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Classical decays in decoherent quantum maps.

Ignacio García-Mata1, Marcos Saraceno, María Elena Spina

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

Physical Review Letters
|August 26, 2003
PubMed
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We investigated linear entropy and Loschmidt echo in open quantum systems. Their long-time decay rates for chaotic maps connect to classical Ruelle-Pollicott resonances.

Area of Science:

  • Quantum information theory
  • Quantum chaos
  • Statistical mechanics

Background:

  • Linear entropy and Loschmidt echo are key measures in quantum information and quantum-to-classical transitions.
  • Understanding their long-time behavior in open quantum systems is crucial for characterizing decoherence and chaos.

Purpose of the Study:

  • To analyze the asymptotic long-time behavior of linear entropy and Loschmidt echo for open quantum maps.
  • To establish a connection between the decay rates of these quantities and the spectral properties of a relevant classical system.

Main Methods:

  • Studying open quantum maps and their evolution under coarse-graining.
  • Analyzing the eigenvalues of a coarse-grained superoperator.
  • Comparing quantum decay rates with classical Ruelle-Pollicott resonances.

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Main Results:

  • The decay rates of linear entropy and Loschmidt echo are linked to eigenvalues of a coarse-grained superoperator.
  • For chaotic maps and specific coarse-graining, these decay rates precisely match the Ruelle-Pollicott resonances of the corresponding classical map.

Conclusions:

  • The study provides a direct link between quantum dynamical properties (entropy, echo) and classical dynamical properties (resonances).
  • This connection offers insights into quantum-classical transitions and the emergence of classical behavior from quantum dynamics.