Flight of a heavy particle nonlinearly coupled to a quantum bath

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 Lévy flights. We suggest condensed matter analogs where similar effects may arise.

Introduction expanded. Appendices added

References in corpus (2)

• Quantum Breathing of an Impurity in a One-dimensional Bath of Interacting Bosons
• Decoherence and Quantum Walks: anomalous diffusion and ballistic tails

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