Markovian properties of the spin-boson model
Dhahri, Ameur (2009), Markovian properties of the spin-boson model, in Donati-Martin, Catherine; Emery, Michel; Rouault, Alain; Stricker, Christophe, Séminaire de Probabilités XLII, Springer : Berlin, p. 397-432. http://dx.doi.org/10.1007/978-3-642-01763-6_15
Book titleSéminaire de Probabilités XLII
Book authorDonati-Martin, Catherine; Emery, Michel; Rouault, Alain; Stricker, Christophe
Number of pages449
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Abstract (EN)We systematically compare the Hamiltonian and Markovian approaches of quantum open system theory, in the case of the spin-boson model. We first give a complete proof of the weak coupling limit and we compute the Lindblad generator of this model. We study properties of the associated quantum master equation such as decoherence, detailed quantum balance and return to equilibrium at inverse temperature 0 < β ≤ ∞. We further study the associated quantum Langevin equation, its associated interaction Hamiltonian. We finally give a quantum repeated interaction model describing the spin‐boson system where the associated Markovian properties are satisfied without any assumption.
Subjects / KeywordsMarkovian approach; Hamiltonian approach; quantum open system theory
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