A Fixed Point Result for Environment-Induced Semigroups

Based on the environment induced semigroup approach to the quantum measurement process, we show that a certain class of these semigroups, referred to as contractive uniformly \(k\)-Lipschitzian semigroups, exhibit a fixed point property. With regard to the quantum measurement problem, semigroups of...

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Bibliographic Details
Published inarXiv.org
Main Author Lisewski, A M
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 30.11.2002
Subjects
Semigroups
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Summary:Based on the environment induced semigroup approach to the quantum measurement process, we show that a certain class of these semigroups, referred to as contractive uniformly \(k\)-Lipschitzian semigroups, exhibit a fixed point property. With regard to the quantum measurement problem, semigroups of this kind ensure decoherence and the selection of a single state from the familiy of pointer states. In fact, the common fixed point is the selected state.
ISSN:2331-8422