Ehrenfest breakdown of the mean-field dynamics of Bose gases

The unstable mean-field dynamics of a Bose gas is shown to break down at time tau(h) = (c1/gamma) ln N, where gamma is the Lyapunov exponent of the mean-field theory, N is the number of bosons, and c(1) is a system-dependent constant. The breakdown time tau(h) is essentially the Ehrenfest time that characterizes the breakdown of the correspondence between classical and quantum dynamics. This breakdown can be well described by a quantum fidelity defined for one-particle reduced density matrices. Our results are obtained with the formalism in particle-number phase space and are illustrated with a triple-well model. The logarithmic quantum-classical correspondence time may be verified experimentally with Bose-Einstein condensates.