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.     

Bose-Einstein condensation in the relativistic ideal Bose gas

The Bose-Einstein condensation (BEC) critical temperature in a relativistic ideal Bose gas of identical bosons, with and without the antibosons expected to be pair-produced abundantly at sufficiently hot temperatures, is exactly calculated for all boson number densities, all boson point rest masses, and all temperatures. The Helmholtz free energy at the critical BEC temperature is lower with antibosons, thus implying that omitting antibosons always leads to the computation of a metastable state.     

Bose-Einstein condensation of the magnetized ideal Bose gas

We study the charged non-relativistic Bose gas interacting with a constant magnetic field but which is otherwise free. The notion of Bose-Einstein condensation for the three-dimensional case is clarified, and we show that although there is no condensation in the sense of a phase transition, there is still a maximum in the specific heat which can be used to define a critical temperature. Although the absence of a phase transition persists for all values of the magnetic field, we show how as the magnetic field is reduced the curves for the specific heat approach the free field curve. For large values of the magnetic field we show that the gas undergoes a “dimensional reduction” and behaves effectively as a one-dimensional gas except at very high temperatures. These general features persist for other spatial dimensions D and we show results for D = 5. Finally we examine the magnetization and the Meissner-Ochsenfeld effect.     

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…     

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).     

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.     

Theory of adiabatic variation of critical temperature of the Bose-Einstein condensation of an ideal gas in optical lattice

We calculate the critical temperature of the Bose-Einstein condensation of an ideal Bosegas in the presence of an external periodic potential in one, two, or three directions. A number of assumed approximations enables us to show that the only parameter determining the critical temperature of condensation is the width of the lower energy band with the direct proportionality to the one-third power of this width for each direction of periodicity of the external potential. This also proves the result, obtained earlier by means of numerical calculation, that deepening of the periodic potential (which is known to lead to narrowing of energy bands) leads to lowering of the critical temperature. The fundamental role of quantum tunneling in establishing this regularity is emphasized.     

Bose-Einstein condensation of 87Rb in a levitated crossed dipole trap

We report an apparatus and method capable of producing Bose-Einstein condensates (BECs) of ～1 × 10^{6 87}Rb atoms, and ultimately designed for sympathetic cooling of ¹³³Cs and the creation of ultracold RbCs molecules. The method combines several elements: (i) the large recapture of a magnetic quadrupole trap from a magneto-optical trap; (ii) efficient forced RF evaporation in such a magnetic trap; (iii) the gain in phase-space density obtained when loading the magnetically trapped atoms into a far red-detuned optical dipole trap, and (iv) efficient evaporation to BEC within the dipole trap. We demonstrate that the system is capable of sympathetically cooling the |F = 1, m _F = ?1〉 and |1,0? sublevels with |1, +1〉 atoms. Finally we discuss the applicability of the method to sympathetic cooling of ¹³³Cs with ⁸⁷Rb.     

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.     

简谐势阱中非理想气体玻色-爱因斯坦凝聚转变温度的数值研究

用数值计算的方法研究了简谐势阱中非理想气体的玻色 爱因斯坦凝聚情况.通过计算能级的分布，用图形的方式给出了考虑相互作用时，简谐势阱中体系转变温度相对无相互作用体系转变温度的变化趋势 对于存在排斥作用的体系，转变温度升高；对于存在吸引作用的体系，转变温度降低. 关键词： 玻色－爱因斯坦凝聚 相互作用 能级 转变温度     

The ideal Bose-Einstein gas,revisited

Some questions concerning the ideal Bose-Einstein gas are reviewed and examined further. The bulk behavior including the condensation phenomenon is characterized by the thermodynamical properties, occupations of the states and their fluctuations, and the properties of the density matrices, including the diagonal and off-diagonal long range orders. Particular attention is focused on the difference between the canonical and grand canonical ensembles and a case is made that the latter does not represent any physical system in the condensed region. The properties in a finite region are also examined to study the approach to the bulk limit and secondly to derived the surface properties such as the surface tension (due to the boundary). This is mainly done for the special case of a rectangular parallelopiped (box) for various boundary conditions. The question of the asymptotic behavior of the fluctuations in the occupation of the ground state in the condensed region in the canonical ensemble is examined for these systems. Finally, the local properties near the wall of a half infinite system are calculated and discussed. The surface properties also follow this way and agree with the strictly thermodynamic result. Although it is not intended to be a complete review, it is largely self-contained, with the first section containing the basic formulas and a discussion of some general concepts which will be needed. Especially discussed in detail are the extra considerations that are needed in thermodynamics and statistical mechanics to include the surface properties, and the quantum hierarchy of the density matrices and local conservation laws. In the concluding remarks several problems are mentioned which need further analysis and clarification.     

三维非谐势阱中玻色－爱因斯坦凝聚的数值计算

本文从G－P平均势场理论出发,探讨了三维球对称非谐势阱中玻色－爱因斯坦凝聚(BEC)的G－P方程;用数值计算方法研究了三维球对称非谐势阱中原子间有相互作用的玻色－爱因斯坦凝聚气体的基态解;分析了非谐振势能项对玻色－爱因斯坦凝聚体的分布、能量和化学势的影响。     

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)     

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.     

The condensation of ideal Bose gas in a gravitational field

Bose–Einstein condensation of two- and three-dimensional boson gases confined in the one-dimensional gravitational field is investigated. Using the semiclassical approximation method, the expressions for the BEC transition temperature, condensate fraction, heat capacity and the entropy of the system are obtained. The heat capacities of the systems with D  =1, 2, 3 (D$D$ is the dimension) at the critical temperature are discussed. We find that for the 1-D and 2-D boson systems, the heat capacities are continuous, but for the 3-D case there is a gap at the critical temperature T_c$T_c$. The entropies of the systems with D=1, 2, 3 are also studied in detail. It is found that the entropies increase with the increasing of the temperature T.     

Bose-Einstein condensation in a cavity

The effect of the physically correct boundary conditions and the nonvanishing ground state energy on Bose-Einstein condensation of quantum particles confined to a cubic volumeV=L ³ is evaluated. The transition point is shifted towards higher temperatures by the confinement, the specific heat below the onset of condensation is no longer proportional toT ^3/2, and the pressure does depend on the volume. Precise expressions for the modification of the ground state population and for the shift of the condensation temperature are derived, together with an expansion of the internal energy and of the specific heat. Numerical computations confirm the accuracy of our analytical approximations.Dedicated to Herbert Wagner, whose work on quantum Fermi liquids proved to be also very stimulating for quantum Bose liquids.