arXiv subjects

Md. Muktadir Rahman

Publications and source records attributed to Md. Muktadir Rahman.

4 recordsLinked to original sources

arXiv2017

Planck scale effect on the thermodynamics of photon gas

A particular framework for quantum gravity is the doubly special relativity (DSR) formalism that introduces a new observer independent scale (the Planck scale). We resort to the methods of statistical mechanics in this framework to determine how the deformed dispersion relation affects the thermodynamics of a photon gas. The ensuing modifications to the density of states, partition function, pressure, internal energy, entropy, free energy and specific heat are calculated. These results are compared with the outcome obtained in the Lorentz violating model of Camacho and Marcias (Gen. Relativ. Gravit. 39: 1175-1183, 2007). The two types of models predict different results due to different spacetime structure near the Planck scale. The resulting modifications can be interpreted as a consequence of the deformed Lorentz symmetry present in the particular model we have considered. In the low energy limit, our calculation coincides with usual results of photon thermodynamics in special relativity (SR) theory, in contrast to the study presented in (Phys. Rev. D81, 085039 (2010)).

hep-th↗

arXiv2015

Energy fluctuation of ideal Fermi gas trapped under generic power law potential $U=\sum_{i=1} ^d c_i |\frac{x_i}{a_i}|^{n_i}$ in d dimension

Energy fluctuation of ideal Fermi gas trapped under generic power law potential $U=\sum_{i=1} ^d c_i |\frac{x_i}{a_i}|^{n_i}$ have been calculated in arbitrary dimension. Energy fluctuation is scrutinized further in the degenerate limit $μ>> K_BT$ with the help of Sommerfeld expansion. The dependence of energy fluctuation on dimensionality and power law potential is studied in detail. Most importantly our general result can exactly reproduce the recently published result regarding free and harmonically trapped ideal Fermi gas in d=3 (S Biswas, J Mitra, S Bhattacharyya, J. Stat. Mech. P03013, 2015.)

cond-mat.quant-gas↗

arXiv2015

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 $Δε^2=kT^2 C_V$ 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.

cond-mat.quant-gas↗

arXiv2015

Investigation of Bose condensation in ideal Bose gas trapped under generic power law potential in $d$ dimension

The changes in characteristics of Bose condensation of ideal Bose gas due to an external generic power law potential $U=\sum_{i=1} ^d c_i |\frac{x_i}{a_i}|^{n_i}$ are studied carefully. Detailed calculation of Kim $et$ $al.$ (S. H. Kim, C. K. Kim and K. Nahm, J Phys. Condens. Matter 11 10269 (1999).) yielded the hierarchy of condensation transitions with changing fractional dimensionality. In this manuscript, some theorems regarding specific heat at constant volume $C_V$ are presented. Careful examination of these theorems reveal the existence of hidden hierarchy of the condensation transition in trapped systems as well.

cond-mat.quant-gas↗