Measurement theory in the Lax-Phillips formalism |
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| Authors: | S. Tasaki E. Eisenberg L. P. Horwitz |
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| Affiliation: | (1) International Solvay Institutes for Physics and Chemistry, Campus Plaine ULB, Boulevard de Triomphe, CP 231, 1050 Brussels, Belgium;(2) Department of Physics, Bar-Ilan University, 52900 Ramat-Gan, Israel;(3) Present address: Institute for Fundamental Chemistry, 34-4 Takano-Nishihiraki-cho, Sakyo-ku, 606 Kyoto, Japan;(4) Institute for Advanced Study, School of Natural Sciences, 08540 Princeton, New Jersey;(5) Present address: School of Physics, Tel Aviv University, Ramat Aviv, Isreal |
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| Abstract: | It is shown that the application of the Lax-Phillips scattering theory to quantum mechanics provides a natural framework for the realization of the ideas of the  Many-Hilbert-Space theory of Machida and Namiki to describe the development of decoherence in the process of measurement. We show that if the quantum mechanical evolution is pointwise in time, then decoherence occurs only if the Hamiltonian is time-dependent. If the evolution is not pointwise in time (as in Liouville space), then the decoherence may occur even for closed systems. These conclusions apply as well to the general problem of mixing of states. |
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