Bose–Einstein condensation for an exponential density of states function and Lerch zeta function

Davood Momeni

Physica A: Statistical Mechanics and its Applications, 2020, vol. 541, issue C

Abstract: I show how Bose–Einstein condensation (BEC) in a non interacting bosonic system with exponential density of states function yields to a new class of Lerch zeta functions. By looking on the critical temperature, I suggest that a possible strategy to prove the ”Riemann hypothesis” problem. In a theorem and a lemma I suggested that the classical limit ħ→0 of BEC can be used as a tool to find zeros of real part of the Riemann zeta function with complex argument. It reduces the Riemann hypothesis to a softer form. Furthermore I propose a pair of creation–annihilation operators for BEC phenomena. This set of creation–annihilation operators is defined on a complex Hilbert space. They build a set up to interpret this type of BEC as a creation–annihilation phenomenon for a virtual hypothetical particle.

Keywords: General statistical methods; Bose–Einstein condensation; Special functions of mathematical physics; Lerch zeta function; Riemann hypothesis (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:541:y:2020:i:c:s037843711931831x

DOI: 10.1016/j.physa.2019.123264

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