Geometric approach to non-relativistic quantum dynamics of mixed states
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Title
Geometric approach to non-relativistic quantum dynamics of mixed statesDate
2013-05Publisher
AIP Publishing LLCBibliographic citation
GIMENO, Vicent; SOTOCA, José M. Geometric approach to non-relativistic quantum dynamics of mixed states. Journal of Mathematical Physics, 2013, 54.5: 052108.Type
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In this paper we propose a geometrization of the non-relativistic quantum mechanics for mixed states. Our geometric approach makes use of the Uhlmann's principal fibre bundle to describe the space of mixed states and ... [+]
In this paper we propose a geometrization of the non-relativistic quantum mechanics for mixed states. Our geometric approach makes use of the Uhlmann's principal fibre bundle to describe the space of mixed states and as a novelty tool, to define a dynamic-dependent metric tensor on the principal manifold, such that the projection of the geodesic flow to the base manifold gives the temporal evolution predicted by the von Neumann equation. Using that approach we can describe every conserved quantum observable as a Killing vector field, and provide a geometric proof for the Poincaré quantum recurrence in a physical system with finite energy levels. [-]
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Journal of Mathematical Physics Volume 54, Issue 5, May 2013Rights
© 2013 AIP Publishing LLC.
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