Quantum friction in the Hydrodynamic Model

TL;DR

This paper investigates quantum friction between a moving atom and a metallic surface modeled by hydrodynamics, revealing a velocity threshold for friction onset and providing quantitative force predictions.

Contribution

It introduces a hydrodynamic model for metals to analyze quantum friction, highlighting a velocity threshold and extending predictions to all perturbation orders.

Findings

Quantum friction exists without intrinsic damping in the metal.

Friction only occurs when atom velocity exceeds the metal's effective sound speed.

Threshold behavior persists at all perturbation orders.

Abstract

We study the phenomenon of quantum friction in a system consisting of a polarizable atom moving at a constant speed parallel to a metallic plate. The metal is described using a charged hydrodynamic model for the electrons. This model featuring long-range interactions is appropriate for a clean metal in a temperature range where scattering due to Coulomb interactions dominates over the scattering of electron by impurities. We find that a quantum friction force between the atom and the metal surface exists even in the absence of intrinsic damping in the metal, but that it only starts once the velocity of the atom exceeds the effective speed of sound in the metal. We argue that this condition can be fulfilled most easily in metals with nearly empty or nearly filled bands. We make quantitative predictions for the friction force to the second and fourth order in the atomic polarizability, and show that the threshold behavior persists to all orders of the perturbation theory.