Exact path-integral evaluation of the heat distribution function of a trapped Brownian oscillator

Chatterjee, Debarati and Cherayil, Binny J (2010) Exact path-integral evaluation of the heat distribution function of a trapped Brownian oscillator. In: Physical Review E - Statistical, Nonlinear and Soft Matter Physics, 82 (5, Par).

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Abstract

Using path integrals, we derive an exact expression-valid at all times t-for the distribution P(Q,t) of the heat fluctuations Q of a Brownian particle trapped in a stationary harmonic well. We find that P(Q, t) can be expressed in terms of a modified Bessel function of zeroth order that in the limit t > infinity exactly recovers the heat distribution function obtained recently by Imparato et al. Phys. Rev. E 76, 050101(R) (2007)] from the approximate solution to a Fokker-Planck equation. This long-time result is in very good agreement with experimental measurements carried out by the same group on the heat effects produced by single micron-sized polystyrene beads in a stationary optical trap. An earlier exact calculation of the heat distribution function of a trapped particle moving at a constant speed v was carried out by van Zon and Cohen Phys. Rev. E 69, 056121 (2004)]; however, this calculation does not provide an expression for P(Q, t) itself, but only its Fourier transform (which cannot be analytically inverted), nor can it be used to obtain P(Q, t) for the case v=0.

Item Type:	Journal Article
Publication:	Physical Review E - Statistical, Nonlinear and Soft Matter Physics
Publisher:	The American Physical Society
Additional Information:	Copyright of this article belongs to The American Physical Society.
Department/Centre:	Division of Chemical Sciences > Inorganic & Physical Chemistry
Date Deposited:	29 Nov 2010 05:35
Last Modified:	29 Nov 2010 05:35
URI:	http://eprints.iisc.ac.in/id/eprint/33966

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