Stability Characteristics of 1-Dimensional Quantum Lattices Featuring Nonstandard Potentials

Our investigation focuses on the behavior of two distinct 1D quantum lattices, where particle interactions stem from nonstandard potential frameworks. One model incorporates a "graphene-like" interaction profile, while the other mirrors Hollomon's law, capturing "strain-hardening" phenomena observed in select elastic substances. While parallels to conventional analytical cases are evident, significant divergences emerge—particularly regarding local and global stability traits absent in polynomial-based systems such as 1D Fermi-Pasta-Ulam-Tsingou (FPUT) lattices. By examining motion near fundamental periodic orbits as system size (NN) and energy (EE) expand, we observe striking outcomes: the graphene-inspired configuration maintains robustness until reaching energy thresholds triggering collapse, whereas the Hollomon variant remains perpetually stable yet vulnerable at reduced energy levels, stabilizing exclusively when harmonic forces prevail. These findings, validated for substantial NN values, prompt further inquiry into analogous patterns within continuum mechanics, where 1D structures evolve into string-like entities.

Authors: Oikonomou, T. and collaborators

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• #Engineering and Computer Science

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