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

The well known relation for ideal classical gas $Δ ϵ^{2} = k T^{2} C_{V}$ 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 $e t .$ $a l .$ , J. Stat. Mech. P03013, 2015.) relating hump in energy fluctuation and discontinuity of specific heat is proved and precised in this manuscript.

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

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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

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A proof to Biswas-Mitra-Bhattacharyya conjecture for ideal quantum gas trapped under generic power law potential U=∑i=1dci∣xiai∣niU=∑i=1d​ci​∣ai​xi​​∣ni​ in dd dimension

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A proof to Biswas-Mitra-Bhattacharyya conjecture for ideal quantum gas trapped under generic power law potential U=∑i=1dci∣xiai∣niU=∑i=1d​ci​∣ai​xi​​∣ni​ in dd dimension

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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

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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

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