Evolution of Pure States into Mixed States

Abstract

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