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

Memory effects for a stochastic fractional oscillator in a magnetic field

The problem of random motion of harmonically trapped charged particles in a constant external magnetic field is studied. A generalized three-dimensional Langevin equation with a power-law memory kernel is used to model the interaction of Brownian particles with the complex structure of viscoelastic media (e.g., dusty plasmas). The influence of a fluctuating environment is modeled by an additive fractional Gaussian noise. In the long-time limit the exact expressions of the first-order and second-order moments of the fluctuating position for the Brownian particle subjected to an external periodic force in the plane perpendicular to the magnetic field have been calculated. Also, the particle's angular momentum is found. It is shown that an interplay of external periodic forcing, memory, and colored noise can generate a variety of cooperation effects, such as memory-induced sign reversals of the angular momentum, multiresonance versus Larmor frequency, and memory-induced particle confinement in the absence of an external trapping field. Particularly in the case without external trapping, if the memory exponent is lower than a critical value, we find a resonancelike behavior of the anisotropy in the particle position distribution versus the driving frequency, implying that it can be efficiently excited by an oscillating electric field. Similarities and differences between the behaviors of the models with internal and external noises are also discussed.

Extracting work from magnetic-field-coupled Brownian particles

Thermodynamics of the magnetic-field-coupled Brownian particles is studied. We show that in the presence of the magnetic field, work can be extracted from the reservoir even when the measurement operation and the potential change operation are applied in different spatial directions. In particular, we show that more work can be extracted if the measurements are applied in two different directions simultaneously. In all these cases, we show that the generalized second law involving the measurement information and potential change is satisfied. In addition, we show how the continuous potential change and measurement position affect the work extraction.

Power fluctuation theorem for a Brownian harmonic oscillator

In this paper we study the validity of the total power fluctuation theorem spent on a Brownian harmonic oscillator when the system is driven out of equilibrium through the drag of the potential minimum. The theorem is first proved for an ordinary harmonic oscillator in two cases: The first one considers the particle in a thermal bath under the action of Gaussian white noise, and in the second one the drift is provided by an additional external Gaussian colored noise satisfying the characteristics of an Ornstein-Uhlenbeck process. We go further, by considering a charged harmonic oscillator under the action of an electromagnetic field. The theorem is also proven as in the two cases given above. In both of those cases, we illustrate the theorem for a uniform motion of the trap potential minimum and show that in the presence of external colored noise, the theorem is only valid in the stationary state.