Resonant states and classical damping

TL;DR

This paper demonstrates that classical damping can be understood through resonant states of Koopman's operator, revealing discrete complex spectra in simple damped systems and providing a new spectral perspective on classical dissipation.

Contribution

It introduces a novel interpretation of classical damping as resonant states of Koopman's operator, linking spectral theory with classical dissipative systems.

Findings

Classical damping corresponds to resonant states of Koopman's operator.

Simple damped systems exhibit discrete complex spectra.

Generalized eigenvectors can be viewed as classical resonant states.

Abstract

Using Koopman's approach to classical dynamical systems we show that the classical damping may be interpreted as appearance of resonant states of the corresponding Koopman's operator. It turns out that simple classical damped systems give rise to discrete complex spectra. Therefore, the corresponding generalized eigenvectors may be interpreted as classical resonant states.