Emergence of Classical Dynamics from a Random Matrix Schr\"odinger Model

TL;DR

This paper demonstrates how classical Newtonian dynamics emerge from a quantum Schrödinger model with a random matrix Hamiltonian, explaining the transition from microscopic to macroscopic behavior.

Contribution

It extends previous work by deriving classical dynamics from a quantum model incorporating environmental interactions via random matrices.

Findings

Classical behavior arises from quantum models with random Hamiltonians.

Parameters of the random walk explain microscopic vs. macroscopic differences.

The approach extends derivations of the Born rule to more complex systems.

Abstract

The Newtonian motion of a macroscopic particle is derived from the linear Schr\"odinger equation with a Hamiltonian consisting of the free-particle term and a random Hamiltonian drawn from the Gaussian Unitary Ensemble. The random term models interaction with the environment. We show that the parameters governing the resulting state-space random walk, together with the treatment of experimentally indistinguishable states as equivalence classes, explain the contrasting behavior of microscopic and macroscopic systems. The analysis extends previous work deriving the Born rule for microscopic particles when the free-particle term is negligible.