Entanglement and the factorization-approximation |
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Authors: | J Gemmer G Mahler |
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Institution: | Institut für Theoretische Physik, Universit?t Stuttgart, Pfaffenwaldring 57, 70550 Stuttgart, Germany, DE
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Abstract: | For a bi-partite quantum system defined in a finite dimensional Hilbert-space we investigate in what sense entanglement change
and interactions imply each other. For this purpose we introduce an entanglement-operator, which is then shown to represent
a non-conserved property for any bi-partite system and any type of interaction. This general relation does not exclude the
existence of special initial product states, for which the entanglement remains small over some period of time, despite interactions.
For this case we derive an approximation to the full Schr?dinger-equation, which allows the treatment of the composite systems
in terms of product states. The induced error is estimated. In this factorization-approximation one subsystem appears as an
effective potential for the other. A pertinent example is the Jaynes-Cummings model, which then reduces to the semi-classical
rotating wave approximation.
Received 8 June 2001 |
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