Dissipation and quantization for composite systems

TL;DR

This paper explores how classical Bateman's oscillators can be quantized into a quantum isotonic oscillator, revealing effective magnetic and spin-orbit interactions, and simplifying to independent quantum harmonic oscillators at large separations.

Contribution

It demonstrates a novel method to derive quantum systems from classical oscillators within 't Hooft's quantization framework, including effective magnetic and spin-orbit interactions.

Findings

Classical Bateman's oscillators can be quantized into a quantum isotonic oscillator.

The system exhibits effective magnetic and spin-orbit interactions under certain parameters.

At large separations, the system simplifies to two independent quantum harmonic oscillators.

Abstract

In the framework of 't Hooft's quantization proposal, we show how to obtain from the composite system of two classical Bateman's oscillators a quantum isotonic oscillator. In a specific range of parameters, such a system can be interpreted as a particle in an effective magnetic field, interacting through a spin-orbit interaction term. In the limit of a large separation from the interaction region one can describe the system in terms of two irreducible elementary subsystems which correspond to two independent quantum harmonic oscillators.