Relaxation time of a Brownian rotator in a potential with nonparabolic barriers

Roland Bastardis, Pierre-Michel Déjardin and Yuri P. Kalmykov

Physica A: Statistical Mechanics and its Applications, 2008, vol. 387, issue 14, 3432-3442

Abstract: The extension of the Kramers theory of the escape rate of a Brownian particle from a potential well to the entire range of damping proposed by Mel’nikov and Meshkov [V.I. Mel’nikov, S.V. Meshkov, J. Chem. Phys. 85 (1986) 1018] is applied to the inertial rotational Brownian motion of a fixed axis rotator in a potential V(θ)=−K1cos2θ−K2cos4θ, where θ is the angle specifying the orientation of the rotator and K1 and K2 are constants. It is shown that in the neighbourhood of K1∼4K2 (flat barrier), the Mel’nikov–Meshkov method must suitably be adapted so that the effect of a nonparabolic barrier top can be correctly accounted for in the calculation of the relaxation time. The results obtained are compared with numerical calculations of the longest relaxation time (inverse smallest nonvanishing eigenvalue) using a matrix continued fraction algorithm and reasonable agreement is obtained for K1≥4K2 and all values of the dissipation parameter.

Keywords: Rotational Brownian motion; Fokker–Planck equation; Escape rate; Nonparabolic barrier; Universal turnover formula (search for similar items in EconPapers)
Date: 2008
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437108001970
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:387:y:2008:i:14:p:3432-3442

DOI: 10.1016/j.physa.2008.02.027

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().