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Zeitschrift für Naturforschung A

On Energy Differences in Many Body Systems

Eberhard E. Müller, Wolfgang Feist

Published Dec 1, 1983• 0 citations
Publisher

Abstract

Abstract Number-and operator-valued energy differences in von Neumann algebras are discussed by means of the Tomita-Takesaki theory. Small energy differences can be evaluated by the anti-commutator of a sort of relative entropy operator and the energy operator. The New-Tamm-Dancoff procedure is studied in terms of the standard form.
DOI
10.1515/zna-1983-1202

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The quantum entanglement measure of concurrence is shown to be directly calculable from a Tomita- Takesaki modular operator framework constructed from the local von Neumann algebras of observables for two quantum systems. Specifically, the Tomita-Takesaki modular conjugation operator JJJ that links two separate systems with respect to their von Neumann algebras is related to the quantum concurrence CCC of a pure bivariate entangled state composed from these systems. This concurrence relation provides a direct physical meaning to JJJ as both a symmetry operator and a quantitative measure of entanglement. This procedure is then demonstrated for a supersymmetric quantum mechanical system and a real scalar field interacting with two entangled spin-12\frac{1}{2}21​ Unruh-DeWitt qubit detectors. For the latter system, the concurrence result is shown to be consistent with some known results on the Bell-CHSH inequality for such a system.