Effect of an electromagnetic field on the barrier crossing rate

We investigate the spectrum for the rate constant of an electric field-driven charged Brownian particle in the presence of a magnetic field (MF). For the cross fields with low or high values of the cyclotron frequency, an asymmetric splitting of the spectrum occurs with two peaks. Anharmonicity-induced additional splitting may appear around the lower resonating frequency at the intermediate strength of the applied MF. Another observation is that if the magnetic field is tilted from the z-direction, an additional peak appears between the two peaks. The position of the middle peak may be independent of the strength of the applied MF. In some cases, only one peak appears even in the presence of a magnetic field. We explain these observations considering the dynamics around the stable fixed point and determine the position of the peak in the spectrum for the rate constant as a function of the strength of the applied magnetic field. Thus the present study may find applications for tuning the conductivity of a solid electrolyte, which is very important in recent technology. Other applications may be in areas such as electromagnetic field-induced modulation of (a) thermally activated tunneling ionization, (b) thermally stimulated ionization, etc.