金属中自由电子气体的非广延统计研究

Nonextensive thermostatistical investigation of free electronic gas in metal

采用分解近似的方法讨论了在Tsallis量子统计物理框架中,金属中自由电子气体的非广延参数q的热力学统计处理,计算出了总粒子数、总能量、自由能、热容量等热力学量,得出结论:在低温区域,q→1时,所有结果都可以回到传统的Fermi-Dirac分布,非广延参数q控制着系统的非广延程度.最后,详细讨论了q与热容量之间的关系,并与以前的结果作了比较.

The relevant aspects of the q-thermostatistical treatment for the free electronic gas which is an ideal Fermi system are discussed. Thermodynamical quantities of the free electronic gas such as total number of particles, total energy, heat capacity, free energy, etc., are calculated within the Tsallis thermo-statistics where the factorization approach is incorporated, and the ensuing statistics is derived. Special attention is paid to heat capacity. The limiting cases of interest are discussed in some detail, namely, low-temperature regimes, and the approximate results pertaining to the case q→1 （the conventional Fermi-Dirac statistics corresponds to q →1 ）. We also compare our results with previous Tsallis＇ works.