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by A. Bouzouina, D. Robert
Duke Math. Journal
http://www.ma.utexas.edu/mp_arc/c/01/01-323.ps.gz
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Abstract:
We prove here that the semi-classical asymptotic expansion for the propagation of quantum observables, for C 1-Hamiltonians growing at most quadratically at innity, is uniformly dominated at any order, by an exponential term who's argument is linear in time. In particular, we recover the Ehrenfest time for the validity of the semiclassical approximation. This extends the result proved in [BGP]. Furthermore, if the Hamiltonian and the initial observables are holomorphic in a complex neighborhood of the phase space, we prove that the quantum observable is an analytic semi-classical observable. Other results about the large time behavior of observables with emphasis on the classical dynamic are also given. In particular, precise Gevrey estimates are established for classically integrable systems. 1 Introduction and main results According to the Bohr's correspondance principle, the quantum evolution of an observable
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