# Zeno Friction and Anti-friction from Quantum Collision Models

## TL;DR

This paper models quantum friction using collision models, revealing a $1/v$ decay at high velocities, and explores conditions for anti-friction phenomena where the system accelerates due to surface interactions.

## Contribution

It introduces quantum collision models to analyze friction, deriving velocity-dependent friction behavior and conditions for anti-friction effects in quantum systems.

## Key findings

- Friction decreases as 1/v at high velocities.
- Analytic expressions for friction-velocity dependence are obtained.
- Anti-friction phenomena are theoretically possible in quantum systems.

## Abstract

We analyze the quantum mechanics of the friction experienced by a small system as it moves non-destructively with velocity $v$ over a surface. Specifically, we model the interactions between the system and the surface with a \textit{collision model}. We show that, under weak assumptions, the magnitude of the friction induced by this interaction decreases as $1/v$ for large velocities. Specifically, we predict that this phenomenon occurs in the Zeno regime, where each of the system's successive couplings to subsystems of the surface is very brief. In order to investigate the friction at low velocities and with velocity-dependent coupling strengths, we motivate and develop \textit{one-dimensional convex collision models}. Within these models, we obtain an analytic expression for the general friction-velocity dependence. We are thus able to determine exactly the conditions under which the usual friction-velocity dependency arises. Finally, we give examples that demonstrate the possibility, in principle, of anti-friction, in which case the system is accelerated by its interaction with the surface, a phenomenon associated with active materials and inverted level populations.