Detection of weak signals through nonlinear relaxation times for a Brownian particle in an electromagnetic field

Resonance behavior of a charged particle in presence of a time dependent magnetic field

In this article, we have explored the resonance behavior of a particle in the presence of a time dependent magnetic field (TDMF). The particle is bound in a harmonic potential well. Based on the Hamiltonian description of the system in terms of action and angle variables, we have derived the resonance condition for the applied TDMF along z-direction which is valid for arbitrary frequencies along x and y directions of the two dimensional harmonic oscillator. We have also derived resonance condition for the applied magnetic field which is lying in a plane. Finally, we have explored resonance condition for the isotropic magnetic field. To check the validity of the theoretical calculation, we have solved equations of motion numerically for the parameter sets which satisfy the derived resonance condition. The numerical experiment fully agrees with the theoretically derived resonance conditions.

Detection of weak signals in memory thermal baths

The nonlinear relaxation time and the statistics of the first passage time distribution in connection with the quasideterministic approach are used to detect weak signals in the decay process of the unstable state of a Brownian particle embedded in memory thermal baths. The study is performed in the overdamped approximation of a generalized Langevin equation characterized by an exponential decay in the friction memory kernel. A detection criterion for each time scale is studied: The first one is referred to as the receiver output, which is given as a function of the nonlinear relaxation time, and the second one is related to the statistics of the first passage time distribution.

Decay of unstable states driven by colored noise in an electromagnetic field

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.