Ergodicity and mixing in quantum theory. I

Quantum chaos is defined by the following property: Simple dynamical variables (position, momentum, etc.) are represented by pseudorandom matrices, when the Hamiltonian is diagonal. As a consequence, the expectation values of these variables tend to equilibrium values which are insensitive to the initial preparation, for nearly all preparations involving many energy levels. Moreover, the fluctuations around these equilibrium values are, on the average, very small.