Partition of kinetic energy and magnetic moment in dissipative diamagnetism

In this paper, we analyze dissipative diamagnetism, arising due to dissipative cyclotron motion in two dimensions, in the light of the quantum counterpart of energy equipartition theorem. We consider a charged quantum particle moving in a harmonic well, in the presence of a uniform magnetic field, and coupled to a quantum heat bath which is taken to be composed of an infinite number of independent quantum oscillators. The quantum counterpart of energy equipartition theorem tells us that it is possible to express the mean kinetic energy of the dissipative oscillator as a two-fold average, where, the first averaging is performed over the Gibbs canonical state of the heat bath while the second one is governed by a probability distribution function $P_k(\omega)$. We analyze this result further, and also demonstrate its consistency in the weak-coupling limit. Following this, we compute the equilibrium magnetic moment of the system, and reveal an interesting connection with the quantum counterpart of energy equipartition theorem. The expressions for kinetic energy and magnetic moment are reformulated in the context of superstatistics, i.e. the superposition of two statistics. A comparative study of the present results with those obtained from the more traditional Gibbs approach is performed and a perfect agreement is obtained.
Comment: v1: Preliminary version: 11 pages, 5 figures; v2: Minor changes; v3: Substantial changes, figures changed, new section added, title modified; v4: To appear in Physica A