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arXiv · 1303.6742

Work fluctuations in a time-dependent harmonic potential: rigorous results and beyond the overdamped limit

Chulan Kwon·Jae Dong Noh·Hyunggyu Park
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Abstract

We investigate the stochastic motion of a Brownian particle in the harmonic potential with a time-dependent force constant. It may describe the motion of a colloidal particle in an optical trap where the potential well is formed by a time-dependent field. We use the path integral formalism to solve the Langevin equation and the associated Fokker-Planck (Kramers) equation. Rigorous relations are derived to generate the probability density function for the time-dependent nonequilibrium work production beyond the overdamped limit. We find that the work distribution exhibits an exponential tail with a power-law prefactor, accompanied by an interesting oscillatory feature (multiple pseudo locking-unlocking transitions) due to the inertial effect. Some exactly solvable cases are also discussed in the overdamped limit.

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Chulan Kwon, Jae Dong Noh, Hyunggyu Park. 2013-03-27. Work fluctuations in a time-dependent harmonic potential: rigorous results and beyond the overdamped limit. https://doi.org/10.1103/physreve.88.062102

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