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The Generalized Fibonacci Oscillator as an Open Quantum System
Symmetry, integrability and geometry: methods and applications, Tome 18 (2022) Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider an open quantum system with Hamiltonian $H_S$ whose spectrum is given by a generalized Fibonacci sequence weakly coupled to a Boson reservoir in equilibrium at inverse temperature $\beta$. We find the generator of the reduced system evolution and explicitly compute the stationary state of the system, that turns out to be unique and faithful, in terms of parameters of the model. If the system Hamiltonian is generic we show that convergence towards the invariant state is exponentially fast and compute explicitly the spectral gap for low temperatures, when quantum features of the system are more significant, under an additional assumption on the spectrum of $H_S$.
Keywords: open quantum system, Fibonacci Hamiltonian, deformation of canonical commutation relations, spectral gap, weak-coupling limit, quantum Markov semigroup. 
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     author = {Franco Fagnola and Chul Ki Ko and Hyun Jae Yoo},
     title = {The {Generalized} {Fibonacci} {Oscillator} as an {Open} {Quantum} {System}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2022},
     volume = {18},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2022_18_a34/}
}
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Franco Fagnola; Chul Ki Ko; Hyun Jae Yoo. The Generalized Fibonacci Oscillator as an Open Quantum System. Symmetry, integrability and geometry: methods and applications, Tome 18 (2022). http://geodesic.mathdoc.fr/item/SIGMA_2022_18_a34/

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