F. Bonechi, S. De Bivre, Controlling strong scarring for quantized ergodic total automorphisms, rap_arc 02-81, february 2002, Duke Math. J., to appear Home/Search Document Details and Download
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Scarred Eigenstates for Quantum Cat Maps of Minimal.. - Faure, Nonnenmacher.. (2002) (2 citations) (Correct)
....to be suciently numerous to drastically reduce (if not to lift) the degeneracies of the eigenvalues. F)nally, one may wonder if it would be possible to construct a sequence of eigenfunctions of M that has as a limit measure T 1 (1 j=0 with fi 1 2 and possibly fi = 1. It is proven in [BonDB2] that this is not possible for fi ( 1) 2 0.62. The intuition behind our result in this paper make it reasonable to conjecture that this bound is not sharp, the maximum possible value of fi being fi = 1 2. 2 Linear dynamics on the plane In this section we recall some known results we will need ....
F. Bonechi, S. De Bivre, Controlling strong scarring for quantized ergodic total automorphisms, rap_arc 02-81, february 2002, Duke Math. J., to appear
Semi-classical Propagation on |log h|-Time-Scales - De Bièvre, Robert (2002) Self-citation (Evre) (Correct)
....a distance h of its center. 1 Introduction There has been a growing interest in the last few years in the rigorous study of quantum dynamical systems in the semi classical limit ( h 0) for long times, meaning for times t going to infinity as h tends to 0 [DB] CR] BGP] BR] BDB1] HJ] [BDB2]. If the classical dynamics is stable, such as in completely integrable systems, standard techniques of semi classical analysis allow one to obtain control on the quantum dynamics in terms of (semi )classical expressions up to times of order h , for some k 0. In the presence of instabilities ....
....understanding of the quantum dynamics on as long a time scale as possible is important in quantum chaos, and has attracted considerable attention in this context [BB] CC] OTH] TH] but not much is known rigorously. In the case of certain chaotic quantum maps, it was shown in [DB] and [BDB1] [BDB2] that already on the relatively short logarithmic time scale, interesting phenomena occur. Here we want to address this same question in the context of a one dimensional Schr odinger equation, close to a hyperbolic fixed point of the dynamics. This is arguably the simplest exponential instability ....
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F. Bonechi, S. De Bi evre, Controlling strong scarring for quantized ergodic toral automorphisms, mp arc 02-81(2002), Duke Math. Journal, to appear.
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