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

Two-dimensional chaotic thermostat and behavior of a thermalized charge in a weak magnetic field

A two-dimensional version of a chaotic thermostat is investigated. Its structure follows the concept previously introduced by the author [G. J. Morales, Phys. Rev. E 97, 032203 (2018)2470-004510.1103/PhysRevE.97.032203] to generate a one-dimensional chaotic thermostat, namely, the usual friction force of a deterministic thermostat is supplemented with a self-consistent fluctuating force that depends on the drag coefficient associated with coupling to the heat bath. Azimuthal symmetry requires the thermostat to have two internal degrees of freedom, thus the Martyna-Klein-Tuckerman [G. J. Martyna et al., J. Chem. Phys. 97, 2635 (1992)JCPSA60021-960610.1063/1.463940] model is chosen for the heat bath. The unmagnetized system exhibits two-dimensional diffusive behavior, achieves symmetric Maxwellian velocity distributions in the absence of an external potential, and satisfies the Einstein relation when an external force is applied. The velocity fluctuations display the characteristic exponential frequency spectrum associated with chaotic systems. The model is used to explore the diffusive motion of a thermalized charge in a weak magnetic field and the associated Hall and Pedersen mobilities. Over a range of magnetic field strengths the charge exhibits absolute negative mobility.

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.

Non-Markovian stationary probability density for a harmonic oscillator in an electromagnetic field

We calculate the exact solution of the Fokker-Planck equation for the stationary-state probability density of a harmonic oscillator embedded in an electromagnetic field. The magnetic field is assumed to be a constant and the electric field an external stochastic force with the properties of a Gaussian and exponentially correlated noise (Ornstein-Uhlenbeck process). In this work, we first study the problem in the absence of the magnetic field, then we obtain the complete solution and corroborate that the latter reduces to the former when the magnetic field is suppressed.