Vidal E J G G, Lima R P A, Lyra M L
Instituto de Física, Universidade Federal de Alagoas, Maceió AL, Brazil.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Jun;83(6 Pt 1):061137. doi: 10.1103/PhysRevE.83.061137. Epub 2011 Jun 23.
In this work, we provide exact solutions for the ideal boson lattice gas on the infinitely ramified star and wheel graphs. Within a tight-binding description, we show that Bose-Einstein condensation (BEC) takes place at a finite temperature after a proper rescaling of the hoping integral ɛ connecting a central site to the peripheral ones. Analytical expressions for the transition temperature, the condensed gas fraction, and the specific heat are given for the star graph as a function of the density of particles n. In particular, the specific heat has a mean-field character, being null in the high-temperature noncondensed phase with a discontinuity at T(c). In the wheel graph, on which the peripheral sites form a closed chain with hopping integral t, BEC takes place only above a critical value of the ratio ɛ/t for which a gap ΔE appears between the ground state and a one-dimensional band. A detailed analysis of the BEC characteristics as a function of n and ΔE is provided. The specific heat in the high-temperature phase of the wheel graph remains finite due to correlations among the peripheral sites.
在这项工作中，我们给出了无限分支星型图和轮型图上理想玻色子晶格气体的精确解。在紧束缚描述下，我们表明在对连接中心位点与周边位点的跳跃积分ɛ进行适当重标度后，玻色 - 爱因斯坦凝聚（BEC）在有限温度下发生。针对星型图，给出了作为粒子密度n的函数的转变温度、凝聚气体分数和比热的解析表达式。特别地，比热具有平均场特征，在高温非凝聚相中为零，在T(c)处有间断。在轮型图中，周边位点形成具有跳跃积分t的闭合链，BEC仅在ɛ/t的临界值之上发生，此时基态与一维能带之间出现能隙ΔE。提供了作为n和ΔE的函数的BEC特性的详细分析。由于周边位点之间的相关性，轮型图高温相中的比热保持有限。
