Non-Markovian quantum friction of bright solitons in superfluids

TL;DR

This paper derives a non-Markovian quantum Langevin equation describing the dissipative dynamics of bright solitons in superfluids, revealing the absence of Ohmic friction and resolving causality paradoxes associated with Markovian approximations.

Contribution

It introduces a first-principles derivation of non-Markovian quantum friction for solitons, clarifying the role of inelastic scattering and correcting classical Abraham-Lorentz force analogies.

Findings

No Ohmic friction in integrable systems

Markovian approximation leads to Abraham-Lorentz force

Exact equations resolve causality paradoxes

Abstract

We explore the quantum dynamics of a bright matter-wave soliton in a quasi-one-dimensional bosonic superfluid with attractive interactions. Specifically, we focus on the dissipative forces experienced by the soliton due to its interaction with Bogoliubov excitations. Using the collective coordinate approach and the Keldysh formalism, a Langevin equation of motion for the soliton is derived from the first principle. The equation contains a stochastic Langevin force (associated with quantum noise) and a non-local in time dissipative force, which appears due to inelastic scattering of Bogoliubov quasiparticles off of the moving soliton. It is shown that Ohmic friction (i.e., a term proportional to the soliton's velocity) is absent in the integrable setup. However, the Markovian approximation gives rise to the Abraham-Lorentz force (i.e., a term proportional to the derivative of the soliton's acceleration), which is known from classical electrodynamics of a charged particle interacting with its own radiation. These Abraham-Lorentz equations famously contain a fundamental causality paradox, where the soliton/particle interacts with excitations/radiation originating from future events. We show, however, that the causality paradox is an artifact of the Markovian approximation, and our exact non-Markovian dissipative equations give rise to physical trajectories. We argue that the quantum friction discussed here should be observable in current quantum gas experiments.