Flight of a heavy particle nonlinearly coupled to a quantum bath

TL;DR

This paper explores how a heavy particle nonlinearly coupled to a quantum bath exhibits anomalous diffusion, differing from traditional linear coupling models, with potential implications for condensed matter systems.

Contribution

It introduces a model of a heavy particle quadratically coupled to a quantum bath, revealing fundamentally different diffusion behavior from linear coupling scenarios.

Findings

Particle undergoes anomalous, power-law diffusion.

Nonlinear coupling leads to behavior akin to Lévy flights.

Potential condensed matter analogs suggested.

Abstract

Fluctuation and dissipation are by-products of coupling to the `environment.' The Caldeira-Leggett model, a successful paradigm of quantum Brownian motion, views the environment as a collection of harmonic oscillators linearly coupled to the system. However, symmetry considerations may forbid a linear coupling, e.g. for a neutral particle in quantum electrodynamics. We argue that nonlinear couplings can lead to a fundamentally different behavior. Specifically, we consider a heavy particle quadratically coupled to quantum fluctuations of the bath. In one dimension the particle undergoes anomalous diffusion, unfolding as a power-law distribution in space, reminiscent of L\'evy flights. We suggest condensed matter analogs where similar effects may arise.