Magnetism of Two Coupled Harmonic Oscillators

TL;DR

This paper analyzes the thermodynamical properties of two coupled harmonic oscillators in a magnetic field, deriving energy spectra and discussing quantum corrections to magnetism.

Contribution

It provides a generalized approach to coupled oscillators in magnetic fields, including new quantum correction results to magnetism.

Findings

Quantum corrections to Landau diamagnetism identified

Orbital paramagnetism effects analyzed

Generalized thermodynamical potential derived

Abstract

The thermodynamical properties of a system of two coupled harmonic oscillators in the presence of an uniform magnetic field B are investigated. Using an unitary transformation, we show that the system can be diagonalized in simple way and then obtain the energy spectrum solutions. These will be used to determine the thermodynamical potential in terms of different physical parameters like the coupling parameter \alpha. This allows us to give a generalization of already significant published work and obtain different results, those could be used to discuss the magnetism of the system. Different limiting cases, in terms of \alpha and B, have been discussed. In fact, quantum corrections to the Landau diamagnetism and orbital paramagnetism are found.