Macroscopic limit of quantum systems

TL;DR

This paper demonstrates how classical physics emerges from quantum mechanics in the macroscopic limit using a quantum central limit theorem, showing classical trajectories arise from large quantum systems.

Contribution

It introduces a quantum central limit theorem for observables, elucidating the transition from quantum to classical behavior in macroscopic systems.

Findings

Classical trajectories emerge from quantum systems in the macroscopic limit.

The quantum central limit theorem is derived for observables and expectation values.

Classical laws are practically recovered due to the large number of particles.

Abstract

Classical physics is approached from quantum mechanics in the macroscopic limit. The technical device to achieve this goal is the quantum version of the central limit theorem, derived for an observable at a given time and for the time-dependent expectation value of the coordinate. The emergence of the classical trajectory can be followed for the average of an observable over a large set of independent microscopical systems, and the deterministic classical laws can be recovered in all practical purposes, owing to the largeness of Avogadro's number. This result refers to the observed system without considering the measuring apparatus. The emergence of a classical trajectory is followed qualitatively in Wilson's cloud chamber.