Memory in a nonlocally damped oscillator

TL;DR

This paper investigates a novel nonlocal damping model in oscillators, revealing how memory effects influence classical and quantum dynamics and break traditional composition laws.

Contribution

It introduces a new nonlocal damping equation for oscillators, analyzing its classical and quantum properties and demonstrating the breakdown of local composition laws.

Findings

Nonlocal damping induces memory effects in oscillators.

Classical and quantum dynamics are significantly altered by nonlocal damping.

Standard composition laws are violated in the nonlocal system.

Abstract

We analyze the new equation of motion for the damped oscillator. It differs from the standard one by a damping term which is nonlocal in time and hence it gives rise to a system with memory. Both classical and quantum analysis is performed. The characteristic feature of this nonlocal system is that it breaks local composition low for the classical Hamiltonian dynamics and the corresponding quantum propagator.