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Generalized quantum baker maps as perturbations of a simple kernel.

Leonardo Ermann1, Marcos Saraceno

  • 1Departamento de Física, Comisión Nacional de Energía Atómica, Avenida del Libertador 8250 (C1429BNP), Buenos Aires, Argentina. ermann@tandar.cnea.gov.ar

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 13, 2006
PubMed
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We introduce a versatile quantum baker map applicable to various quantum systems. This essential baker's map provides an accurate approximation for spectral properties, simplifying quantum analysis.

Area of Science:

  • Quantum mechanics
  • Quantum chaos
  • Mathematical physics

Background:

  • The baker map is a classical dynamical system known for its chaotic behavior.
  • Previous quantum baker maps were limited in their applicability.
  • Understanding quantum chaos is crucial for developing quantum technologies.

Purpose of the Study:

  • To generalize the quantum baker map to a broader class of systems.
  • To identify a common underlying structure in these generalized maps.
  • To analyze the spectral properties of these quantum baker maps.

Main Methods:

  • Developing a broad family of quantum baker maps.
  • Identifying an "essential" baker's map kernel.
  • Analytical diagonalization for qubit Hilbert spaces.

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  • Approximating spectral properties (eigenvalues and eigenfunctions).

    • Main Results:

    • The proposed quantum baker maps generalize previous work to any even Hilbert space.
    • A common structure, an "essential" baker's map, was identified.
    • This essential map has a distinct semiclassical limit.
    • Analytical diagonalization was achieved for qubit systems.
    • The kernel accurately approximates spectral properties for all presented maps.

    Conclusions:

    • The generalized quantum baker maps offer a flexible framework for studying quantum chaos.
    • The "essential" baker's map kernel is a powerful tool for spectral analysis.
    • This work simplifies the study of spectral properties in various quantum systems.