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

doi:https://doi.org/10.1007/S10955-017-1927-3

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

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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:

Chu, Weiqi; Li, Xiantao ^[1]

The Pennsylvania State University (United States)

Publication Date:: 2018-01-15

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.

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                    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

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                    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.

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@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}

}

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