Langevin dynamics of a heavy particle and orthogonality effects

TL;DR

This paper explores how a heavy particle's Langevin dynamics in a quantum environment are influenced by orthogonality effects, linking scattering matrix properties with dissipation and fluctuations out of equilibrium.

Contribution

It establishes a connection between Anderson orthogonality catastrophe and mesoscopic reaction forces via Loschmidt echo calculations in non-equilibrium conditions.

Findings

Decay of Loschmidt echo relates to fluctuations and dissipation.

Orthogonality effects significantly impact reaction forces.

Different quench protocols affect system dynamics.

Abstract

The dynamics of a classical heavy particle moving in a quantum environment is determined by a Langevin equation which encapsulates the effect of the environment-induced reaction forces on the particle. For an open quantum system these include a Born-Oppenheimer force, a dissipative force and a stochastic force due to shot and thermal noise. Recently it was shown that these forces can be expressed in terms of the scattering matrix of the system by considering the classical heavy particle as a time-dependent scattering center, allowing to demonstrate interesting features of these forces when the system is driven out of equilibrium. At the same time, it is well known that small changes in a scattering potential can have a profound impact on a fermionic system due to the Anderson orthogonality catastrophe. In this work, by calculating the Loschmidt echo, we relate Anderson orthogonality effects with the mesoscopic reaction forces for an environment that can be taken out of equilibrium. In particular we show how the decay of the Loschmidt echo is characterized by fluctuations and dissipation in the system and discuss different quench protocols.