Barrier crossing dynamics of a charged particle in the presence of a magnetic field: A new turnover phenomenon

Abstract

In this paper we have investigated the effect of a magnetic field on the barrier crossing rate of a charged particle. At the low friction regime we have observed a new turnover phenomenon for the variation of rate as a function of field strength. Thus although the force due to the magnetic field is not dissipative in nature, it plays a role in the steady state barrier crossing rate similar to that of a dissipative force in the weak damping regime. For appreciable damping strength, the rate monotonically decreases with the increase of field strength. We have demonstrated an interesting resonance effect due to the variation of frequency of the harmonic oscillator associated with the y-component motion at low damping and magnetic field strength.

Mechanism of barrier crossing dynamics in the presence of both time dependent and independent magnetic fields

“…It reduces the frequency which may be associated with dynamics. Therefore the barrier crossing frequency may depend on the damping strength [7]. The activation energy also may depend on γ 0 [13] if the stationary state is not a Boltzmann one since the probability at top of the energy barrier depends on the energy dissipation rate at the steady state.…”

“…These are examples of the Kramers' problem [22][23][24][25][26][27]. Still active research is going on this issue [7][8][9][10][11][12][28][29][30][31][32][33][34][35]. Ion moves to the neighboring site along the direction of transport through hopping.…”

“…There are several examples where the Brownian motion of the charged particle is found to occur in the condensed phase [2,17,[40][41][42][43]. It is to be noted here that although the study of the Brownian motion of charged particle in the presence of the magnetic field is getting strong attention in different contexts [3][4][5][6][7][8][9][10][11][12][44][45][46][47][48][49][50][51][52] but till now few studies have been reported considering the non-Markovian dynamics [8,9,11,[49][50][51][52]. Most of these studies with non-Markovian dynamics have been done based on the Langevin equation of motion.…”

“…In the very recent Refs. [3][4][5][6][7][8][9][10][11][12], it has been shown that the conductivity of an electrolytic material can be tuned by an applied magnetic field. The objective of the present study is related to this issue.…”

“…But the above discussion was missing in earlier Refs. [7,10,12]. The barrier crossing rate has been calculated quantitatively in Refs.…”