J. I. Jiménez-Aquino

Work-fluctuation theorems for a particle in an electromagnetic field

The theoretical study about the transient and stationary fluctuation theorems is extended to include the effects of electromagnetic fields on a charged Brownian particle. In particular, we consider a harmonic trapped Brownian particle under the action of a constant magnetic field pointing perpendicular to a plane and a time-dependent electric field acting on this plane. The electric field is seen to be responsible for the motion of the center in the harmonic trap, giving as a result a time-dependent dragging. Our study is focused on the solution of the Smoluchowski equation associated with the over-damped Langevin equation and also considers two particular cases for the motion of the harmonic trap minimum. The first one is produced by a linear time-dependent electric field and, in the second case an oscillating electric field produces a circular motion. In this last case we have found resonant behavior in the mean work when the electric field is tuned with Larmors frequency. Some comparisons are made with other works in the absence of the magnetic field.

Work-fluctuation theorem for a charged harmonic oscillator

The solution of the Langevin equation including the inertia term is used to prove the transient work-fluctuation theorem for an electrically charged Brownian harmonic oscillator in an electromagnetic field. The theorem is proved for the physical situation in which the system is driven out of equilibrium by an arbitrary time-dependent dragging of the trap potential minimum. The proof is first given for a harmonic oscillator in the absence of an electromagnetic field, and then is extended to include the case of a charged harmonic oscillator under the action of crossed electric and magnetic fields. The case of a linear motion for the potential minimum is explicitly addressed.