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

Abstract

The well known relation for ideal classical gas $\Delta {\epsilon }^2=k{T}^2{C}_V$ 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.

References in corpus (4)

• Thermodynamic Measurements in a Strongly Interacting Fermi Gas
• Energy fluctuation and discontinuity of specific heat
• Unified statistical thermodynamics of quantum gases trapped under generic power law potential in $d$ dimension and equivalence in $d=1$
• A note on Fermi energy of Fermi gas trapped under generic power law potential in $d$-dimension

Cited by in corpus (1)

• Planck scale effect on the thermodynamics of photon gas