1999/01/18 by Mieke De Cock, De Cock, Mieke, M. Fannes +4 · 1 citation
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #Quantum chaos and dynamical systems #Random Matrices and Applications #math-ph #math.MP #quant-ph
paper · pdf · doi:10.48550/arxiv.math-ph/9901009
LaTeX, 7 pages, 1 PostScript figure, revised, added references
openalex publication_date 1999/01/18 · arxiv created 1999/05/26 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose to analyse the statistical properties of a sequence of vectors using the spectrum of the associated Gram matrix. Such sequences arise e.g. by the repeated action of a deterministic kicked quantum dynamics on an initial condition or by a random process. We argue that, when the number of time-steps, suitably scaled with respect to ℏ, 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. This idea is subsequently applied to study the long-time properties of sequences of random vectors at the time scale of the dimension of the Hilbert space of available states.