Title: Quantum dynamics and Gram's matrix
Authors: De Cock, Mieke ×
Fannes, Mark
Spincemaille, Pascal #
Issue Date: Feb-2000
Publisher: E d p sciences
Series Title: Europhysics letters vol:49 issue:4 pages:403-409
Abstract: We propose to analyse the statistical properties of long sequences of vectors using the spectrum of the associated Gram matrix. Such sequences arise, e.g., by stroboscopic observation of a Hamiltonian evolution or by repeated action of a kicked quantum dynamics on an initial condition. One should distinguish between dynamical systems with a classical limit and infinite quantum systems with continuous dynamical spectrum. For the first class, we argue that when the number of time steps, suitably scaled with respect to A, increases, the limiting eigenvalue distribution of the Gram matrix reflects the possible quantum chaoticity of the original system as it tends to its classical limit. On the one hand, we consider the extreme model of a system with integrable classical limit. A random system, on the other hand, mimics the quantum dynamics of a system with a completely chaotic classical counterpart. For infinite systems the eigenvalue distribution of the Gram matrix can be related to well-known characteristics of chaos such as positive dynamical entropy.
ISSN: 0295-5075
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Theoretical Physics Section
Teacher Training Physics (-)
× corresponding author
# (joint) last author

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