Sharpening an inequality in quantum ergodic theory
Philip Pechukas · Journal of Mathematical Physics · 1984
The fundamental inequality of quantum ergodic theory, which bounds the ensemble-averaged dispersion of a time-averaged occupation probability, is due to von Neumann and to Bocchieri and Loinger. Here this inequality is strengthened by combining the ensemble averaging of von Neumann and Bocchieri and Loinger. In this sharper form, the inequality says that the time average of an occupation probability is liable to be much closer to the statistical expectation than is its instantaneous value, the more so the less degenerate is the spectrum of the Hamiltonian.