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Inertial effects and long-term transport properties of particle motion in washboard potential

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  • Venditti, Claudia
  • Adrover, Alessandra
  • Giona, Massimiliano

Abstract

The motion of non-interacting Brownian particles in the washboard potential is investigated in inertial regimes, when the overdamped approximation does not yield accurate predictions. The analysis is based on homogenization methods, deriving closed-form expressions for the long-term transport properties, i.e. effective velocity and diffusion coefficient. Different reduced models of increasing complexity, improving the overdamped approximation, are developed starting from the basic assumption that the velocity variable can be split into an “almost” deterministic and a fully stochastic contribution. The almost deterministic velocity term can be estimated from a fully deterministic or from a stochastic slow inertial manifold. The latter approach provides accurate predictions for all the asymptotic transport properties.

Suggested Citation

  • Venditti, Claudia & Adrover, Alessandra & Giona, Massimiliano, 2022. "Inertial effects and long-term transport properties of particle motion in washboard potential," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 585(C).
    • Handle: RePEc:eee:phsmap:v:585:y:2022:i:c:s0378437121006804
    DOI: 10.1016/j.physa.2021.126407
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    References listed on IDEAS

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    1. Festa, R. & d'Agliano, E.Galleani, 1978. "Diffusion coefficient for a Brownian particle in a periodic field of force," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 90(2), pages 229-244.
    2. I.G. Marchenko & I.I. Marchenko & A.V. Zhiglo, 2014. "Particle transport in space-periodic potentials in underdamped systems," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 87(1), pages 1-7, January.
    3. E. Neumann & A. Pikovsky, 2003. "Slow-fast dynamics in Josephson junctions," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 34(3), pages 293-303, August.
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    Cited by:

    1. Venditti, Claudia & Adrover, Alessandra & Giona, Massimiliano, 2022. "On the dynamic role of energy in underdamped particle motion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 597(C).

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