Effects of rotation on the thermodynamic properties of a quantum dot

TL;DR

This paper investigates how uniform rotation in a rotating frame impacts the thermodynamics of a quantum dot with radial confinement. By solving the Schrödinger equation with a centrifugal term and a radial potential, it derives the energy spectrum $E_{n,m}$ and wavefunctions, then computes the density of states and thermodynamic quantities such as magnetization, entropy, and heat capacity as functions of $\omega$, $B$, and $T$ under zero external magnetic field. Key findings include rotation-induced lifting of degeneracies, magnetization arising from the Barnett effect, and oscillatory signatures analogous to de Haas–van Alphen and Aharonov–Bohm effects, along with a magnetocaloric-like behavior where adiabatic changes in $\omega$ lower the system temperature. These results advance understanding of rotational control in mesoscopic quantum systems and point to future work including spin effects and anisotropic confinement.

Abstract

In this work, we investigate the effects of rotation on the physical properties of a quantum dot described by a radial potential and subjected to a rotating reference frame. The interplay between rotation and confinement is analyzed by solving the Schrödinger equation for the system, yielding energy levels and wavefunctions as functions of angular velocity. We compute key thermodynamic properties, including the density of states, magnetization, entropy, and heat capacity, in the absence of an external magnetic field. Our results demonstrate that rotation induces significant modifications to the energy spectrum, removing degeneracies and generating oscillatory behaviors in magnetization akin to de Haas-van Alphen and Aharonov-Bohm-type oscillations. Furthermore, we observe an effect analogous to the magnetocaloric effect, where an increase in angular velocity leads to a decrease in temperature during adiabatic processes. These results reveal the potential of rotational effects to influence quantum systems and provide insights for future studies in mesoscopic physics.

Figures (5)

• Figure 1: Energy levels of a quantum dot as a function of relative frequency.
• Figure 2: Magnetization of a quantum dot as a temperature function for different relative frequency values.
• Figure 3: Entropy of a quantum dot as a temperature function for different relative frequency values.
• Figure 4: In an adiabatic process, the temperature of a quantum dot is a function of relative frequency.
• Figure 5: Heat capacity of a quantum dot as a temperature function for different relative frequency values.