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Generalized metric phase space for quantum systems and the uncertainty principle

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  • Sarris, C.M.
  • Proto, A.N.

Abstract

We demonstrate that when the Gibbs entropy is an invariant of motion, following Information Theory procedures it is possible to define a generalized metric phase space for the temporal evolution of the mean values of a given Hamiltonian. The metric is positive definite and this fact leads to a metric tensor, K(t), whose properties are well defined. Working with these properties we shown that: (a) the Generalized Uncertainty Principle (GUP), is always the summation over the principal minors of order 2 belonging to K(t); (b) several invariants of motion can be derived from the metric tensor; and (c) particularly, under certain conditions, the GUP itself, is also a motion invariant.

Suggested Citation

  • Sarris, C.M. & Proto, A.N., 2007. "Generalized metric phase space for quantum systems and the uncertainty principle," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 377(1), pages 33-42.
    • Handle: RePEc:eee:phsmap:v:377:y:2007:i:1:p:33-42
    DOI: 10.1016/j.physa.2006.10.093
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