title: Local discretization method for overdamped Brownian motion on a potential with multiple deep wells.
abstract: We present a general method for transforming the continuous diffusion equation describing overdamped Brownian motion on a time-independent potential with multiple deep wells to a discrete master equation. The method is based on an expansion in localized basis states of local metastable potentials that match the full potential in the region of each potential well. Unlike previous basis methods for discretizing Brownian motion on a potential, this approach is valid for periodic potentials with varying multiple deep wells per period and can also be applied to nonperiodic systems. We apply the method to a range of potentials and find that potential wells that are deep compared to five times the thermal energy can be associated with a discrete localized state while shallower wells are better incorporated into the local metastable potentials of neighboring deep potential wells.
authors.affiliation: Scion, Private Bag 3020, Rotorua 3046, New Zealand and Department of Physics, University of Otago, P. O. Box 56, Dunedin 9054, New Zealand.
authors.forename: P T T
authors.initials: PT
authors.lastname: Nguyen
authors.affiliation: Scion, Private Bag 3020, Rotorua 3046, New Zealand.
authors.forename: K J
authors.initials: KJ
authors.lastname: Challis
authors.affiliation: Department of Physics, University of Otago, P. O. Box 56, Dunedin 9054, New Zealand.
authors.forename: M W
authors.initials: MW
authors.lastname: Jack