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Quantum dynamics with non-Markovian fluctuating parameters.

Igor Goychuk1

  • 1Institute of Physics, University of Augsburg, Universitätsstr. 1, D-86135 Augsburg, Germany. goychuk@physik.uni-augsburg.de

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 25, 2004
PubMed
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A new stochastic method models quantum dynamics with non-Markovian noise. This approach generalizes previous theories and provides exact expressions for spectral line shapes under random frequency modulation.

Area of Science:

  • Quantum dynamics
  • Statistical physics
  • Spectroscopy

Background:

  • Stochastic processes are crucial for modeling complex quantum systems.
  • Existing theories often rely on Markovian approximations, limiting their applicability.
  • Non-Markovian noise, with memory effects, presents a significant challenge in quantum dynamics.

Purpose of the Study:

  • To develop a generalized stochastic approach for quantum dynamics under non-Markovian noise.
  • To derive a formally exact expression for the quantum propagator averaged over noise realizations.
  • To provide a non-Markovian generalization of the Kubo-Anderson theory for spectral line shapes.

Main Methods:

  • Development of a stochastic theory for quantum dynamics.
  • Inclusion of discrete state, non-Markovian noise with arbitrary residence time distributions.

Related Experiment Videos

  • Derivation of Laplace-transformed quantum propagator averaged over stationary noise realizations.
  • Application to spectral line shape and relaxation phenomena.

    • Main Results:

    • A formally exact expression for the averaged quantum propagator is obtained.
    • The developed theory encompasses previous Markovian and non-Markovian models.
    • A non-Markovian generalization of the Kubo-Anderson theory is presented.
    • Exact analytical expression for the spectral line shape of a Kubo oscillator with jumplike frequency fluctuations is derived.

    Conclusions:

    • The developed stochastic approach offers a powerful framework for studying quantum dynamics with complex noise.
    • This method provides a unified treatment for various noise models, including Markovian and non-Markovian cases.
    • The findings are directly applicable to understanding spectral line shapes and relaxation processes in quantum systems.