We discover numerically that a moving wave packet in a quantum chaotic
billiard will always evolve into a quantum state, whose density probability
distribution is exponential. This exponential distribution is found to be
universal for quantum chaotic systems with rigorous proof. In contrast, for the
corresponding classical system, the distribution is Gaussian. We find that the
quantum exponential distribution can smoothly change to the classical Gaussian
distribution with coarse graining.Comment: 4 figure