Chirikov criterion

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Chirikov standard map

(1959) Chirikov criterion (1969) Classical map: ¯ p = p + K sin x ¯ x = x + ¯ p (1979) Quantum map (kicked rotator): ¯ ψ = e −î p 2 /2 e −iK / cosˆx ψ (1959-2008) Hamiltonian classical / quantum chaos : H (ˆ p , ˆ x) = ˆ p 2 / 2 + K cosˆx m δ (t − m) [ ˆ p , ˆ x ] = −i (2001) Quantum computations (2008) Ongoing experiments with cold atoms and Bose-Einstein condensates

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We study numerically the statistics of Poincaré recurrences for the Chirikov standard map and the separatrix map at parameters with a critical golden invariant curve. The properties of recurrences are analyzed with the help of a generalized Ulam method. This method allows us to construct the corresponding Ulam matrix whose spectrum and eigenstates are analyzed by the powerful Arnoldi method. We...

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ژورنال

عنوان ژورنال: Scholarpedia

سال: 2009

ISSN: 1941-6016

DOI: 10.4249/scholarpedia.8567