Abstract
The statistics of the first passage time in connection with the quasideterministic (QD) approach is used to characterize the non-Markovian decay process of the unstable state of an electrically charged Brownian particle under the influence of an electromagnetic field. We consider a constant magnetic field and a fluctuating electric field, which satisfies the properties of a Gaussian exponentially correlated noise. It is shown that at the beginning of the decay process, the magnetic field is strongly coupled to the noise correlation time and thus the requirements of the QD approach are not satisfied. Only in the approximation of a weak coupling between both parameters can the time characterization of the decay process be successfully achieved. Our theoretical approach relies on a Langevin equation for the charged particle in an arbitrary two-dimensional unstable potential and applies to a bistable potential as a particular case.
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