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The lax-phillips semigroup of the unstable quantum system

  • Lax-Phillips Semigroup
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Irreversibility and Causality Semigroups and Rigged Hilbert Spaces

Part of the book series: Lecture Notes in Physics ((LNP,volume 504-504))

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Abstract

The scattering theory of Lax and Phillips, designed primarily for hyperbolic systems, such as electromagnetic or acoustic waves, is described. The embedding of the quantum theory into this structure, carried out by Flesia and Piron, is reviewed. We show how the density matrix for an effectively pure state can evolve to an effectively mixed state (decoherence) in this framework. Necessary conditions are given for the realization of the relation between the spectrum of the generator of the semigroup and the singularities of the S-matrix (in energy representation). It is shown that these conditions may be met in the Liouville space formulation of quantum evolution, and in the Hilbert space of relativistic quantum theory.

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Author information

Authors and Affiliations

  1. Department of Physics, Bar-Ilan University, 52900, Ramat-Gan, Israel

    E. Eisenberg & L. P. Horwitz

  2. School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences Tel-Aviv University, 69978, Ramat-Aviv, Israel

    L. P. Horwitz & Y. Strauss

Authors
  1. E. Eisenberg
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  2. L. P. Horwitz
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  3. Y. Strauss
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Editor information

Arno Bohm Heinz-Dietrich Doebner Piotr Kielanowski

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© 1998 Springer-Verlag

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Eisenberg, E., Horwitz, L.P., Strauss, Y. (1998). The lax-phillips semigroup of the unstable quantum system. In: Bohm, A., Doebner, HD., Kielanowski, P. (eds) Irreversibility and Causality Semigroups and Rigged Hilbert Spaces. Lecture Notes in Physics, vol 504-504. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0106790

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  • DOI: https://doi.org/10.1007/BFb0106790

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64305-0

  • Online ISBN: 978-3-540-69725-1

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