The one-dimensional thermal properties for the relativistic harmonic oscillators

Abstract

In this paper, we want to improved the calculations of the thermodynamic quantities of the relativistic Harmonic oscillator using the Hurwitz zeta function. The comparison of our results with those obtained by a method based on the Euler-MacLaurin approach has been made.

Thermodynamics of quantum phase transitions of a Dirac oscillator in a homogenous magnetic field

“…In contrast to what has been proposed in the recent literature on the topic (see [22] and references therein), we notice that the condition for the convergence of the series s/2 > 1 implies c > 2. The integral can therefore be evaluated with the method of residue once a proper closed path has been identified.…”

“…A different representation of the defining series in the partition function that will reveal itself to be more effective when the phase switches from left to right, can be obtained using the Cahen-Mellin integral, as suggested for different systems in [20] and reviewed in [21,22]. The Cahen-Mellin integral is defined as [23] e…”

Thermodynamic properties of the graphene in a magnetic field via the two-dimensional Dirac oscillator

“…In table 1, we show some values of this temperature with the magnetic field B: this temperature increases with the applied magnetic field. Now, using the following formula (see [21] and references therein)…”