  Quantum ergordic theorem for a large class of quantum systems was proved by
von Neumann [Z. Phys. {\bf 57}, 30 (1929)] and again by Reimann [Phys. Rev.
Lett. {\bf 101}, 190403 (2008)] in a more practical and well-defined form.
However, it is not clear whether the theorem applies to quantum chaotic
systems. With the rigorous proof still elusive, we illustrate and verify this
theorem for quantum chaotic systems with examples. Our numerical results show
that a quantum chaotic system with an initial low-entropy state will
dynamically relax to a high-entropy state and reach equilibrium. The quantum
equilibrium state reached after dynamical relaxation bears a remarkable
resemblance to the classical micro-canonical ensemble. However, the
fluctuations around equilibrium are distinct: the quantum fluctuations are
exponential while the classical fluctuations are Gaussian.
