Non-equilibrium quantum Langevin dynamics of orbital diamagnetic moment

Abstract

We investigate the time dependent orbital diamagnetic moment of a charged particle in a magnetic field in a viscous medium via the Quantum Langevin Equation. We study how the interplay between the cyclotron frequency and the viscous damping rate governs the dynamics of the orbital magnetic moment in the high temperature classical domain and the low temperature quantum domain for an Ohmic bath. These predictions can be tested via state of the art cold atom experiments with hybrid traps for ions and neutral atoms. We also study the effect of a confining potential on the dynamics of the magnetic moment. We obtain the expected Bohr Van Leeuwen limit in the high temperature, asymptotic time (γt −→ ∞, where γ is the viscous damping coefficient) limit.PACS numbers:

Statistical physics of flux-carrying Brownian particles

“…This stands in contrast to the conventional Brownian motion in presence of an external magnetic field, in which there is no fluxes at thermal equilibrium [43,44,47]. We notice that the small strength of both the steady flow density and the fluid vorticity is in agreement with the subsidiary condition (45), which establishes that the flux-carrying effects must remain perturbative in comparison with the dissipative effects (otherwise the quantum kinetics (58) would deviate from the low-lying description provided by (1) [25,31]). Finally, we study the kinetic contribution to the stress tensor and the kinetic energy density.…”

“…To derive the diffusion matrix (27) in the weak system-environment coupling regime, it is better to split up the kinetic operator into the conventional Brownian part and the flux contribution as suggested by the effective action in (1). This can be done by virtue of the subsidiary condition (45), which guarantees that Ω flux plays the role of a perturbative parameter. More precisely, we may employ the Baker-Hausdorff formula to expand (48) in Taylor series such that the retarded kinetic propagator can be cast in the following convenient form,…”

“…The subsidiary condition (45) guarantees that the real part of the self-energy in Eq. ( 46) is positive definite (i.e.…”

Quantum Langevin dynamics of a charged particle in a magnetic field: Response function, position–velocity and velocity autocorrelation functions

“…We consider an uniform magnetic field along the z axis. This results in the following solutions to the motion of the charged particle in the x − y plane: [13] x…”

“…Using properties of the random force [14], we can write the position autocorrelation function for the x, y components [13],…”