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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.

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Acknowledgements

This research was supported by NSF under Grants DMS-1522617 and DMS-1619661.

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  1. The Pennsylvania State University, University Park, PA, USA

    Weiqi Chu & Xiantao Li

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  1. Weiqi Chu
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Chu, W., Li, X. On the Asymptotic Behavior of the Kernel Function in the Generalized Langevin Equation: A One-Dimensional Lattice Model. J Stat Phys 170, 378–398 (2018). https://doi.org/10.1007/s10955-017-1927-3

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