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.

Long Time Tails in Quantum Brownian Motion of a charged particle in a magnetic field

“…Using the above equation in Eq. ( 5) [14,15] we obtain the imaginary part ImR x (ω) of the response function denoted by R x (ω):…”

“…In contrast to earlier work [1,2] in which the authors address the issue of decay of temporal correlations of a neutral quantum Brownian particle, in this paper we address the appearance of long time tails in the temporal decay of correlations in the dynamics of a charged quantum Brownian particle in a harmonic potential in the presence of a magnetic field via the quantum Langevin equation [13][14][15]. Moreover, our study pertains to the particle coupled to Ohmic and Drude baths through position coordinate coupling.…”

“…In [14] the growth of the mean-square displacement of a charged Brownian particle in a magnetic field was analysed via the Quantum Langevin Equation of a charged particle in a magnetic field. More recently we had used the same framework for studying the Response function, position-velocity and velocity autocorrelation functions of such a charged Brownian particle [15].…”

Quantum Brownian Motion of a Charged Oscillator in a Magnetic Field Coupled to Aheat Bath Through Momentum Variables

“…The Quantum Brownian Motion of a particle undergoing diffusion driven by quantum fluctuations has been the focus of study for some time [1][2][3][4]. More recently, researchers have investigated the diffusion behaviour of a charged particle in a magnetic field [5][6][7]. To study this problem, one considers a Quantum Langevin Equation which corresponds to a reduced description of the system in which the coupling with the heat bath is described by two terms: an operator valued random force F (t) with mean zero and a mean force characterized by a memory function µ(t) [8].…”

“…Moreover, some of the studies have focused on an anomalous form of these couplings within a similar framework of the Quantum Langevin dynamics [9][10][11]. Although, in most of the literature, one considers a conventional form of coupling between the particle and the bath via position variables [1][2][3][4][5][6][7], several authors have also considered the case of such a quantum Brownian particle coupled to the bath variables through momentum coordinates [12][13][14][15][16][17][18][19].…”