%0 Journal Article %J Physical Review B %D 2016 %T Flight of a heavy particle nonlinearly coupled to a quantum bath %A Mohammad F. Maghrebi %A Matthias Krüger %A Mehran Kardar %X 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\'{e}vy flights. We suggest condensed matter analogs where similar effects may arise. %B Physical Review B %V 93 %P 014309 %8 2016/01/28 %G eng %U http://arxiv.org/abs/1508.00582 %N 1 %R 10.1103/PhysRevB.93.014309