Decoherence of quantum Markov semigroups

Rolando Rebolledo

Displaying similar documents to “Decoherence of quantum Markov semigroups”

Stochastic Dynamics of Quantum Spin Systems

Adam Majewski, Robert Olkiewicz, Bogusław Zegarliński (1998)

Banach Center Publications

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We show that recently introduced noncommutative $L_{p}$ -spaces can be used to constructions of Markov semigroups for quantum systems on a lattice.

On two quantum versions of the detailed balance condition

Franco Fagnola, Veronica Umanità (2010)

Banach Center Publications

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Quantum detailed balance conditions are often formulated as relationships between the generator of a quantum Markov semigroup and the generator of a dual semigroup with respect to a certain scalar product defined by an invariant state. In this paper we survey some results describing the structure of norm continuous quantum Markov semigroups on ℬ(h) satisfying a quantum detailed balance condition when the duality is defined by means of pre-scalar products on ℬ(h) of the form $⟨ x, y ⟩_{s} : = t r (ρ^{1 - s} x * ρ^{s} y)$ (s ∈ [0,1])...

On the transient and recurrent parts of a quantum Markov semigroup

Veronica Umanità (2006)

Banach Center Publications

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We define the transient and recurrent parts of a quantum Markov semigroup 𝓣 on a von Neumann algebra 𝓐 and we show that, when 𝓐 is σ-finite, we can write 𝓣 as the sum of such semigroups. Moreover, if 𝓣 is the countable direct sum of irreducible semigroups each with a unique faithful normal invariant state ρₙ, we find conditions under which any normal invariant state is a convex combination of ρₙ's.

A complete description of dynamics generated by birth-and-death problem: a semigroup approach

Jacek Banasiak (2003)

Banach Center Publications

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We shall present necessary and sufficient conditions for both conservativity and uniqueness of solutions to birth-and-death system of equations using methods of semigroup theory. The derived conditions correspond to the uniqueness criteria for forward and backward birth-and-death systems due to Reuter, [10,11,1], that were derived in a different context by Markov processes' techniques.

Some Analytical Results on the Ornstein-Uhlenbeck Semigroup in Infinitely Many Dimensions

P. A. Meyer (1982)

Recherche Coopérative sur Programme n°25

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On analyticity of Ornstein-Uhlenbeck semigroups

Beniamin Goldys (1999)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Let $(R_{t}$ be a transition semigroup of the Hilbert space-valued nonsymmetric Ornstein-Uhlenbeck process and let $μ$ denote its Gaussian invariant measure. We show that the semigroup $(R_{t}$ is analytic in $L^{2} (μ)$ if and only if its generator is variational. In particular, we show that the transition semigroup of a finite dimensional Ornstein-Uhlenbeck process is analytic if and only if the Wiener process is nondegenerate.

m-Semigroups, semigroups, and function representations

D. Monk, F. Sioson (1966)

Fundamenta Mathematicae

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On the relationship between the reversibility of dynamics and balance conditions

W. A. Majewski (1983)

Annales de l'I.H.P. Physique théorique

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On existence of the identity element in a semigroup

S. Lajos (1965)

Matematički Vesnik

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$A$ -systems

R. Gorton (1976)

Compositio Mathematica

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Wreath product of a semigroup and a Γ-semigroup

Mridul K. Sen, Sumanta Chattopadhyay (2008)

Discussiones Mathematicae - General Algebra and Applications

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Let S = {a,b,c,...} and Γ = {α,β,γ,...} be two nonempty sets. S is called a Γ -semigroup if aαb ∈ S, for all α ∈ Γ and a,b ∈ S and (aαb)βc = aα(bβc), for all a,b,c ∈ S and for all α,β ∈ Γ. In this paper we study the semidirect product of a semigroup and a Γ-semigroup. We also introduce the notion of wreath product of a semigroup and a Γ-semigroup and investigate some interesting properties of this product.