Journal of Mathematical Physics

Local properties of quantum systems

Boris Leaf

Published Jun 1, 1986• 2 citations

Abstract

Local properties of a quantum system are defined as the expectation values of its observables in a microstate of some complete set of commuting observables. An equation for the time evolution of local properties is obtained for any system whose statistical operator (density matrix) evolves by unitary transformation in accordance with the von Neumann equation. The formalism is applied to the example of a system of one particle. In this case the local properties are fields, the time-evolution equation is an equation of continuity with source terms. For constants of motion the source terms vanish, giving equations of continuity for the fields. For each scalar field a flux vector for its transport current is defined. For momentum, a stress tensor is obtained. The effects on local properties of realization of a latent ensemble of the statistical operator (an entropy-increasing mechanism recently proposed to explain approach to equilibrium) are also considered; a non-negative local entropy production is identified, as well as a discontinuous redistribution of local properties among microstates.

DOI: 10.1063/1.527386

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