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