The Generalized Fibonacci Oscillator as an Open Quantum System

Franco Fagnola; Chul Ki Ko; Hyun Jae Yoo

doi:10.3842/SIGMA.2022.035

The Generalized Fibonacci Oscillator as an Open Quantum System

Franco Fagnola, Chul Ki Ko, Hyun Jae Yoo

University College

Research output: Contribution to journal › Article › peer-review

Abstract

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 β. 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.

Original language	English
Article number	035
Journal	Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
Volume	18
DOIs	https://doi.org/10.3842/SIGMA.2022.035
Publication status	Published - 2022

Bibliographical note

Funding Information:
The work of HJY was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIT) (no. 2020R1F1A101075). FF is a member of GNAM-PA-INdAM Italy. FF first met Michael Schürmann at the conference Quantum Probability and Applications III held in Oberwolfach, January 25–31, 1987, organized by their respective advisors Professors Luigi Accardi and Wilhelm von Waldenfels [30]. Over most of these years he has had the pleasure of meeting him at the annual QP conferences, that nowadays reached the number 42, visiting him in Greifswald, exchange views and follow reports on his scientific work. He would like to congratulate Michael on his retirement and wish him endless happy days with his friends and family.

Funding Information:
The work of HJY was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIT) (no. 2020R1F1A101075). FF is a member of GNAMPA-INdAM Italy. FF first met Michael Schürmann at the conference Quantum Probability and Applications III held in Oberwolfach, January 25–31, 1987, organized by their respective advisors Professors Luigi Accardi and Wilhelm von Waldenfels [30]. Over most of these years he has had the pleasure of meeting him at the annual QP conferences, that nowadays reached the number 42, visiting him in Greifswald, exchange views and follow reports on his scientific work. He would like to congratulate Michael on his retirement and wish him endless happy days with his friends and family.

Publisher Copyright:
© 2022, Institute of Mathematics. All rights reserved.

All Science Journal Classification (ASJC) codes

Analysis
Mathematical Physics
Geometry and Topology

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10.3842/SIGMA.2022.035

Cite this

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abstract = "We consider an open quantum system with Hamiltonian HS whose spectrum is given by a generalized Fibonacci sequence weakly coupled to a Boson reservoir in equilibrium at inverse temperature β. 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 HS.",

author = "Franco Fagnola and Ko, {Chul Ki} and Yoo, {Hyun Jae}",

note = "Funding Information: The work of HJY was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIT) (no. 2020R1F1A101075). FF is a member of GNAM-PA-INdAM Italy. FF first met Michael Sch{\"u}rmann at the conference Quantum Probability and Applications III held in Oberwolfach, January 25–31, 1987, organized by their respective advisors Professors Luigi Accardi and Wilhelm von Waldenfels [30]. Over most of these years he has had the pleasure of meeting him at the annual QP conferences, that nowadays reached the number 42, visiting him in Greifswald, exchange views and follow reports on his scientific work. He would like to congratulate Michael on his retirement and wish him endless happy days with his friends and family. Funding Information: The work of HJY was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIT) (no. 2020R1F1A101075). FF is a member of GNAMPA-INdAM Italy. FF first met Michael Sch{\"u}rmann at the conference Quantum Probability and Applications III held in Oberwolfach, January 25–31, 1987, organized by their respective advisors Professors Luigi Accardi and Wilhelm von Waldenfels [30]. Over most of these years he has had the pleasure of meeting him at the annual QP conferences, that nowadays reached the number 42, visiting him in Greifswald, exchange views and follow reports on his scientific work. He would like to congratulate Michael on his retirement and wish him endless happy days with his friends and family. Publisher Copyright: {\textcopyright} 2022, Institute of Mathematics. All rights reserved.",

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The Generalized Fibonacci Oscillator as an Open Quantum System

Abstract

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