$d$维广义幂律势$U=\sum_{i=1} ^d c_i |\frac {x_i}{a_i}|^{n_i}$下理想量子气体Biswas-Mitra-Bhattacharyya猜想的证明
A proof to Biswas-Mitra-Bhattacharyya conjecture for ideal quantum gas trapped under generic power law potential $U=\sum_{i=1} ^d c_i |\frac {x_i}{a_i}|^{n_i}$ in $d$ dimension
摘要：
重新讨论了理想经典气体$Δε^2=kT^2 C_V$的关系式，该关系式在量子系统中不再成立。建立了量子气体的能量涨落与比热之间的新联系，这种联系在经典极限和简并量子区都是有效的。最重要的是，提出的Biswas-Mitra-Bhattacharyya（BMB）猜想（Biswas $et.$ $al.$，J. Stat. P03013，2015年）本文证明了能量涨落峰与比热不连续性的关系。
英文摘要：
The well known relation for ideal classical gas $Δε^2=kT^2 C_V$ which does not remain valid for quantum system is revisited. A new connection is established between energy fluctuation and specific heat for quantum gases, valid in the classical limit and the degenerate quantum regime as well. Most importantly the proposed Biswas-Mitra-Bhattacharyya (BMB) conjecture (Biswas $et.$ $al.$, J. Stat. Mech. P03013, 2015.) relating hump in energy fluctuation and discontinuity of specific heat is proved and precised in this manuscript.
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