Evolution of Pure States into Mixed States

TL;DR

This paper develops evolution equations for quantum density matrices that transform pure states into mixed states while maintaining physical properties, offering a novel approach to quantum state evolution.

Contribution

It introduces new evolution equations for density matrices that do not commute with the Hamiltonian, enabling pure states to evolve into mixed states while preserving key physical properties.

Findings

Equations preserve normalization and positivity of density matrices.

Evolution equations conserve energy.

The approach differs from systems with random sources.

Abstract

In the formulation of Banks, Peskin and Susskind, we show that one can construct evolution equations for the quantum mechanical density matrix $\rho$ with operators which do not commute with hamiltonian which evolve pure states into mixed states, preserve the normalization and positivity of $\rho$ and conserve energy. Furthermore, it seems to be different from a quantum mechanical system with random sources.