Global minimization via classical tunneling assisted by collective force field formation

TL;DR

This paper introduces a collective tunneling mechanism driven by a Lyapunov force that guides large, complex systems towards their global minimum, with potential applications in physics and optimization.

Contribution

It reveals a novel collective tunneling effect in high-dimensional systems that aids in global minimization, bridging physics and optimization techniques.

Findings

Identifies a collective tunneling mechanism called 'Lyapunov force'.

Demonstrates the mechanism's relevance in nanoscale physics and optimization.

Suggests applications in Monte Carlo methods and machine learning.

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.