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    Nonlinear Schrödinger equation and dissipative quantum dynamics in periodic fields

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    ChuShih-I_10-15-1989.pdf (521.5Kb)
    Issue Date
    1989-10-15
    Author
    Chu, Shih-I
    Huang, Youhong
    Hirschfelder, Joseph O.
    Publisher
    American Physical Society
    Type
    Article
    Article Version
    Scholarly/refereed, publisher version
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    Abstract
    The nonlinear dynamics of dissipative quantum systems in periodic fields is studied in the framework of a Gisin-like nonlinear Schrödinger equation with deterministic nonunitary quantum friction terms describing the system-bath couplings. The virtue of this nonunitary evolution is that it is compatible with Dirac’s superposition principle and the Hilbert-space structure of quantum kinematics. Floquet theory and the generalized Van Vleck nearly degenerate perturbation method are used to facilitate both analytical and numerical solutions. Closed-form analytic solutions can be obtained in the long-time average approximation or within the rotating-wave approximation. The methods are applied to the study of dissipative quantum dynamics of two-level systems driven by intense periodic fields. It is found that the system asymptotically approaches a limit cycle (whose orientation is subject to the quantum friction constraint), regardless of the strength of the perturbed fields and the nonlinearity constant, indicating quantum suppression of classical chaos. Further, each point of the limit cycle is found to be an attractor and ψ(t) exhibits a fractal-like evolution pattern in the course of time. The structure of the limit cycle depends strongly upon field intensity and frequency as well as the order of nonlinear multiphoton transitions. The power spectrum of the Bloch vector trajectory exhibits a dynamical symmetry inherent in the dissipative system and in the asymptotic limit cycle. A theoretical analysis is presented for the understanding of the origin and the role of the dynamical symmetry.
    Description
    This is the published version, also available here: http://dx.doi.org/10.1103/PhysRevA.40.4171.
    URI
    http://hdl.handle.net/1808/16000
    DOI
    https://doi.org/10.1103/PhysRevA.40.4171
    Collections
    • Chemistry Scholarly Works [552]
    Citation
    Chu, Shih-I., Huang, Youhong., Hirschfelder, Joseph O. "Nonlinear Schrödinger equation and dissipative quantum dynamics in periodic fields." Phys. Rev. A 40, 4171 – Published 15 October 1989. http://dx.doi.org/10.1103/PhysRevA.40.4171.

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    Lawrence, KS 66045
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    Contact KU ScholarWorks
    785-864-8983
    KU Libraries
    1425 Jayhawk Blvd
    Lawrence, KS 66045
    785-864-8983

    KU Libraries
    1425 Jayhawk Blvd
    Lawrence, KS 66045
    Image Credits
     

     

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