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     

非相对论弱相互作用玻色气体的有效场理论处理

采用有效场理论研究了非相对论弱相互作用玻色-爱因斯坦凝聚量子气体的一般性质.在分析了系统的不可重整化性质后,从有效拉氏量出发,计算了最低阶环路修正下拉氏量参量的运动耦合常数(running coupling constant)的形式,并且得到了相应的微分方程.研究结果表明,不同于相对论玻色气体的有效理论,对非相对论弱相互作用的玻色气体,可以移除该有效理论中的内禀能量尺度,即可令该有效理论的内禀能量尺度取无穷大值.所得的分析结果将有助于对玻色-爱因斯坦凝聚的临界性质和行为的深入研究.     

BE凝聚临界温度TC的一个普遍表示式

本讨论强简并理想玻色气体发生ＢＥ凝聚的条件，导出了临界温度ＴＣ的一个普遍表示式。     

谐振势阱中旋转广义玻色系统的热力学性质

以非广延Tsallis统计理论为基础,导出了广义玻色-爱因斯坦统计分布表达式,并用其分别讨论了三维和二维谐振势阱约束的旋转广义玻色气体的热力学性质.结合系统粒子数、玻色-爱因斯坦凝聚(BEC)临界温度、基态粒子占据率和比热等物理量的解析表达式,分析了非广延参数和势阱旋转频率等因素对系统热力学性质的影响.     

凝聚玻色气体在临界温度下发生的相变是一种三级相变

给出了一种可发生凝聚的理想玻色气体，处于临界温度下所发生的相变是三级相变的证明方法。     

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).     

从气体吸附率看范德瓦耳斯气体模型的局限性

利用占据数方法和正则系综理论分别求出了费米气体、玻色气体和范德瓦耳斯气体的化学势,比较了这三种气体与理想气体吸附率的差异.指出:费米气体的吸附率高于理想气体,玻色气体则低于理想气体.存在一个临界温度,高于此温度,用范德瓦耳斯气体描述费米气体不如理想气体模型;低于此温度,用范德瓦耳斯气体描述玻色气体不如理想气体模型.     

谐振势阱中有弱相互作用的玻色爱因斯坦凝聚

应用数值计算的方法计算了谐振势阱中有弱相互作用的玻色气体凝聚的临界温度和基态占据库，计算结果表明，二者都随着散射长度的增大而减小；但与理想玻色气体相比仅差约０．４％。     

匀强磁场与简谐势阱中的低维荷电自旋-1玻色气体

采用截断求和法和半经典近似,以二维理想玻色气体为例,研究了磁场和简谐势阱中低维荷电自旋-1玻色子的相变及磁性质.结果表明,电荷-磁场和自旋-磁场作用的竞争导致玻色-爱因斯坦凝聚临界温度随磁场的增大先略微上升后缓慢下降.截断求和法能够有效的改进半经典近似的不足.最后,讨论了磁化强度由抗磁性到顺磁性的转变及自旋因子临界值随磁场和温度的变化.     

玻色-爱因斯坦凝聚临界温度的估算

引进有效数密度的概念，对球谐势阱中理想玻色气体的临界温度作了简便的估算，并以此为例讨论应如何将玻色－爱因斯坦凝聚的研究引入教学，同时还阐述了这种引入的重要意义。     

Kawasaki Dynamics with Two Types of Particles: Stable/Metastable Configurations and Communication Heights

This is the second in a series of three papers in which we study a two-dimensional lattice gas consisting of two types of particles subject to Kawasaki dynamics at low temperature in a large finite box with an open boundary. Each pair of particles occupying neighboring sites has a negative binding energy provided their types are different, while each particle has a positive activation energy that depends on its type. There is no binding energy between particles of the same type. At the boundary of the box particles are created and annihilated in a way that represents the presence of an infinite gas reservoir. We start the dynamics from the empty box and are interested in the transition time to the full box. This transition is triggered by a critical droplet appearing somewhere in the box.     

Kawasaki Dynamics with Two Types of Particles: Critical Droplets

This is the third in a series of three papers in which we study a two-dimensional lattice gas consisting of two types of particles subject to Kawasaki dynamics at low temperature in a large finite box with an open boundary. Each pair of particles occupying neighboring sites has a negative binding energy provided their types are different, while each particle has a positive activation energy that depends on its type. There is no binding energy between particles of the same type. At the boundary of the box particles are created and annihilated in a way that represents the presence of an infinite gas reservoir. We start the dynamics from the empty box and are interested in the transition time to the full box. This transition is triggered by a critical droplet appearing somewhere in the box. In the first paper we identified the parameter range for which the system is metastable, showed that the first entrance distribution on the set of critical droplets is uniform, computed the expected transition time up to and including a multiplicative factor of order one, and proved that the nucleation time divided by its expectation is exponentially distributed, all in the limit of low temperature. These results were proved under three hypotheses, and involved three model-dependent quantities: the energy, the shape and the number of critical droplets. In the second paper we proved the first and the second hypothesis and identified the energy of critical droplets. In the third paper we prove the third hypothesis and identify the shape and the number of critical droplets, thereby completing our analysis. Both the second and the third paper deal with understanding the geometric properties of subcritical, critical and supercritical droplets, which are crucial in determining the metastable behavior of the system, as explained in the first paper. The geometry turns out to be considerably more complex than for Kawasaki dynamics with one type of particle, for which an extensive literature exists. The main motivation behind our work is to understand metastability of multi-type particle systems.     

