Diffusion of a massive particle in a periodic potential: Application to adiabatic ratchets

Viktor M Rozenbaum, Makhnovskii Yurii A, Irina V Shapochkina, Sheh-Yi Sheu, Dah-Yen Yang, Sheng Hsien Lin

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Abstract

We generalize a theory of diffusion of a massive particle by the way in which transport characteristics are described by analytical expressions that formally coincide with those for the overdamped massless case but contain a factor comprising the particle mass which can be calculated in terms of Risken's matrix continued fraction method (MCFM). Using this generalization, we aim to elucidate how large gradients of a periodic potential affect the current in a tilted periodic potential and the average current of adiabatically driven on-off flashing ratchets. For this reason, we perform calculations for a sawtooth potential of the period L with an arbitrary sawtooth length (l < L) instead of the smooth potentials typically considered in MCFM-solvable problems. We find nonanalytic behavior of the transport characteristics calculated for the sharp extremely asymmetric sawtooth potential at l -> 0 which appears due to the inertial effect. Analysis of the temperature dependences of the quantities under study reveals the dominant role of inertia in the high-temperature region. In particular, we show, by the analytical strong-inertia approach developed for this region, that the temperature-dependent contribution to the mobility at zero force and to the related effective diffusion coefficient are proportional to T-3/2 and T-1/2, respectively, and have a logarithmic singularity at l -> 0.
Original languageEnglish
Article number062132
JournalPhysical Review E
Volume92
Issue number6
DOIs
StatePublished - 18 Dec 2015

Keywords

  • BROWNIAN MOTORS; KRAMERS PROBLEM; JUMP RATE; TRANSPORT; MOTION; EQUATION

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