Quantum Friction near the Instability Threshold

TL;DR

This paper develops an analytical framework to understand quantum friction near instability thresholds, revealing a logarithmic divergence of frictional forces as the system approaches criticality, supported by numerical verification.

Contribution

It provides the first analytical proof of quantum friction divergence at the instability threshold, bridging quantum and classical regimes.

Findings

Quantum friction force diverges logarithmically near the instability threshold.

Analytical expressions for friction in stable and near-critical regimes.

Numerical simulations confirm the analytical divergence behavior.

Abstract

In this work, we develop an analytical framework to understand quantum friction across distinct stability regimes, providing approximate expressions for frictional forces both in the deep stable regime and near the critical threshold of instability. Our primary finding is analytical proof that, near the instability threshold, the quantum friction force diverges logarithmically. This result, verified through numerical simulations, sheds light on the behavior of frictional instabilities as the system approaches criticality. Our findings offer new insights into the role of instabilities, critical divergence and temperature in frictional dynamics across quantum and classical regimes.