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Dynamics in discrete phase spaces and time interval operators

Author

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  • Galetti, D.
  • Ruzzi, M.

Abstract

The von Neumann-Liouville time evolution equation is represented in a discrete quantum phase space. The mapped Liouville operator and the corresponding Wigner function are explicitly written for the problem of a magnetic moment interacting with a magnetic field and the precessing solution is found. The propagator is also discussed and a time interval operator, associated to a unitary operator which shifts the energy levels in the Zeeman spectrum, is introduced. This operator is associated to the particular dynamical process and is not the continuous parameter describing the time evolution. The pair of unitary operators which shifts the time and energy is shown to obey the Weyl–Schwinger algebra.

Suggested Citation

  • Galetti, D. & Ruzzi, M., 1999. "Dynamics in discrete phase spaces and time interval operators," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 264(3), pages 473-491.
  • Handle: RePEc:eee:phsmap:v:264:y:1999:i:3:p:473-491 DOI: 10.1016/S0378-4371(98)00457-9
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    References listed on IDEAS

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    1. Aleksander Janicki & Aleksander Weron, 1994. "Simulation and Chaotic Behavior of Alpha-stable Stochastic Processes," HSC Books, Hugo Steinhaus Center, Wroclaw University of Technology, number hsbook9401.
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    Cited by:

    1. Marchiolli, Marcelo A., 2003. "Nonclassical statistical properties of finite-coherent states in the framework of the Jaynes–Cummings model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 319(C), pages 331-354.

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