditions of the BEC. An anomalous increase of the scaled variances of neutral and charged pion number fluctuations then appears. The size of this increase is restricted by the finite size of the pion system which should increase with the collision energy.     

Exact and approximate results of non-extensive quantum statistics

We develop an analytical technique to derive explicit forms of thermodynamical quantities within the asymptotic approach to non-extensive quantum distribution functions. Using it, we find an expression for the number of particles in a boson system which we compare with other approximate scheme (i.e. factorization approach), and with the recently obtained exact result. To do this, we investigate the predictions on Bose-Einstein condensation and the blackbody radiation. We find that both approximation techniques give results similar to (up to ) the exact ones, making them a useful tool for computations. Because of the simplicity of the factorization approach formulae, it appears that this is the easiest way to handle with physical systems which might exhibit slight deviations from extensivity. Received 19 August 1999 and Received in final form 1 November 1999