Effective Long-distance Interaction from Short-distance Interaction in Periodically Driven One-dimensional Classical System

TL;DR

This paper demonstrates that in a periodically driven 1D classical system, short-distance interactions can be effectively transformed into long-distance interactions in phase space using the rotating wave approximation, revealing new interaction dynamics.

Contribution

The study introduces a method to map short-distance 1D interactions to long-distance 2D phase space interactions via RWA, providing new insights into driven classical many-body systems.

Findings

Short-distance interactions become long-distance in phase space under RWA

Fast oscillations act as force carriers enabling extended interactions

Effective interactions depend on phase space distance rather than real space

Abstract

We study the classical dynamics of many interacting particles in a periodically driven one-dimensional (1D) system. We show that under the rotating wave approximation (RWA), a short-distance 1D interaction ($\delta$ function or hard-core interaction), becomes a long-distance two-dimensional (2D) interaction which only depends on the distance in the phase space of the rotating frame. The RWA interaction describes the effect of the interaction on the slowly changing amplitude and phase of the oscillating particles, while the fast oscillations take on the role of a force carrier, which allows for interaction over much larger effective distances.