Abstract
We investigate properties of a class of quantum stochastic processes subject to a condition of irreducibility. These processes must be recurrent or transient and an equilibrium state can only exist in the former case. Every finite dimensional process is recurrent and it is possible to establish convergence in time to a unique equilibrium state. We study particularly the class of transition processes, which describe photon emissions of simple quantum mechanical systems in excited states.
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Davies, E. B., Lewis, J. T.: An operational approach to quantum probability. Commun. Math. Phys.17, 239–260 (1970).
—— On the repeated measurement of continuous observables in quantum mechanics. To appear in J. Functional Analysis.
—— Quantum stochastic processes. Commun. Math. Phys.15, 277–304 (1969).
Chung, K. L.: Markov chains with stationary transition probabilities. Berlin-Göttingen-Heidelberg: Springer 1960.
Phelps, R. R.: Lectures on Choquet's theorem, 1st edition. Princeton-London-Toronto: van Nostrand, 1966.
Edwards, C. M.: The operational approach to algebraic quantum theory 1. Commun. math. Phys.16, 207–230 (1970).
Kato, T.: Perturbation theory for linear operators. Berlin-Heidelberg-New York: Springer 1966.
Albert, A. A.: Structure of algebras. Am. Math. Soc. Coll. Publ. vol. XXIV, 1st edition (1961).
Neumann, J. von: Mathematical foundations of quantum mechanics, translated from the German edition by R. T. Beyer. Princeton: Princeton Univ. Press 1955.
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Work supported by U.S.A.F. contract number F 44620-67-C-0029.
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Davies, E.B. Quantum stochastic processes II. Commun.Math. Phys. 19, 83–105 (1970). https://doi.org/10.1007/BF01646628
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DOI: https://doi.org/10.1007/BF01646628