The unstable mean-field dynamics of a Bose gas is shown to break down at time ${\ensuremath{\tau}}_{h}=({c}_{1}/\ensuremath{\gamma})lnN$, where $\ensuremath{\gamma}$ 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 ${\ensuremath{\tau}}_{h}$ 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.The unstable mean-field dynamics of a Bose gas is shown to break down at time ${\ensuremath{\tau}}_{h}=({c}_{1}/\ensuremath{\gamma})lnN$, where $\ensuremath{\gamma}$ 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 ${\ensuremath{\tau}}_{h}$ 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.

arXiv:1506.04020Physical Review AFeb 12, 201616 citations

Classical limit and spontaneous breakdown of symmetry as an environment effect in quantum field theory

E. Celeghini, Elvira Graziano, Giuseppe Vitiello

Physics Letters AMar 1, 199014 citations

Beyond the classical theory

Springer eBooksMar 21, 20061 citation

N

is the number of bosons, and

{c}_{1}

is a system-dependent constant. The breakdown time ${\ensuremath{\tau}}_{h}$ 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.