Thursday, January 31, 2013

1301.7278 (Mario Castagnino et al.)

Toward a definition of the Quantum Ergodic Hierarchy: Kolmogorov and
Bernoulli systems

Mario Castagnino, Ignacio Gomez
In this paper we translate the two higher levels of the Ergodic Hierarchy, the Kolmogorov level and the Bernoulli level, to quantum language. This paper can be considered as the second part of the paper [M. Castagnino, O. Lombardi, Physica A, 388, 247-267, 2009] to complete the quantum language translation of all levels of the Hierarchy Ergodic. As in paper [M. Castagnino, O. Lombardi, Physica A, 388, 247-267, 2009], we consider the formalism where the states are positive functionals on the algebra of observables and we use the properties of the Wigner transform [M. Hillery, M. O'Connell, R. Scully, E. Wigner, Phys. Rep. 106, 121-167, 1984]. Further conclusions are analyzed on the validity of this approach as a formal treatment of quantum chaos.
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