The Magnetic Maze: A System With Tunable Scale Invariance

TL;DR

This paper introduces a high-dimensional quantum model with a random magnetic field, revealing a tunable scale-invariant and chaotic behavior at low temperatures, advancing understanding of magnetic systems and quantum chaos.

Contribution

It develops a path integral framework for a charged particle in a random magnetic maze, deriving a novel scale-invariant quantum theory with tunable dynamical and chaos exponents.

Findings

Discovery of a scale-invariant quantum regime with tunable exponents.

Demonstration of chaos with a tunable chaos exponent approaching the bound.

Analytical solutions for dynamics in high-dimensional random magnetic fields.

Abstract

Random magnetic field configurations are ubiquitous in nature. Such fields lead to a variety of dynamical phenomena, including localization and glassy physics in some condensed matter systems and novel transport processes in astrophysical systems. Here we consider the physics of a charged quantum particle moving in a ``magnetic maze'': a high-dimensional space filled with a randomly chosen vector potential and a corresponding magnetic field. We derive a path integral description of the model by introducing appropriate collective variables and integrating out the random vector potential, and we solve for the dynamics in the limit of large dimensionality. We derive and analyze the equations of motion for Euclidean and real-time dynamics, and we calculate out-of-time-order correlators. We show that a special choice of vector potential correlations gives rise, in the low temperature limit, to a novel scale-invariant quantum theory with a tunable dynamical exponent. Moreover, we show that the theory is chaotic with a tunable chaos exponent which approaches the chaos bound at low temperature and strong coupling.