Can the Schrodinger dynamics explain measurement?

TL;DR

This paper explores whether Schrödinger dynamics can account for measurement phenomena by modeling Hamiltonians with random matrices, linking quantum chaos to classical measurement behavior and the micro-macro boundary.

Contribution

It demonstrates that Schrödinger evolution with Gaussian unitary ensemble Hamiltonians can model measurement processes and explain classicality and irreversibility.

Findings

Schrödinger evolution models measurement on macro and micro systems.

Derivation of the Born rule from chaotic Hamiltonian dynamics.

Identification of the micro-macro boundary through random matrix theory.

Abstract

The motion of a ball through an appropriate lattice of round obstacles models the behavior of a Brownian particle and can be used to describe measurement on a macro system. On another hand, such motion is chaotic and a known conjecture asserts that the Hamiltonian of the corresponding quantum system must follow the random matrix statistics of an appropriate ensemble. We use the Hamiltonian represented by a random matrix in the Gaussian unitary ensemble to study the Schr\"odinger evolution of non-stationary states. For Gaussian states representing a classical system, the Brownian motion that describes the behavior of the system under measurement is obtained. For general quantum states, the Born rule for the probability of transition between states is derived. It is then shown that the Schr\"odinger evolution with such a Hamiltonian models measurement on macroscopic and microscopic systems, provides an explanation for the classical behavior of macroscopic bodies and for irreversibility of a measurement, and identifies the boundary between micro and macro worlds.