TY - JOUR

T1 - Brownian Motion of a Charged Particle in Electromagnetic Fluctuations at Finite Temperature

AU - Hsiang, Jen Tsung

AU - Wu, Tai Hung

AU - Lee, Da Shin

N1 - Funding Information:
Acknowledgements We would like to thank Larry H. Ford and C.-H. Wu for stimulating discussions. This work was supported in part by the National Science Council, ROC under grant NSC95-2112-M-259-011-MY2, and the National Center for Theoretical Sciences, Taiwan.

PY - 2011/1

Y1 - 2011/1

N2 - The fluctuation-dissipation theorem is a central theorem in nonequilibrium statistical mechanics by which the evolution of velocity fluctuations of the Brownian particle under a fluctuating environment is intimately related to its dissipative behavior. This can be illuminated in particular by an example of Brownian motion in an ohmic environment where the dissipative effect can be accounted for by the first-order time derivative of the position. Here we explore the dynamics of the Brownian particle coupled to a supraohmic environment by considering the motion of a charged particle interacting with the electromagnetic fluctuations at finite temperature. We also derive particle's equation of motion, the Langevin equation, by minimizing the corresponding stochastic effective action, which is obtained with the method of Feynman-Vernon influence functional. The fluctuation-dissipation theorem is established from first principles. The backreaction on the charge is known in terms of electromagnetic self-force given by a third-order time derivative of the position, leading to the supraohmic dynamics. This self-force can be argued to be insignificant throughout the evolution when the charge barely moves. The stochastic force arising from the supraohmic environment is found to have both positive and negative correlations, and it drives the charge into a fluctuating motion. Although positive force correlations give rise to the growth of the velocity dispersion initially, its growth slows down when correlation turns negative, and finally halts, thus leading to the saturation of the velocity dispersion. The saturation mechanism in a supraohmic environment is found to be distinctly different from that in an ohmic environment. The comparison is discussed.

AB - The fluctuation-dissipation theorem is a central theorem in nonequilibrium statistical mechanics by which the evolution of velocity fluctuations of the Brownian particle under a fluctuating environment is intimately related to its dissipative behavior. This can be illuminated in particular by an example of Brownian motion in an ohmic environment where the dissipative effect can be accounted for by the first-order time derivative of the position. Here we explore the dynamics of the Brownian particle coupled to a supraohmic environment by considering the motion of a charged particle interacting with the electromagnetic fluctuations at finite temperature. We also derive particle's equation of motion, the Langevin equation, by minimizing the corresponding stochastic effective action, which is obtained with the method of Feynman-Vernon influence functional. The fluctuation-dissipation theorem is established from first principles. The backreaction on the charge is known in terms of electromagnetic self-force given by a third-order time derivative of the position, leading to the supraohmic dynamics. This self-force can be argued to be insignificant throughout the evolution when the charge barely moves. The stochastic force arising from the supraohmic environment is found to have both positive and negative correlations, and it drives the charge into a fluctuating motion. Although positive force correlations give rise to the growth of the velocity dispersion initially, its growth slows down when correlation turns negative, and finally halts, thus leading to the saturation of the velocity dispersion. The saturation mechanism in a supraohmic environment is found to be distinctly different from that in an ohmic environment. The comparison is discussed.

KW - Brownian motion

KW - Fluctuation-dissipation theorem

KW - Langevin equation

KW - Negative correlation

KW - Non-equilibrium field theory

KW - Supraohmic environment

UR - http://www.scopus.com/inward/record.url?scp=78651472127&partnerID=8YFLogxK

U2 - 10.1007/s10701-009-9333-6

DO - 10.1007/s10701-009-9333-6

M3 - 期刊論文

AN - SCOPUS:78651472127

SN - 0015-9018

VL - 41

SP - 77

EP - 87

JO - Foundations of Physics

JF - Foundations of Physics

IS - 1

ER -