Work distribution in a time-dependent logarithmic-harmonic potential: exact results and asymptotic analysis

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Author list: Ryabov A, Dierl M, Chvosta P, Einax M, Maass P

Publisher: IOP Publishing

Place: BRISTOL

Publication year: 2013

Journal: Journal of Physics A: Mathematical and Theoretical (1751-8113)

Journal acronym: J PHYS A-MATH THEOR

Volume number: 46

Issue number: 7

Number of pages: 11

ISSN: 1751-8113

eISSN: 1751-8121

Languages: English-Great Britain (EN-GB)

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Abstract

We investigate the distribution of work performed on a Brownian particle in a time-dependent asymmetric potential well. The potential has a harmonic component with a time-dependent force constant and a time-independent logarithmic barrier at the origin. For an arbitrary driving protocol, the problem of solving the Fokker-Planck equation for the joint probability density of work and particle position is reduced to the solution of the Riccati differential equation. For a particular choice of the driving protocol, an exact solution of the Riccati equation is presented. An asymptotic analysis of the resulting expression yields the tail behavior of the work distribution for small and large work values. In the limit of a vanishing logarithmic barrier, the work distribution for the breathing parabola model is obtained.

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