Potter Geoffrey G, Müller Gerhard, Karbach Michael
Department of Physics, University of Rhode Island, Kingston, Rhode Island 02881, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2007 Jun;75(6 Pt 1):061120. doi: 10.1103/PhysRevE.75.061120. Epub 2007 Jun 21.
We present exact and explicit results for the thermodynamic properties (isochores, isotherms, isobars, response functions, velocity of sound) of a quantum gas in dimensions D > or = 1 and with fractional exclusion statistics 0 < or = g < or =1 connecting bosons (g=0) and fermions (g=1) . In D=1 the results are equivalent to those of the Calogero-Sutherland model. Emphasis is given to the crossover between bosonlike and fermionlike features, caused by aspects of the statistical interaction that mimic long-range attraction and short-range repulsion. A phase transition along the isobar occurs at a nonzero temperature in all dimensions. The T dependence of the velocity of sound is in simple relation to isochores and isobars. The effects of soft container walls are accounted for rigorously for the case of a pure power-law potential.
我们给出了维度(D\geq1)且具有分数排斥统计量(0\leq g\leq1)（连接玻色子((g = 0))和费米子((g = 1))）的量子气体热力学性质（等容线、等温线、等压线、响应函数、声速）的精确且明确的结果。在(D = 1)时，结果等同于卡洛杰罗 - 萨瑟兰模型的结果。重点在于由模拟长程吸引和短程排斥的统计相互作用方面所导致的类玻色子和类费米子特征之间的交叉。在所有维度中，沿着等压线会在非零温度下发生相变。声速对温度的依赖与等容线和等压线有简单的关系。对于纯幂律势的情况，严格考虑了软容器壁的影响。
