On Singular Perturbations of Quantum Dynamical Semigroups
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We consider two examples of quantum dynamical semigroups obtained by singular perturbations of a standard generator which are special case of unbounded completely positive perturbations studied in detail in . In Sec. 2, we propose a generalization of an example in  aimed to give a positive answer to a conjecture of Arveson. In Sec. 3 we consider in greater detail an improved and simplified construction of a nonstandard dynamical semigroup outlined in our short communication .
Keywordsquantum dynamical semigroup singular perturbation nonstandard generator
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- 4.A. M. Chebotarev, Lectures on Quantum Probability, Sociedad Matematica Mexicana, Textos 14, Mexico 2000.Google Scholar
- 13.M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vol. 2: Fourier Analysis and Self-Adjointness (Academic Press, New York, 1975; Mir, Moscow, 1978).Google Scholar
- 16.S. Alazzawi and B. Baumgartner, Generalized Kraus Operators and Generators of Quantum Dynamical Semigroups, arXiv:1306.4531.Google Scholar
- 17.S. M. Nikol’sky, “Approximation of Functions of Several Variables and Embedding Theorems,” Nauka, Moscow 1977, Sec. 4.1.Google Scholar
- 18.V. S. Vladimirov, Equations ofMathematical Physics, 5th ed. (Nauka, Moscow, 1988).Google Scholar