Abstract
The dynamical evolution of a Brownian particle in an inhomogeneous medium with spatially varying friction and temperature field is important to understand conceptually. It requires to address the basic problem of relative stability of states in nonequilibrium systems which has been a subject of debate for over several decades. The theoretical treatments adopted so far are mostly phenomenological in nature. In this work we give a microscopic treatment of this problem. We derive the Langevin equation of motion and the associated Fokker-Planck equation. The correct reduced description of the Kramers equation in the overdamped limit (Smoluchowski equation) is obtained. Our microscopic treatment may be helpful in understanding the working of thermal ratchets, a problem of much current interest.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
N G van Kampen,Stochastic processes in physics and chemistry (North Holland, Amsterdam, 1981)
C W Gardiner,Handbook of stochastic methods (Springer Verlag, Berlin, 1983)
R Landauer,Helv. Phys. Acta 56, 847 (1983);J. Stat. Phys. 53, 233 (1988), and references therein
R Landauer,Physica A194, 551 (1993), and references therein
R Landauer,Physics Today 31, 23 (November 1978)
R Landauer,Ann. NY Acad. Sci. 316, 433 (1979)
N G van Kampen,IBM J. Res. Develop. 32, 107 (1988)
N G van Kampen,Z. Phys. B68, 135 (1987)
N G van Kampen,J. Maths. Phys. 29, 1220 (1988)
M Buettiker,Z. Phys. B68, 161 (1987)
M M Millonas,Phys. Rev. Lett. 74, 10 (1995), and references therein
A M Jayannavar and M C Mahato, unpublished
A M Jayannavar, unpublished
A O Caldeira and A J Leggett,Physica A121, 587 (1983);Ann. Phys. 149, 374 (1983)
K Lindenberg and V Seshadri,Physica A109, 483 (1981)
A M Jayannavar,Z. Phys. B82, 153 (1991)
N G van Kampen,Phys. Rep. C24, 172 (1976)
E A Novikov,Zh. Eksp. Teor. Fiz. 47, 1919 (1964);Sov. Phys. JETP 20, 1290 (1965)
A M Jayannavar and N Kumar,Phys. Rev. Lett. 48, 553 (1982)
A M Jayannavar,Phys. Rev. E48, 837 (1993)
J M Sancho, M San Miguel and D Duerr,J. Stat. Phys. 28, 291 (1982)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Jayannavar, A.M., Mahato, M.C. Macroscopic equation of motion in inhomogeneous media: A microscopic treatment. Pramana - J Phys 45, 369–376 (1995). https://doi.org/10.1007/BF02848625
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02848625