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Spectral properties and classical decays in quantum open systems.

Ignacio García-Mata1, Marcos Saraceno

  • 1Departamento de Física, Comisión Nacional de Energía Atómica, Avenida del Libertador 8250 (1429), Buenos Aires, Argentina. garciama@tandar.cnea.gov.ar

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|July 13, 2004
PubMed
Summary

We explore quantum map spectral properties and classical Ruelle-Pollicott resonances. These resonances predict long-term behaviors like entropy and echo in quantum systems.

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Area of Science:

  • Quantum mechanics
  • Statistical physics
  • Dynamical systems theory

Background:

  • Diffusive open quantum maps exhibit complex spectral properties.
  • Ruelle-Pollicott resonances characterize classical chaotic dynamics.
  • Understanding the interplay is crucial for predicting quantum system evolution.

Purpose of the Study:

  • To investigate the connection between quantum map spectra and classical resonances.
  • To establish how classical resonances influence quantum dynamical quantities.
  • To develop efficient computational tools for spectral analysis.

Main Methods:

  • Analysis of spectral properties of diffusive open quantum maps.
  • Comparison with the classical spectrum of Ruelle-Pollicott resonances.

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  • Development of a numerical method using truncated basis adapted to dynamics.

    • Main Results:

    • The leading Ruelle-Pollicott resonances dictate the asymptotic time behavior.
    • This applies to key quantities such as linear entropy and Loschmidt echo.
    • An efficient numerical method for calculating the leading spectrum was established.

    Conclusions:

    • A direct relationship exists between quantum spectral properties and classical resonances.
    • Classical resonances provide insights into the long-time dynamics of quantum systems.
    • The developed numerical method facilitates efficient spectral calculations.