Nonlinear excitations in two-dimensional molecular structures with impurities

    Research output: Contribution to journalJournal articleResearchpeer-review

    161 Downloads (Pure)

    Abstract

    We study the nonlinear dynamics of electronic excitations interacting with acoustic phonons in two-dimensional molecular structures with impurities. We show that the problem is reduced to the nonlinear Schrodinger equation with a varying coefficient. The latter represents the influence of the impurity. Transforming the equation to the noninertial frame of reference coupled with the center of mass we investigate the soliton behavior in the close vicinity of the impurity. With the help of the lens transformation we show that the soliton width is governed by an Ermakov-Pinney equation. We also investigate bound state of the soliton with impurity and show that in addition to the radially symmetric bound state a dipolelike state can exist if the number of excitations in the soliton does not exceed some threshold value. We study both the equilibrium states and the dynamics of the dipolelike excitations. Analytical results are in good agreement with numerical simulations of the nonlinear Schrodinger equation.
    Original languageEnglish
    JournalPhysical Review E. Statistical, Nonlinear, and Soft Matter Physics
    Volume52
    Issue number3
    Pages (from-to)2951-2962
    ISSN1063-651X
    DOIs
    Publication statusPublished - 1995

    Bibliographical note

    Copyright (1995) by the American Physical Society.

    Keywords

    • SYSTEMS
    • SCHRODINGER-EQUATION
    • ASSEMBLIES
    • ENERGY-TRANSFER
    • SOLITON
    • DYNAMICS
    • MONOLAYERS

    Cite this

    @article{63d7c2cdb6e74dca96c45e3b89f59e67,
    title = "Nonlinear excitations in two-dimensional molecular structures with impurities",
    abstract = "We study the nonlinear dynamics of electronic excitations interacting with acoustic phonons in two-dimensional molecular structures with impurities. We show that the problem is reduced to the nonlinear Schrodinger equation with a varying coefficient. The latter represents the influence of the impurity. Transforming the equation to the noninertial frame of reference coupled with the center of mass we investigate the soliton behavior in the close vicinity of the impurity. With the help of the lens transformation we show that the soliton width is governed by an Ermakov-Pinney equation. We also investigate bound state of the soliton with impurity and show that in addition to the radially symmetric bound state a dipolelike state can exist if the number of excitations in the soliton does not exceed some threshold value. We study both the equilibrium states and the dynamics of the dipolelike excitations. Analytical results are in good agreement with numerical simulations of the nonlinear Schrodinger equation.",
    keywords = "SYSTEMS, SCHRODINGER-EQUATION, ASSEMBLIES, ENERGY-TRANSFER, SOLITON, DYNAMICS, MONOLAYERS",
    author = "Gaididei, {Yuri Borisovich} and Kim Rasmussen and Christiansen, {Peter Leth}",
    note = "Copyright (1995) by the American Physical Society.",
    year = "1995",
    doi = "10.1103/PhysRevE.52.2951",
    language = "English",
    volume = "52",
    pages = "2951--2962",
    journal = "Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)",
    issn = "2470-0045",
    publisher = "American Physical Society",
    number = "3",

    }

    Nonlinear excitations in two-dimensional molecular structures with impurities. / Gaididei, Yuri Borisovich; Rasmussen, Kim; Christiansen, Peter Leth.

    In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, Vol. 52, No. 3, 1995, p. 2951-2962.

    Research output: Contribution to journalJournal articleResearchpeer-review

    TY - JOUR

    T1 - Nonlinear excitations in two-dimensional molecular structures with impurities

    AU - Gaididei, Yuri Borisovich

    AU - Rasmussen, Kim

    AU - Christiansen, Peter Leth

    N1 - Copyright (1995) by the American Physical Society.

    PY - 1995

    Y1 - 1995

    N2 - We study the nonlinear dynamics of electronic excitations interacting with acoustic phonons in two-dimensional molecular structures with impurities. We show that the problem is reduced to the nonlinear Schrodinger equation with a varying coefficient. The latter represents the influence of the impurity. Transforming the equation to the noninertial frame of reference coupled with the center of mass we investigate the soliton behavior in the close vicinity of the impurity. With the help of the lens transformation we show that the soliton width is governed by an Ermakov-Pinney equation. We also investigate bound state of the soliton with impurity and show that in addition to the radially symmetric bound state a dipolelike state can exist if the number of excitations in the soliton does not exceed some threshold value. We study both the equilibrium states and the dynamics of the dipolelike excitations. Analytical results are in good agreement with numerical simulations of the nonlinear Schrodinger equation.

    AB - We study the nonlinear dynamics of electronic excitations interacting with acoustic phonons in two-dimensional molecular structures with impurities. We show that the problem is reduced to the nonlinear Schrodinger equation with a varying coefficient. The latter represents the influence of the impurity. Transforming the equation to the noninertial frame of reference coupled with the center of mass we investigate the soliton behavior in the close vicinity of the impurity. With the help of the lens transformation we show that the soliton width is governed by an Ermakov-Pinney equation. We also investigate bound state of the soliton with impurity and show that in addition to the radially symmetric bound state a dipolelike state can exist if the number of excitations in the soliton does not exceed some threshold value. We study both the equilibrium states and the dynamics of the dipolelike excitations. Analytical results are in good agreement with numerical simulations of the nonlinear Schrodinger equation.

    KW - SYSTEMS

    KW - SCHRODINGER-EQUATION

    KW - ASSEMBLIES

    KW - ENERGY-TRANSFER

    KW - SOLITON

    KW - DYNAMICS

    KW - MONOLAYERS

    U2 - 10.1103/PhysRevE.52.2951

    DO - 10.1103/PhysRevE.52.2951

    M3 - Journal article

    VL - 52

    SP - 2951

    EP - 2962

    JO - Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)

    JF - Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)

    SN - 2470-0045

    IS - 3

    ER -