In this paper, we investigate the thermodynamic properties of an Aharonov-Bohm (AB) quantum ring in a heat bath for both relativistic and non-relativistic cases. For accomplishing this, we used the partition function which was obtained numerically using the Euler-Maclaurin formula. In particular, we determined the energy spectra as well as the behavior of the main thermodynamic functions of the canonical ensemble, namely, the Helmholtz free energy, the mean energy, the entropy and the heat capacity. The so-called Dulong-Petit law was verified only for the relativistic case. We noticed that in the low energy regime, the relativistic thermodynamic functions are reduced to the non-relativistic case as well.

In this paper, we investigate the thermodynamic properties of a set of neutral Dirac particles in the presence of an electromagnetic field in contact with a heat bath for the relativistic and nonrelativistic cases. In order to perform the calculations, the high-temperature limit is considered and the Euler-MacLaurin formula is taking into account. Next, we explicitly determine the behavior of the main thermodynamic functions of the canonical ensemble: the Helmholtz free energy, the mean energy, the entropy, and the heat capacity. As a result, we verified that the mean energy and the heat capacity for the relativistic case are two times the values of the non-relativistic case, thus, satisfying the so-called Dulong-Petit law. In addition, we also verified that the Helmholtz free energy and the entropy in both cases increase as a function of the electric field. Finally, we note that there exists no influence on the thermodynamic functions due to the magnetic field.

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In the present paper, we investigate the influence of topological, noninertial and spin effects on the 2D Dirac oscillator in the presence of the Aharonov-Casher effect. Next, we determine the two-component Dirac spinor and the relativistic energy spectrum for the bound states. We observe that this spinor is written in terms of the confluent hypergeometric functions and this spectrum explicitly depends on the quantum numbers n and m l , parameters s and η associated to the topological and spin effects, quantum phase Φ AC , and of the angular velocity Ω associated to the noninertial effects of a rotating frame. In the nonrelativistic limit, we obtain the quantum harmonic oscillator with two types of couplings: the spin-orbit coupling and the spin-rotation coupling. We note that the relativistic and nonrelativistic spectra grow in absolute values as functions of η, Ω, and Φ AC and its periodicities are broken due to the rotating frame. Finally, we compared our problem with other works, where we verified that our results generalizes some particular planar cases of the literature.

In this work, we study the Aharonov-Bohm-Coulomb (ABC) system for a relativistic Dirac particle with position-dependent mass (PDM). To solve our system, we use the lef t-handed and right-handed projection operators. Next, we explicitly obtain the eigenfunctions and the energy spectrum of the particle. We verify that these eigenfunctions are written in terms of the generalized Laguerre polynomials and the energy spectrum depends on the parameters Z, Φ AB and κ. We notice that the parameter κ has the function of increasing the values of the energy levels of the system. In addition, the usual ABC system is recovered when one considers the limit of constant mass (κ → 0). Moreover, also we note that even in the absence of ABC system (Z = Φ AB = 0), the particle with PDM still has a discrete energy spectrum.