A proof of the Biswas-Mitra-Bhattacharyya conjecture for the ideal quantum gas trapped under the generic power law potential U = Sigma(d)(i=1) C-i vertical bar x(i)/a(i)vertical bar n(i)

摘要

The well known relation for the ideal classical gas Delta epsilon(2)=kT(2)CV, which does not remain valid for quantum systems, is revisited. A new connection is established between the energy fluctuation and specific heat for quantum gases, which is valid in both the classical limit and the degenerate quantum regime. Most importantly, the proposed Biswas-Mitra-Bhattacharyya conjecture (Biswas et al 2015 J. Stat. Mech. P03013) relating the hump in energy fluctuation and the discontinuity of specific heat is essentially proved and made precise in this manuscript.