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Irreversible quantum baker map.

Artur Łoziński1, Prot Pakoński, Karol Zyczkowski

  • 1Instytut Fizyki im. M. Smoluchowskiego, Uniwersytet Jagielloński, ul. Reymonta 4, 30-059 Kraków, Poland. lozinski@if.uj.edu.pl

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|January 7, 2003
PubMed
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We generalize the classical baker map, creating an irreversible quantum system. This quantum system

Area of Science:

  • Quantum chaos
  • Statistical mechanics
  • Dynamical systems

Background:

  • The classical baker map on a torus is a fundamental model in dynamical systems and chaos theory.
  • Standard quantum mechanics typically describes reversible processes using unitary operators.
  • Irreversible processes in quantum mechanics require more general frameworks, such as completely positive maps.

Purpose of the Study:

  • To introduce a generalized baker map model with overlapping phase space regions.
  • To develop a quantum mechanical description for this irreversible classical map.
  • To analyze the spectral properties of the resulting quantum superoperator and its relation to entropy increase.

Main Methods:

  • Generalization of the classical baker map to include overlapping regions.

Related Experiment Videos

  • Construction of a quantum system using a completely positive map on density matrices.
  • Investigation of the spectral properties of the quantum superoperator.

    • Main Results:

    • The proposed transformation is irreversible and cannot be quantized by a unitary Floquet operator.
    • The quantum system is described by a superoperator acting on density matrices.
    • Spectral analysis reveals a connection between the superoperator's properties and the entropy increase of pure states.

    Conclusions:

    • The generalized baker map provides a model for irreversible quantum dynamics.
    • Completely positive maps are essential for describing such irreversible quantum systems.
    • The study links spectral properties of the superoperator to fundamental concepts like entropy increase in quantum chaos.