On the Asymptotic Behavior of the Kernel Function in the Generalized Langevin Equation: A One-dimensional lattice model
Provides theoretical insights into memory kernel behavior for lattice models, but is incremental as it extends known Mori-Zwanzig formalism to a specific interaction setup.
The paper derives explicit estimates for the memory kernel in the generalized Langevin equation from a 1D lattice model, showing power-law decay in space and time and analyzing coarse-graining effects.
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.