Thermodynamic properties of an Aharonov-Bohm quantum ring

Abstract

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.

Topological and noninertial effects in an Aharonov–Bohm ring

“…Moreover, we note also that the quantum number n and the parameters ω, Φ and η have the function of increasing the energies of the spectrum, i.e., in the limits η → 0 (extremely dense cosmic string) and n = ω = Φ → ∞, we have |E σ n | → ∞. Now, comparing the spectrum (34) with the literature, we verified that in the absence of the topological and noninertial effects (η = 1 and ω = 0) we recover the usual spectrum of a Dirac particle confined in a relativistic AB ring [33,35].…”

“…Since we are working now in a (1 + 1)-dimensional spacetime, it is convenient to write the Dirac matrices α = (0, α 2 , 0) = (0, −α 2 , 0) and γ 0 and the spin operator S = (0, 0, 1 2 Σ 3 ) in terms of the 2 × 2 Pauli matrices, i.e., α 2 = σ 2 and γ 0 = Σ 3 = σ 3 [35,60,75]. In this way, setting the following ansatz for the two-component Dirac spinor [35,60]…”

“…Posteriorly, it was formulated a relativistic AB ring model for Dirac particles; however, the nonrelativistic limit (low-energy regime) of this ring not was analyzed and much less compared with the usual results of literature [33]. Recently, AB rings were studied in de Sitter expanding universe [34], and their thermodynamic properties were calculated theoretically in the high and low-energy regime [35].…”

Thermodynamic properties of neutral Dirac particles in the presence of an electromagnetic field

“…According to the literature, when the mean energy and the specific heat capacity are twice of the value encountered in the non-relativistic case, we say that these cases satisfy the so-called Dulong-Petit law [47]. It is important to mention that this peculiar behavior is also observed in others relativistic quantum systems, such as in the Dirac oscillator [20] and in the Aharonov-Bohm quantum ring [28]. Last but not least, it is worth mentioning that, since the partition function in both cases does not depend on the magnetic field (Eq.…”

“…Moreover, this study also has a particular relevance from a theoretical viewpoint, mainly when the physical system is either relativistic [18][19][20][21][22] or non-relativistic quantum [23][24][25][26][27]. In addition, it is worth mentioning that recently the thermodynamic properties of an Aharonov-Bohm quantum ring were performed in the high and low-energy regime [28].…”