Critical Temperature of Deconfinement in a Constrained Space Using a Bag Model at Vanishing Baryon Density

The geometry of fireballs in relativistic heavy ion collisions is approximated by a static box, which is infinite in two directions while finite in the other direction. The critical temperature of deconfinement phase transition is calculated explicitly in the MIT bag model at vanishing baryon density. It is found that the critical temperature shifts to a value higher than that in an unconstrained space.     

The Boundary Condition in the Classical Derivation of the BBR

The classical derivation of the black body radiation (BBR) spectrum by Boyer was based on an equilibrium mechanism such that in the absence of thermal radiation particles in a container can gain kinetic energy from the random electromagnetic zero point field (ZPF) radiation. Their loss of that energy was to be by means of their collisions with the walls of the container. Theoretically, energy dissipation through collisions with the walls might lead to a divergent kinetic energy value for the particles. This is because the box can be taken large enough to minimize the collisions probability, and that can lead to a particle’s indefinite growth in energy. Furthermore, a derivation of a general phenomenon such as the BBR should be possible without relying on the walls boundary of a box. Therefore, a new boundary condition is proposed here which is related to relativistic effects. It is shown that with the new boundary condition one may still recover the BBR spectrum. A discussion is presented that shows how the new boundary condition is indeed responsible for energy dissipations.     

Relativistic particle in a three-dimensional box

We generalize the work of Alberto, Fiolhais and Gil and solve the problem of a Dirac particle confined in a 3-dimensional box. The non-relativistic and ultra-relativistic limits are considered and it is shown that the size of the box determines how relativistic the low-lying states are. The consequences for the density of states of a relativistic fermion gas are briefly discussed.     

Gibbs ensembles in relativistic classical and quantum mechanics

Classical and quantum Gibbs ensembles are constructed for equilibrium statistical mechanics in the framework of an extension to many-body theory of a relativistic mechanics proposed by Stueckelberg. In addition to the usual chemical potential in the grand canonical ensemble, there is a new potential corresponding to the mass degree of freedom of relativistic systems. It is shown that in the nonrelativistic limit the relativistic ensembles we have obtained reduce to the usual ones, and mass fluctuations for the free-particle gas approach the fluctuations in N. The ultrarelativistic limit of the canonical ensemble for the free-particle gas differs from the corresponding limit of the ensemble proposed by Jüttner and Pauli. Due to the mass degree of freedom, the quantum counting of states is different from that of the nonrelativistic theory. If the mass distribution is sufficiently sharp, the thermodynamical effects of this multiplicity will not be large. There may, however, be detectable effects such as a shift in the Fermi level and the critical temperature for Bose-Einstein condensation, and some change in specific heats.     

Surface properties of an ideal relativistic Bose gas with pair production

The surface properties of an ideal relativistic charged Bose gas are calculated analytically in three dimensions. The surface specific heat is found to have a discontinuity at the bulk critical temperature in contrast with the logarithmic divergence found in the usual nonrelativistic case. Various special cases including that of a photon gas are discussed.     

Condensation of N interacting bosons: a hybrid approach to condensate fluctuations

We present a new method of calculating the distribution function and fluctuations for a Bose-Einstein condensate (BEC) of N interacting atoms. The present formulation combines our previous master equation and canonical ensemble quasiparticle techniques. It is applicable both for ideal and interacting Bogoliubov BEC and yields remarkable accuracy at all temperatures. For the interacting gas of 200 bosons in a box we plot the temperature dependence of the first four central moments of the condensate particle number and compare the results with the ideal gas. For the interacting mesoscopic BEC, as with the ideal gas, we find a smooth transition for the condensate particle number as we pass through the critical temperature.     

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.     

Towards a realistic equation of state of strongly interacting matter

We consider a relativistic strongly interacting Bose gas. The interaction is manifested in the off-shellness of the equilibrium distribution. The equation of state that we obtain for such a gas has the properties of a realistic equation of state of strongly interacting matter, i.e., at low temperature it agrees with the one suggested by Shuryak for hadronic matter, while at high temperature it represents the equation of state of an ideal ultrarelativistic Stefan-Boltzmann gas, implying a phase transition to an effectively weakly interacting phase.