Quantum Variance and Ergodicity for the baker's map

Mirko Degli Esposti (1) , Stéphane Nonnenmacher (2) , Brian Winn (1)

1 Department of Mathematics [Bologna]
2 SPhT - Service de Physique Théorique

We prove a Egorov theorem, or quantum-classical correspondence, for the quantised baker's map, valid up to the Ehrenfest time. This yields a logarithmic upper bound for the decay of the quantum variance, and, as a corollary, a quantum ergodic theorem for this map.

Mots clés: Quantum chaotic map; quantum ergodicity; semiclassics

Domaines: Physique mathématique [math-ph]

Mirko Degli Esposti, Stéphane Nonnenmacher, Brian Winn. Quantum Variance and Ergodicity for the baker's map. Communications in Mathematical Physics, 2006, 263, Number 2, pp.325 - 352. ⟨10.1007/s00220-005-1397-3⟩. ⟨hal-00003608v3⟩