Time evolution of a pair of distinguishable interacting spins subjected to controllable and noisy magnetic fields

R. Grimaudo, Yu Belousov, Hiromichi Nakazato, A. Messina

    Research output: Contribution to journalArticle

    6 Citations (Scopus)

    Abstract

    The quantum dynamics of a Jˆ2=(jˆ1+jˆ2)2-conserving Hamiltonian model describing two coupled spins jˆ1 and jˆ2 under controllable and fluctuating time-dependent magnetic fields is investigated. Each eigenspace of Jˆ2 is dynamically invariant and the Hamiltonian of the total system restricted to any one of such (j1+j2)−|j1−j2|+1 eigenspaces, possesses the SU(2) structure of the Hamiltonian of a single fictitious spin acted upon by the total magnetic field. We show that such a reducibility holds regardless of the time dependence of the externally applied field as well as of the statistical properties of the noise, here represented as a classical fluctuating magnetic field. The time evolution of the joint transition probabilities of the two spins jˆ1 and jˆ2 between two prefixed factorized states is examined, bringing to light peculiar dynamical properties of the system under scrutiny. When the noise-induced non-unitary dynamics of the two coupled spins is properly taken into account, analytical expressions for the joint Landau–Zener transition probabilities are reported. The possibility of extending the applicability of our results to other time-dependent spin models is pointed out.

    Original languageEnglish
    Pages (from-to)242-259
    Number of pages18
    JournalAnnals of Physics
    Volume392
    DOIs
    Publication statusPublished - 2018 May 1

    Fingerprint

    magnetic fields
    transition probabilities
    time dependence

    Keywords

    • Fluctuation and noise
    • Isotropic Heisenberg interaction
    • Quantum spin models

    ASJC Scopus subject areas

    • Physics and Astronomy(all)

    Cite this

    Time evolution of a pair of distinguishable interacting spins subjected to controllable and noisy magnetic fields. / Grimaudo, R.; Belousov, Yu; Nakazato, Hiromichi; Messina, A.

    In: Annals of Physics, Vol. 392, 01.05.2018, p. 242-259.

    Research output: Contribution to journalArticle

    @article{2b50c3d505d84269871602e1b71224f0,
    title = "Time evolution of a pair of distinguishable interacting spins subjected to controllable and noisy magnetic fields",
    abstract = "The quantum dynamics of a Jˆ2=(jˆ1+jˆ2)2-conserving Hamiltonian model describing two coupled spins jˆ1 and jˆ2 under controllable and fluctuating time-dependent magnetic fields is investigated. Each eigenspace of Jˆ2 is dynamically invariant and the Hamiltonian of the total system restricted to any one of such (j1+j2)−|j1−j2|+1 eigenspaces, possesses the SU(2) structure of the Hamiltonian of a single fictitious spin acted upon by the total magnetic field. We show that such a reducibility holds regardless of the time dependence of the externally applied field as well as of the statistical properties of the noise, here represented as a classical fluctuating magnetic field. The time evolution of the joint transition probabilities of the two spins jˆ1 and jˆ2 between two prefixed factorized states is examined, bringing to light peculiar dynamical properties of the system under scrutiny. When the noise-induced non-unitary dynamics of the two coupled spins is properly taken into account, analytical expressions for the joint Landau–Zener transition probabilities are reported. The possibility of extending the applicability of our results to other time-dependent spin models is pointed out.",
    keywords = "Fluctuation and noise, Isotropic Heisenberg interaction, Quantum spin models",
    author = "R. Grimaudo and Yu Belousov and Hiromichi Nakazato and A. Messina",
    year = "2018",
    month = "5",
    day = "1",
    doi = "10.1016/j.aop.2018.03.012",
    language = "English",
    volume = "392",
    pages = "242--259",
    journal = "Annals of Physics",
    issn = "0003-4916",
    publisher = "Academic Press Inc.",

    }

    TY - JOUR

    T1 - Time evolution of a pair of distinguishable interacting spins subjected to controllable and noisy magnetic fields

    AU - Grimaudo, R.

    AU - Belousov, Yu

    AU - Nakazato, Hiromichi

    AU - Messina, A.

    PY - 2018/5/1

    Y1 - 2018/5/1

    N2 - The quantum dynamics of a Jˆ2=(jˆ1+jˆ2)2-conserving Hamiltonian model describing two coupled spins jˆ1 and jˆ2 under controllable and fluctuating time-dependent magnetic fields is investigated. Each eigenspace of Jˆ2 is dynamically invariant and the Hamiltonian of the total system restricted to any one of such (j1+j2)−|j1−j2|+1 eigenspaces, possesses the SU(2) structure of the Hamiltonian of a single fictitious spin acted upon by the total magnetic field. We show that such a reducibility holds regardless of the time dependence of the externally applied field as well as of the statistical properties of the noise, here represented as a classical fluctuating magnetic field. The time evolution of the joint transition probabilities of the two spins jˆ1 and jˆ2 between two prefixed factorized states is examined, bringing to light peculiar dynamical properties of the system under scrutiny. When the noise-induced non-unitary dynamics of the two coupled spins is properly taken into account, analytical expressions for the joint Landau–Zener transition probabilities are reported. The possibility of extending the applicability of our results to other time-dependent spin models is pointed out.

    AB - The quantum dynamics of a Jˆ2=(jˆ1+jˆ2)2-conserving Hamiltonian model describing two coupled spins jˆ1 and jˆ2 under controllable and fluctuating time-dependent magnetic fields is investigated. Each eigenspace of Jˆ2 is dynamically invariant and the Hamiltonian of the total system restricted to any one of such (j1+j2)−|j1−j2|+1 eigenspaces, possesses the SU(2) structure of the Hamiltonian of a single fictitious spin acted upon by the total magnetic field. We show that such a reducibility holds regardless of the time dependence of the externally applied field as well as of the statistical properties of the noise, here represented as a classical fluctuating magnetic field. The time evolution of the joint transition probabilities of the two spins jˆ1 and jˆ2 between two prefixed factorized states is examined, bringing to light peculiar dynamical properties of the system under scrutiny. When the noise-induced non-unitary dynamics of the two coupled spins is properly taken into account, analytical expressions for the joint Landau–Zener transition probabilities are reported. The possibility of extending the applicability of our results to other time-dependent spin models is pointed out.

    KW - Fluctuation and noise

    KW - Isotropic Heisenberg interaction

    KW - Quantum spin models

    UR - http://www.scopus.com/inward/record.url?scp=85044921357&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=85044921357&partnerID=8YFLogxK

    U2 - 10.1016/j.aop.2018.03.012

    DO - 10.1016/j.aop.2018.03.012

    M3 - Article

    AN - SCOPUS:85044921357

    VL - 392

    SP - 242

    EP - 259

    JO - Annals of Physics

    JF - Annals of Physics

    SN - 0003-4916

    ER -