title: Diffusion of a massive particle in a periodic potential: Application to adiabatic ratchets.
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.
authors.affiliation: Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 106, Taiwan.|Department of Applied Chemistry, National Chiao Tung University, 1001 Ta Hsuen Road, Hsinchu, Taiwan.|Chuiko Institute of Surface Chemistry, National Academy of Sciences of Ukraine, Generala Naumova Street 17, Kiev 03164, Ukraine.
authors.forename: Viktor M
authors.initials: VM
authors.lastname: Rozenbaum
authors.affiliation: Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 106, Taiwan.|Topchiev Institute of Petrochemical Synthesis, Russian Academy of Sciences, Leninsky Prospect 29, 119991 Moscow, Russia.
authors.forename: Yurii A
authors.initials: YA
authors.lastname: Makhnovskii
authors.affiliation: Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 106, Taiwan.|Department of Applied Chemistry, National Chiao Tung University, 1001 Ta Hsuen Road, Hsinchu, Taiwan.|Department of Physics, Belarusian State University, Prospekt Nezavisimosti 4, 220050 Minsk, Belarus.
authors.forename: Irina V
authors.initials: IV
authors.lastname: Shapochkina
authors.affiliation: Department of Life Sciences and Institute of Genome Sciences, Institute of Biomedical Informatics, National Yang-Ming University, Taipei 112, Taiwan.
authors.forename: Sheh-Yi
authors.initials: SY
authors.lastname: Sheu
authors.affiliation: Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 106, Taiwan.
authors.forename: Dah-Yen
authors.initials: DY
authors.lastname: Yang
authors.affiliation: Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 106, Taiwan.|Department of Applied Chemistry, National Chiao Tung University, 1001 Ta Hsuen Road, Hsinchu, Taiwan.
authors.forename: Sheng Hsien
authors.initials: SH
authors.lastname: Lin