Global minimization via classical tunneling assisted by collective force field formation
Abstract
Simple dynamical models can produce intricate behaviors in large networks. These behaviors can often be observed in a wide variety of physical systems captured by the network of interactions. Here we describe a phenomenon where the increase of dimensions self-consistently generates a force field due to dynamical instabilities. This can be understood as an unstable ("rumbling") tunneling mechanism between minima in an effective potential. We dub this collective and nonperturbative effect a "Lyapunov force" which steers the system towards the global minimum of the potential function, even if the full system has a constellation of equilibrium points growing exponentially with the system size. The system we study has a simple mapping to a flow network, equivalent to current-driven memristors. The mechanism is appealing for its physical relevance in nanoscale physics, and to possible applications in optimization, novel Monte Carlo schemes and machine learning.
Cite
@article{arxiv.2102.03385,
title = {Global minimization via classical tunneling assisted by collective force field formation},
author = {Francesco Caravelli and Forrest C. Sheldon and Fabio L. Traversa},
journal= {arXiv preprint arXiv:2102.03385},
year = {2022}
}
Comments
8 pages double column + 7 supplementary ; 8 figures