Structural localization in the classical and quantum Fermi–Pasta–Ulam model

Abstract

We study the statistics of the classical and the quantum Fermi-Pasta-Ulam chain in thermal equilibrium. We construct a numerical scheme that allows us to analyze localization in short chains. The approach is also suited for a structural analysis of arbitrary subsystems of the degrees of freedom, by effectively integrating out the rest of the system. At low temperatures we observe a systematic increase in mobility of the chain when transitioning from classical to quantum mechanics, due to the critical role of dispersion in the latter case. arXiv:1909.13067v1 [quant-ph]

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“…Classic MD simulation has been constructed on the idea of no bond-forming or breaking where Newton's equation of motion is based on the interaction potential for the periodic behavior of a one-dimensional inharmonic chain (Fermi-Pasta-Ulam) and three-dimensional hard-sphere model (Alder-Wainwright) are applied [ 18 ]. In this study, CGMD has been used for the simulation.…”

Introducing Memory in Coarse-Grained Molecular Simulations

“…Amati et al , used the Mori–Zwanzig formalism to study memory effects in the density fluctuations of a Fermi–Pasta–Ulam model, i.e., a linear chain with anharmonic bond potential. The reconstruction technique was based on a series expansion of the numerically calculated ISF.…”

“…85 For detailed discussions, we refer to recent reviews and standard textbooks on related topics such as anomalous transport, 86 molecular hydrodynamics, 80 and memory in glassy systems. 85,87,88 Amati et al 89,90 used the Mori−Zwanzig formalism to study memory effects in the density fluctuations of a Fermi−Pasta− Ulam model, i.e., a linear chain with anharmonic bond potential. The reconstruction technique was based on a series expansion of the numerically calculated ISF.…”