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Generalized metric phase space for quantum systems and the uncertainty principle

✍ Scribed by C.M. Sarris; A.N. Proto

Publisher: Elsevier Science
Year: 2007
Tongue: English
Weight: 198 KB
Volume: 377
Category: Article
ISSN: 0378-4371
DOI: 10.1016/j.physa.2006.10.093

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✦ Synopsis

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, KðtÞ, 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 KðtÞ; (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.

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