Application of statistical mechanics to stochastic transport

Abstract The problem of transport of Brownian particles in spatially periodic structures is presented. Based on the Feynman ratchet, a mathematical model of a thermal ratchet is constructed as the Newton equation with stochastic thermal and nonthermal forces. Conditions for directed motion of Brownian particles are discussed. An example of an exactly soluble model of stochastic transport is demonstrated.

[1]  Mark M. Millonas,et al.  Transport and current reversal in stochastically driven ratchets , 1994, cond-mat/9401046.

[2]  Peter Hänggi,et al.  Periodically Rocked Thermal Ratchets , 1994 .

[3]  Reimann,et al.  Precise numerics versus theory for correlation ratchets. , 1996, Physical review letters.

[4]  M. Magnasco,et al.  Forced thermal ratchets. , 1993, Physical review letters.

[5]  M. Büttiker,et al.  Transport as a consequence of state-dependent diffusion , 1987 .

[6]  P. Español,et al.  Criticism of Feynman’s analysis of the ratchet as an engine , 1996 .

[7]  P. Hänggi,et al.  Symmetric white noise can induce directed current in ratchets , 1997 .

[8]  H. Risken Fokker-Planck Equation , 1996 .

[9]  R. Feynman,et al.  The Feynman Lectures on Physics Addison-Wesley Reading , 1963 .

[10]  A. Ajdari,et al.  Force-Free Motion in Asymmetric Structures: A Mechanism without Diffusive Steps , 1994 .

[11]  J. Łuczka,et al.  Brownian Ratchets: Transport Controlled by Thermal Noise , 1998 .

[12]  Peter Hänggi,et al.  Thermal ratchets driven by Poissonian white shot noise , 1997 .

[13]  Jerzy Luczka,et al.  Brownian transport controlled by dichotomic and thermal fluctuations 1 The paper dedicated to the me , 1998 .

[14]  Peter Hänggi,et al.  Noise-induced transport in symmetric periodic potentials: White shot noise versus deterministic noise , 1996 .

[15]  Riordan,et al.  Nonequilibrium fluctuation-induced transport. , 1994, Physical review letters.

[16]  Bier,et al.  Fluctuation driven ratchets: Molecular motors. , 1994, Physical review letters.

[17]  Peter Hänggi,et al.  White-Noise-Induced Transport in Periodic Structures , 1995 .

[18]  J. Kula,et al.  Transport generated by dichotomous fluctuations , 1996 .

[19]  Christoph F. Schmidt,et al.  Direct observation of kinesin stepping by optical trapping interferometry , 1993, Nature.

[20]  R. Astumian Thermodynamics and kinetics of a Brownian motor. , 1997, Science.