Breatherlike excitations in discrete lattices with noise and nonlinear damping

Peter Leth Christiansen, Yuri B. Gaididei, Magnus Johansson, Kim Rasmussen

    Research output: Contribution to journalJournal articleResearchpeer-review

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    Abstract

    We discuss the stability of highly localized, ''breatherlike,'' excitations in discrete nonlinear lattices under the influence of thermal fluctuations. The particular model considered is the discrete nonlinear Schrodinger equation in the regime of high nonlinearity, where temperature effects are included as multiplicative white noise and nonlinear damping. Numerical analysis shows that the lifetime of the breather is always finite and, in a large parameter regime, inversely proportional to the noise variance for fixed damping and nonlinearity. We also find that the decay rate of the breather decreases with increasing nonlinearity and with increasing damping. Using a collective-coordinate approximation, we show how the qualitative features of the numerical results can be analytically understood. Finally, in the dimer case we show that the multiplicative noise can be transformed into additive noise, and an exact stationary solution to the Fokker-Planck equation is obtained. From this solution, the dimer system is found to exhibit a noise (temperature) induced phase transition.
    Original languageEnglish
    JournalPhysical Review B
    Volume55
    Issue number9
    Pages (from-to)5759-5766
    ISSN2469-9950
    DOIs
    Publication statusPublished - 1997

    Bibliographical note

    Copyright (1997) American Physical Society.

    Keywords

    • SYSTEMS
    • DIMER
    • SCHRODINGER-EQUATION
    • EXISTENCE
    • HAMILTONIAN LATTICES
    • SOLITONS
    • DYNAMICS
    • TIME EVOLUTION
    • TEMPERATURE
    • LOCALIZED EXCITATIONS

    Cite this

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    title = "Breatherlike excitations in discrete lattices with noise and nonlinear damping",
    abstract = "We discuss the stability of highly localized, ''breatherlike,'' excitations in discrete nonlinear lattices under the influence of thermal fluctuations. The particular model considered is the discrete nonlinear Schrodinger equation in the regime of high nonlinearity, where temperature effects are included as multiplicative white noise and nonlinear damping. Numerical analysis shows that the lifetime of the breather is always finite and, in a large parameter regime, inversely proportional to the noise variance for fixed damping and nonlinearity. We also find that the decay rate of the breather decreases with increasing nonlinearity and with increasing damping. Using a collective-coordinate approximation, we show how the qualitative features of the numerical results can be analytically understood. Finally, in the dimer case we show that the multiplicative noise can be transformed into additive noise, and an exact stationary solution to the Fokker-Planck equation is obtained. From this solution, the dimer system is found to exhibit a noise (temperature) induced phase transition.",
    keywords = "SYSTEMS, DIMER, SCHRODINGER-EQUATION, EXISTENCE, HAMILTONIAN LATTICES, SOLITONS, DYNAMICS, TIME EVOLUTION, TEMPERATURE, LOCALIZED EXCITATIONS",
    author = "Christiansen, {Peter Leth} and Gaididei, {Yuri B.} and Magnus Johansson and Kim Rasmussen",
    note = "Copyright (1997) American Physical Society.",
    year = "1997",
    doi = "10.1103/PhysRevB.55.5759",
    language = "English",
    volume = "55",
    pages = "5759--5766",
    journal = "Physical Review B (Condensed Matter and Materials Physics)",
    issn = "1098-0121",
    publisher = "American Physical Society",
    number = "9",

    }

    Breatherlike excitations in discrete lattices with noise and nonlinear damping. / Christiansen, Peter Leth; Gaididei, Yuri B.; Johansson, Magnus; Rasmussen, Kim.

    In: Physical Review B, Vol. 55, No. 9, 1997, p. 5759-5766.

    Research output: Contribution to journalJournal articleResearchpeer-review

    TY - JOUR

    T1 - Breatherlike excitations in discrete lattices with noise and nonlinear damping

    AU - Christiansen, Peter Leth

    AU - Gaididei, Yuri B.

    AU - Johansson, Magnus

    AU - Rasmussen, Kim

    N1 - Copyright (1997) American Physical Society.

    PY - 1997

    Y1 - 1997

    N2 - We discuss the stability of highly localized, ''breatherlike,'' excitations in discrete nonlinear lattices under the influence of thermal fluctuations. The particular model considered is the discrete nonlinear Schrodinger equation in the regime of high nonlinearity, where temperature effects are included as multiplicative white noise and nonlinear damping. Numerical analysis shows that the lifetime of the breather is always finite and, in a large parameter regime, inversely proportional to the noise variance for fixed damping and nonlinearity. We also find that the decay rate of the breather decreases with increasing nonlinearity and with increasing damping. Using a collective-coordinate approximation, we show how the qualitative features of the numerical results can be analytically understood. Finally, in the dimer case we show that the multiplicative noise can be transformed into additive noise, and an exact stationary solution to the Fokker-Planck equation is obtained. From this solution, the dimer system is found to exhibit a noise (temperature) induced phase transition.

    AB - We discuss the stability of highly localized, ''breatherlike,'' excitations in discrete nonlinear lattices under the influence of thermal fluctuations. The particular model considered is the discrete nonlinear Schrodinger equation in the regime of high nonlinearity, where temperature effects are included as multiplicative white noise and nonlinear damping. Numerical analysis shows that the lifetime of the breather is always finite and, in a large parameter regime, inversely proportional to the noise variance for fixed damping and nonlinearity. We also find that the decay rate of the breather decreases with increasing nonlinearity and with increasing damping. Using a collective-coordinate approximation, we show how the qualitative features of the numerical results can be analytically understood. Finally, in the dimer case we show that the multiplicative noise can be transformed into additive noise, and an exact stationary solution to the Fokker-Planck equation is obtained. From this solution, the dimer system is found to exhibit a noise (temperature) induced phase transition.

    KW - SYSTEMS

    KW - DIMER

    KW - SCHRODINGER-EQUATION

    KW - EXISTENCE

    KW - HAMILTONIAN LATTICES

    KW - SOLITONS

    KW - DYNAMICS

    KW - TIME EVOLUTION

    KW - TEMPERATURE

    KW - LOCALIZED EXCITATIONS

    U2 - 10.1103/PhysRevB.55.5759

    DO - 10.1103/PhysRevB.55.5759

    M3 - Journal article

    VL - 55

    SP - 5759

    EP - 5766

    JO - Physical Review B (Condensed Matter and Materials Physics)

    JF - Physical Review B (Condensed Matter and Materials Physics)

    SN - 1098-0121

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    ER -