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The quantized D-transformation.

M. Saraceno1, R. O. Vallejos

  • 1Departamento de Fisica, Comision Nacional de Energia Atomica, Av. del Libertador 8250, 1429 Buenos Aires, Argentina.

Chaos (Woodbury, N.Y.)
|June 1, 1996
PubMed
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Researchers developed a new quantum map, a quantized D-transformation, extending the 2D tent map. This study analyzes its classical, quantum, and semiclassical behaviors, revealing connections to the parity projected baker

Area of Science:

  • Quantum mechanics
  • Dynamical systems
  • Mathematical physics

Background:

  • The tent map is a one-dimensional dynamical system.
  • Extensions to higher dimensions and quantum versions are of interest.

Purpose of the Study:

  • To construct and analyze a novel quantum map, the quantized D-transformation.
  • To investigate its classical, quantum, and semiclassical dynamics.
  • To explore relationships with other quantum maps.

Main Methods:

  • Construction of the quantized D-transformation.
  • Analysis of classical and quantum behaviors.
  • Comparison with the parity projected baker's map.

Main Results:

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  • A new quantum map, the quantized D-transformation, was successfully constructed.
  • Classical, quantum, and semiclassical properties were investigated.
  • Connections between the quantized D-map and the parity projected baker's map were established.

    • Conclusions:

    • The study provides a new example of a quantum map with potential for further research.
    • The construction method is generalizable to dissipative maps, including quantum horseshoe maps.