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

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.

We make sufficient changes compared to version 2. Here, we focus on the classical dynamics and extend the paper. We add new numerical simulation results to this version

References in corpus (9)

• Many-Body Physics with Ultracold Gases
• Tunable gauge potential for neutral and spinless particles in driven lattices
• Irradiated graphene as a tunable Floquet topological insulator
• Scattering Theory for Floquet-Bloch States
• Analytical solutions for the dynamics of two trapped interacting ultracold atoms
• Pairing in a system of a few attractive fermions in a harmonic trap
• Many interacting fermions in a one-dimensional harmonic trap: a quantum-chemical treatment
• Transverse collisional instabilities of a Bose-Einstein condensate in a driven one-dimensional lattice
• Emission spectrum of the driven nonlinear oscillator

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