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Title: The Small-Mass Limit and White-Noise Limit of an Infinite Dimensional Generalized Langevin Equation

Abstract

We study asymptotic properties of the Generalized Langevin Equation (GLE) in the presence of a wide class of external potential wells with a power-law decay memory kernel. When the memory can be expressed as a sum of exponentials, a class of Markovian systems in infinite-dimensional spaces is used to represent the GLE. The solutions are shown to converge in probability in the small-mass limit and the white-noise limit to appropriate systems under minimal assumptions, of which no global Lipschitz condition is required on the potentials. With further assumptions about space regularity and potentials, we obtain L{sup 1} convergence in the white-noise limit.

Authors:
 [1]
  1. Tulane University, Department of Mathematics (United States)
Publication Date:
OSTI Identifier:
22787929
Resource Type:
Journal Article
Journal Name:
Journal of Statistical Physics
Additional Journal Information:
Journal Volume: 173; Journal Issue: 2; Other Information: Copyright (c) 2018 Springer Science+Business Media, LLC, part of Springer Nature; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0022-4715
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ASYMPTOTIC SOLUTIONS; CONVERGENCE; KERNELS; LANGEVIN EQUATION; MARKOV PROCESS; MASS; MATHEMATICAL SPACE; NOISE; PROBABILITY

Citation Formats

Nguyen, Hung D., E-mail: hnguye25@tulane.edu. The Small-Mass Limit and White-Noise Limit of an Infinite Dimensional Generalized Langevin Equation. United States: N. p., 2018. Web. doi:10.1007/S10955-018-2139-1.
Nguyen, Hung D., E-mail: hnguye25@tulane.edu. The Small-Mass Limit and White-Noise Limit of an Infinite Dimensional Generalized Langevin Equation. United States. https://doi.org/10.1007/S10955-018-2139-1
Nguyen, Hung D., E-mail: hnguye25@tulane.edu. Mon . "The Small-Mass Limit and White-Noise Limit of an Infinite Dimensional Generalized Langevin Equation". United States. https://doi.org/10.1007/S10955-018-2139-1.
@article{osti_22787929,
title = {The Small-Mass Limit and White-Noise Limit of an Infinite Dimensional Generalized Langevin Equation},
author = {Nguyen, Hung D., E-mail: hnguye25@tulane.edu},
abstractNote = {We study asymptotic properties of the Generalized Langevin Equation (GLE) in the presence of a wide class of external potential wells with a power-law decay memory kernel. When the memory can be expressed as a sum of exponentials, a class of Markovian systems in infinite-dimensional spaces is used to represent the GLE. The solutions are shown to converge in probability in the small-mass limit and the white-noise limit to appropriate systems under minimal assumptions, of which no global Lipschitz condition is required on the potentials. With further assumptions about space regularity and potentials, we obtain L{sup 1} convergence in the white-noise limit.},
doi = {10.1007/S10955-018-2139-1},
url = {https://www.osti.gov/biblio/22787929}, journal = {Journal of Statistical Physics},
issn = {0022-4715},
number = 2,
volume = 173,
place = {United States},
year = {2018},
month = {10}
}