Numerical Evidence of Quantum Correspondence to the Classical Ergodicity

Numerical experiment in Lipkin model shows that, in quantum system with global chaotic classical limit, the temporal mean of the expectation value of an observable is approximately equal to the average over the basic states of Hilbert space, if the wavefunction is initially either a coherent wave packet or the common eigenstates of a complete set of observables, and the observable is independent of the Hamiltonian. The mechanism is the absence of KAM barrier which prevents the spread of wavefunction. This can serve as a quantum signature of classical chaos.