Dissipation and quantization

TL;DR

This paper explores how dissipation in classical oscillators relates to quantum phenomena, showing that dissipation manifests as a geometric phase responsible for zero point energy, linking classical and quantum physics.

Contribution

It demonstrates that dissipation acts as a geometric phase leading to quantum features in classical systems, inspired by 't Hooft's proposal on information loss and quantization.

Findings

Dissipation manifests as a geometric phase in classical oscillators.

Dissipation is responsible for zero point energy in quantum spectra.

Thermodynamical features of the system are discussed.

Abstract

We show that the dissipation term in the Hamiltonian for a couple of classical damped-amplified oscillators manifests itself as a geometric phase and is actually responsible for the appearance of the zero point energy in the quantum spectrum of the 1D linear harmonic oscillator. We also discuss the thermodynamical features of the system. Our work has been inspired by 't Hooft proposal according to which information loss in certain classical systems may lead to ``an apparent quantization of the orbits which resembles the quantum structure seen in the real world".