We introduce a notion of absorption operators in the context of quantum Markov processes. The absorption problem in invariant domains (enclosures) is treated for a quantum Markov evolution on a separable Hilbert space, both in discrete and continuous times: We define a well-behaving set of positive operators which can correspond to classical absorption probabilities, and we study their basic properties, in general, and with respect to accessibility structure of channels, transience and recurrence. In particular, we can prove that no accessibility is allowed between the null and positive recurrent subspaces. In the case, when the positive recurrent subspace is attractive, ergodic theory will allow us to get additional results, in particular about the description of fixed points.

Carbone, R., Girotti, F. (2021). Absorption in Invariant Domains for Semigroups of Quantum Channels. ANNALES HENRI POINCARE', 22(8), 2497-2530 [10.1007/s00023-021-01016-5].

Absorption in Invariant Domains for Semigroups of Quantum Channels

Girotti F.
2021

Abstract

We introduce a notion of absorption operators in the context of quantum Markov processes. The absorption problem in invariant domains (enclosures) is treated for a quantum Markov evolution on a separable Hilbert space, both in discrete and continuous times: We define a well-behaving set of positive operators which can correspond to classical absorption probabilities, and we study their basic properties, in general, and with respect to accessibility structure of channels, transience and recurrence. In particular, we can prove that no accessibility is allowed between the null and positive recurrent subspaces. In the case, when the positive recurrent subspace is attractive, ergodic theory will allow us to get additional results, in particular about the description of fixed points.
Articolo in rivista - Articolo scientifico
Absorption probabilities; Ergodic theory; Fixed points; Quantum channel; Quantum Markov semigroup; Quantum recurrence;
English
2021
22
8
2497
2530
open
Carbone, R., Girotti, F. (2021). Absorption in Invariant Domains for Semigroups of Quantum Channels. ANNALES HENRI POINCARE', 22(8), 2497-2530 [10.1007/s00023-021-01016-5].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/354316
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