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Random walk on the homogeneous spaces of a group and generalized coherent states

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  • Bertotti, Giorgio
  • Rasetti, Mario

Abstract

The evolution of a quantum system characterized by a dynamical group G and subjected to random interactions can be reduced, through the use of the generalized coherent states associated with a group G, whose algebra is an ideal of the algebra of G, to a random walk on some homogeneous space S of G. G is the group of automorphisms of S. The connection between the symmetry properties of such a random walk and the structure of G are discussed, showing that it is always possible to map the original process into an equivalent process taking place in the manifold of G. The investigation of the general properties of this mapping quite naturally provides a deep characterization of the role played by G in determining the basic transient and stationary features of the evolution of the system.

Suggested Citation

  • Bertotti, Giorgio & Rasetti, Mario, 1984. "Random walk on the homogeneous spaces of a group and generalized coherent states," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 129(1), pages 125-150.
    • Handle: RePEc:eee:phsmap:v:129:y:1984:i:1:p:125-150
    DOI: 10.1016/0378-4371(84)90024-4
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