2018-12-18T23:20:09Zhttp://repositori.uji.es/oai/requestoai:repositori.uji.es:10234/855512018-10-30T16:55:46Zcom_10234_43662com_10234_9com_10234_7038col_10234_43643col_10234_8634
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Gimeno García, Vicent
author
Martínez Sotoca, José
author
2013-05
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.
GIMENO, Vicent; SOTOCA, José M. Geometric approach to non-relativistic quantum dynamics of mixed states. Journal of Mathematical Physics, 2013, 54.5: 052108.
http://hdl.handle.net/10234/85551
http://dx.doi.org/10.1063/1.4807096
non-relativistic quantum mechanics
mixed states
geometrization
Geometric approach to non-relativistic quantum dynamics of mixed states