IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v468y2017icp578-589.html
   My bibliography  Save this article

Symmetry of bilinear master equations for a quantum oscillator

Author

Listed:
  • Tay, B.A.

Abstract

We study the most general continuous transformation on the generators of bilinear master equations of a quantum oscillator. We find that transformation operators that preserve the hermiticity of density operators and conserve the probability of reduced dynamics should be adjoint-symmetric, and they are not limited to the pure product of unitary operators in the bra and ket space but could be a mixture of them. We need to include the more general transformation operators to explore the full symmetry of generic reduced dynamics. We discuss how the operators are related to those considered in previous works, and illustrate how they leave the reduced dynamics form invariant, or map one into the other. The positive semidefinite requirement on the density operator can be imposed to give a valid range of transformation parameters.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:468:y:2017:i:c:p:578-589
    DOI: 10.1016/j.physa.2016.10.067
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437116307543
    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.2016.10.067?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. 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.
    2. Petrosky, T. & Prigogine, I. & Tasaki, S., 1991. "Quantum theory of non-integrable systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 173(1), pages 175-242.
    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).
    2. 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.

    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. Zarezadeh Zakarya & Costantini Giovanni, 2019. "Particle diffusion Monte Carlo (PDMC)," Monte Carlo Methods and Applications, De Gruyter, vol. 25(2), pages 121-130, June.
    2. 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).
    3. Kristina Giesel & Michael Kobler, 2022. "An Open Scattering Model in Polymerized Quantum Mechanics," Mathematics, MDPI, vol. 10(22), pages 1-32, November.
    4. 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.
    5. 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.
    6. Antoniou, Ioannis E. & Prigogine, Ilya, 1993. "Intrinsic irreversibility and integrability of dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 192(3), pages 443-464.
    7. 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.
    8. Sudarshan, E.C.G. & Chiu, Charles B. & Bhamathi, G., 1994. "Perturbation theory on generalized quantum mechanical systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 202(3), pages 540-552.
    9. 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).
    10. 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).
    11. 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.
    12. Petrosky, T. & Prigogine, I., 1991. "Alternative formulation of classical and quantum dynamics for non-integrable systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 175(1), pages 146-209.
    13. 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.
    14. Antoniou, I. & Suchanecki, Z. & Laura, R. & Tasaki, S., 1997. "Intrinsic irreversibility of quantum systems with diagonal singularity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 241(3), pages 737-772.
    15. 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.
    16. 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).
    17. 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:468:y:2017:i:c:p:578-589. 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.