Quantum Brownian motion in a magnetic field: Transition from monotonic to oscillatory behaviour

Abstract

We investigate the Brownian motion of a charged particle in a magnetic field. We study this in the high temperature classical and low temperature quantum domains. In both domains, we observe a transition of the mean square displacement from a monotonic behaviour to a damped oscillatory behaviour as one increases the strength of the magnetic field. When the strength of the magnetic field is negligible, the mean square displacement grows linearly with time in the classical domain and logarithmically with time in the quantum domain. We notice that these features of the mean square displacement are robust and remain essentially the same for an Ohmic dissipation model and a single relaxation time model for the memory kernel. The predictions stemming from our analysis can be tested against experiments in trapped cold ions.

References in corpus (5)

• A trapped single ion inside a Bose-Einstein condensate
• A quantum violation of the second law?
• Low temperature Thermodynamics in the Context of Dissipative Diamagnetism
• Quantum Brownian motion in a Landau level
• A quantum diffusion law

Cited by in corpus (4)

• Quantum Langevin dynamics of a charged particle in a magnetic field : Response function, position-velocity and velocity autocorrelation functions
• Long Time Tails in Quantum Brownian Motion of a charged particle in a magnetic field
• Non-equilibrium Quantum Langevin dynamics of orbital diamagnetic moment
• Quantum Brownian Motion of a charged oscillator in a magnetic field coupled to a heat bath through momentum variables