Quantum energy partition and dissipative diamagnetism: A novel approach

In this paper, we demonstrate a remarkable connection between the recently proposed quantum energy equipartition theorem and dissipative diamagnetism exhibited by a charged particle moving in a two dimensional harmonic potential in the presence of a uniform external magnetic field. The system is coupled to a quantum heat bath through coordinate variables with the latter being modelled as a collection of independent quantum oscillators. In the full frequency domain: $\omega \in (-\infty,\infty)$, the equilibrium magnetic moment $M_z$ can be expressed as an integral over the bath spectrum involving the relaxation function $\Phi(\omega)$, and subsequently, it is possible to propose a fruitful connection between the quantum counterpart of energy equipartition theorem and magnetic moment of the oscillator. We discuss an alternate picture, which emerges upon restricting the integration domain to $\omega \in [0,\infty)$. In these limits, the magnetic moment can be written as an integral over a distribution function $P_M (\omega)$ which has two wings corresponding to positive and negative segments. At high temperatures, these two contributions identically cancel each other. However, at low temperatures, the cancellation is incomplete resulting in a non-zero diamagnetic moment. A comparative study of the present results with those obtained from the more traditional Gibbs approach is performed and a perfect agreement is obtained.