标题： 广义排斥统计的热力学性质 显示英文标题

标题： Thermodynamic Properties of Generalized Exclusion Statistics

摘要： 我们解析计算了服从广义排除统计的理想$g$-on 气体的一些热力学量。 我们表明，在粒子数守恒的情况下，$g$-on 气体（$g \neq 0$）的比热在任何维度下随着$T \to 0$线性消失，并表现出一种有趣的对偶对称性，该对称性将低温度下的粒子统计与$g$处的粒子统计与$1/g$处的空穴统计联系起来。 我们推导出簇系数$b_l(g)$作为哈德纳统计相互作用$g$在$D$维度中的完整解。 我们还发现，团簇系数$b_l(g)$和virial系数$a_l(g)$关于$g=1/2$完全镜像对称（$l$=奇）或反对称（$l$=偶）。 在二维情况下，我们完全确定了广义排除统计的团簇和virial系数的闭合形式，这些结果与线性能量的anyon气体的virial系数完全一致。 我们表明，具有零化学势的$g$-on 气体表现出与光子统计相似的热力学性质。 我们讨论了我们的结果的一些物理意义。 显示英文摘要

摘要： We analytically calculate some thermodynamic quantities of an ideal $g$-on gas obeying generalized exclusion statistics. We show that the specific heat of a $g$-on gas ($g \neq 0$) vanishes linearly in any dimension as $T \to 0$ when the particle number is conserved and exhibits an interesting dual symmetry that relates the particle-statistics at $g$ to the hole-statistics at $1/g$ at low temperatures. We derive the complete solution for the cluster coefficients $b_l(g)$ as a function of Haldane's statistical interaction $g$ in $D$ dimensions. We also find that the cluster coefficients $b_l(g)$ and the virial coefficients $a_l(g)$ are exactly mirror symmetric ($l$=odd) or antisymmetric ($l$=even) about $g=1/2$. In two dimensions, we completely determine the closed forms about the cluster and the virial coefficients of the generalized exclusion statistics, which exactly agree with the virial coefficients of an anyon gas of linear energies. We show that the $g$-on gas with zero chemical potential shows thermodynamic properties similar to the photon statistics. We discuss some physical implications of our results.