Nonlinear Schroedinger equation and dissipative quantum dynamics in periodic fields
- Department of Chemistry, University of Kansas, Lawrence, Kansas 66045 (USA)
- Department of Chemistry, University of Wisconsin, Madison, Wisconsin 53706 (USA)
The nonlinear dynamics of dissipative quantum systems in periodic fields is studied in the framework of a Gisin-like nonlinear Schroedinger 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 {psi}({ital 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.
- OSTI ID:
- 5216100
- Journal Information:
- Physical Review (Section) A: General Physics; (USA), Vol. 40:8; ISSN 0556-2791
- Country of Publication:
- United States
- Language:
- English
Similar Records
Floquet-Liouville supermatrix approach: Time development of density-matrix operator and multiphoton resonance fluorescence spectra in intense laser fields
Case studies of atomic processes in strong fields: New aspects of multiphoton and nonlinear dynamics
Related Subjects
GENERAL PHYSICS
QUANTUM MECHANICS
ENERGY LOSSES
ELECTROMAGNETIC FIELDS
IRREVERSIBLE PROCESSES
MOLECULES
NONLINEAR PROBLEMS
SCHROEDINGER EQUATION
STATISTICAL MECHANICS
DIFFERENTIAL EQUATIONS
EQUATIONS
LOSSES
MECHANICS
PARTIAL DIFFERENTIAL EQUATIONS
WAVE EQUATIONS
657002* - Theoretical & Mathematical Physics- Classical & Quantum Mechanics