Exact calculations of the thermal properties of two-electron GaAs quantum dots with inverse-square interactions

Abstract

In this study, we theoretically scrutinize the effect of the inverse-square interaction on the thermal properties of two electrons trapped in a parabolic GaAs quantum dot. The analytical energy spectrum was used to calculate the thermal properties of the system using the canonical ensemble formalism. It was found that the thermal energy increased with the increase in temperature, while it remained almost constant for sufficiently low temperatures; it was also demonstrated that the inverse-square interaction increased the thermal mean energy. Moreover, the heat capacity increased sharply within a low-temperature window and saturated to the value of 2kB in the high-temperature limit. As expected, entropy increased linearly with increasing temperature. It was also shown that both entropy and heat capacity decreased rapidly when the confinement strength increased (or the dot size decreased) in the low-temperature limit, regardless of the influence of the interaction between the electrons. We also show that the number of allowed states of the system decreased as the interaction strength increased (Z(λ = 0) > Z(λ ≠ 0)). Finally, the stability of the system was investigated through F–T curves. The three-dimensional surface for the temperature-dependent mean energy and heat capacity was also plotted. It should be noted that, for the thermal mean energy, partition function, and Helmholtz free energy, the normal physical behavior of the two-oscillator system with Fermi statistics is recovered for λ → 0. However, heat capacity and entropy show exact two-fermion oscillator system behavior. The most impressive result found in this work is that the inverse-square interaction does not affect the heat capacity and entropy at all despite its noticeable effects on the thermal mean energy. This, in turn, facilitates theoretical studies related to finding the distinctive parameters of quantum dots without going into the heavy calculations resulting from the effects of interactions.

Harnessing the Shannon Entropy‐Based Magnetocaloric Effect in GaAs Quantum Dot under the Influence of Noise‐Anharmonicity Interplay

“…Therefore, one can find a plethora of studies concerned with thermodynamics of LDSN. [33][34][35][36][37][37][38][39][40][41][42][43][44][45] The Shannon entropy is a specific form of the entropy functional widely regarded as the cornerstone of the information-theory-based statistical thermodynamics. [46] The magnetocaloric effect (MCE) is a magneto-thermodynamic phenomenon that can be conceived as an in-built response of the magnetic materials as a result of change in the magnetic field (ΔB) and possesses a straightforward connection with the entropy change (ΔS).…”

“…Therefore, one can find a plethora of studies concerned with thermodynamics of LDSN. [ 33–37,37–45 ] The Shannon entropy is a specific form of the entropy functional widely regarded as the cornerstone of the information‐theory‐based statistical thermodynamics. [ 46 ]…”