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Title: On the Asymptotic Behavior of the Kernel Function in the Generalized Langevin Equation: A One-Dimensional Lattice Model

Abstract

We present some estimates for the memory kernel function in the generalized Langevin equation, derived using the Mori–Zwanzig formalism from a one-dimensional lattice model, in which the particles interactions are through nearest and second nearest neighbors. The kernel function can be explicitly expressed in a matrix form. The analysis focuses on the decay properties, both spatially and temporally, revealing a power-law behavior in both cases. The dependence on the level of coarse-graining is also studied.

Authors:
;  [1]
  1. The Pennsylvania State University (United States)
Publication Date:
OSTI Identifier:
22784061
Resource Type:
Journal Article
Journal Name:
Journal of Statistical Physics
Additional Journal Information:
Journal Volume: 170; 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; 97 MATHEMATICAL METHODS AND COMPUTING; ASYMPTOTIC SOLUTIONS; FUNCTIONS; KERNELS; LANGEVIN EQUATION; LATTICE PARAMETERS; MATRICES; ONE-DIMENSIONAL CALCULATIONS; PARTICLE INTERACTIONS; PARTICLES; SIMULATION

Citation Formats

Chu, Weiqi, and Li, Xiantao. On the Asymptotic Behavior of the Kernel Function in the Generalized Langevin Equation: A One-Dimensional Lattice Model. United States: N. p., 2018. Web. doi:10.1007/S10955-017-1927-3.
Chu, Weiqi, & Li, Xiantao. On the Asymptotic Behavior of the Kernel Function in the Generalized Langevin Equation: A One-Dimensional Lattice Model. United States. https://doi.org/10.1007/S10955-017-1927-3
Chu, Weiqi, and Li, Xiantao. Mon . "On the Asymptotic Behavior of the Kernel Function in the Generalized Langevin Equation: A One-Dimensional Lattice Model". United States. https://doi.org/10.1007/S10955-017-1927-3.
@article{osti_22784061,
title = {On the Asymptotic Behavior of the Kernel Function in the Generalized Langevin Equation: A One-Dimensional Lattice Model},
author = {Chu, Weiqi and Li, Xiantao},
abstractNote = {We present some estimates for the memory kernel function in the generalized Langevin equation, derived using the Mori–Zwanzig formalism from a one-dimensional lattice model, in which the particles interactions are through nearest and second nearest neighbors. The kernel function can be explicitly expressed in a matrix form. The analysis focuses on the decay properties, both spatially and temporally, revealing a power-law behavior in both cases. The dependence on the level of coarse-graining is also studied.},
doi = {10.1007/S10955-017-1927-3},
url = {https://www.osti.gov/biblio/22784061}, journal = {Journal of Statistical Physics},
issn = {0022-4715},
number = 2,
volume = 170,
place = {United States},
year = {2018},
month = {1}
}