System of classical nonlinear oscillators as a coarse-grained quantum system

TL;DR

This paper develops a coarse-grained quantum description of nonlinear oscillators using constrained Hamiltonian dynamics, showing how classical behavior emerges from quantum fluctuations at large scales.

Contribution

It introduces a novel mathematical framework for coarse-graining quantum nonlinear oscillators, linking quantum fluctuations to classical dynamics.

Findings

Quantum fluctuations are preserved in the coarse-grained description.

Classical behavior emerges at large scales due to minimal quantum fluctuations.

The approach provides a new way to understand quantum-to-classical transition.

Abstract

Constrained Hamiltonian dynamics of a quantum system of nonlinear oscillators is used to provide the mathematical formulation of a coarse-grained description of the quantum system. It is seen that the evolution of the coarse-grained system preserves constant and minimal quantum fluctuations of the fundamental observables. This leads to the emergence of the corresponding classical system on a sufficiently large scale.