IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v477y2017icp42-64.html
   My bibliography  Save this article

Solutions of generic bilinear master equations for a quantum oscillator—Positive and factorized conditions on stationary states

Author

Listed:
  • Tay, B.A.

Abstract

We obtain the solutions of the generic bilinear master equation for a quantum oscillator with constant coefficients in the Gaussian form. The well-behavedness and positive semidefiniteness of the stationary states could be characterized by a three-dimensional Minkowski vector. By requiring the stationary states to satisfy a factorized condition, we obtain a generic class of master equations that includes the well-known ones and their generalizations, some of which are completely positive. A further subset of the master equations with the Gibbs states as stationary states is also obtained. For master equations with not completely positive generators, an analysis on the stationary states for a given initial state suggests conditions on the coefficients of the master equations that generate positive evolution.

Suggested Citation

  • Tay, B.A., 2017. "Solutions of generic bilinear master equations for a quantum oscillator—Positive and factorized conditions on stationary states," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 477(C), pages 42-64.
    • Handle: RePEc:eee:phsmap:v:477:y:2017:i:c:p:42-64
    DOI: 10.1016/j.physa.2017.02.020
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437117301449
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2017.02.020?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Tameshtit, Allan, 2013. "On the standard quantum Brownian equation and an associated class of non-autonomous master equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(3), pages 427-443.
    2. Caldeira, A.O. & Leggett, A.J., 1983. "Path integral approach to quantum Brownian motion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 121(3), pages 587-616.
    3. Tay, B.A., 2017. "Symmetry of bilinear master equations for a quantum oscillator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 578-589.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Tay, B.A., 2020. "Eigenvalues of the Liouvillians of quantum master equation for a harmonic oscillator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 556(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Tay, B.A., 2020. "Eigenvalues of the Liouvillians of quantum master equation for a harmonic oscillator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 556(C).
    2. Zarezadeh Zakarya & Costantini Giovanni, 2019. "Particle diffusion Monte Carlo (PDMC)," Monte Carlo Methods and Applications, De Gruyter, vol. 25(2), pages 121-130, June.
    3. Tanaka, Shigenori & Umegaki, Toshihito & Nishiyama, Akihiro & Kitoh-Nishioka, Hirotaka, 2022. "Dynamical free energy based model for quantum decision making," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 605(C).
    4. Kristina Giesel & Michael Kobler, 2022. "An Open Scattering Model in Polymerized Quantum Mechanics," Mathematics, MDPI, vol. 10(22), pages 1-32, November.
    5. Jasmina Jekni'c-Dugi'c & Sonja Radi' c & Igor Petrovi'c & Momir Arsenijevi'c & Miroljub Dugi'c, 2018. "Quantum Brownian oscillator for the stock market," Papers 1901.10544, arXiv.org.
    6. Tay, B.A., 2017. "Symmetry of bilinear master equations for a quantum oscillator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 578-589.
    7. Meng, Xiangyi & Zhang, Jian-Wei & Guo, Hong, 2016. "Quantum Brownian motion model for the stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 452(C), pages 281-288.
    8. Ali, Md. Manirul & Dinakaran, Rohith & Radhakrishnan, Chandrashekar, 2023. "Coherence crossover dynamics in the strong coupling regime," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 614(C).
    9. Bhattacharjee, Suraka & Satpathi, Urbashi & Sinha, Supurna, 2022. "Quantum Brownian motion of a charged oscillator in a magnetic field coupled to a heat bath through momentum variables," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 605(C).
    10. Ramírez, J.E. & Herrera, J.N. & Martínez, M.I., 2016. "Getting a stochastic process from a conservative Lagrangian: A first approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 448(C), pages 1-9.
    11. Dorofeyev, Illarion, 2016. "Dynamics of two externally driven coupled quantum oscillators interacting with separate baths based on path integrals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 445(C), pages 200-220.
    12. Saša Nježić & Jasna Radulović & Fatima Živić & Ana Mirić & Živana Jovanović Pešić & Mina Vasković Jovanović & Nenad Grujović, 2022. "Chaotic Model of Brownian Motion in Relation to Drug Delivery Systems Using Ferromagnetic Particles," Mathematics, MDPI, vol. 10(24), pages 1-19, December.
    13. Satpathi, Urbashi & Sinha, Supurna, 2018. "Quantum Brownian motion in a magnetic field: Transition from monotonic to oscillatory behaviour," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 692-701.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:477:y:2017:i:c:p:42-64. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.