Level dynamics and universality of spectral fluctuations

The spectral fluctuations of quantum (or wave) systems with a chaotic class ical (or ray) limit are mostly universal and faithful to random-matrix theo ry. Taking zip ideas of Pechukas and Yukawa we show that equilibrium statis tical mechanics for the fictitious gas of particles associated with the par ametric motion of levels yields spectral fluctuations of the random-matrix type. Previously known clues to that goal are an appropriate equilibrium en semble and a certain ergodicity of level dynamics. We here complete the rea soning by establishing a power law for the h dependence of the mean paramet ric separation of avoided level crossings. Due to that law universal spectr al fluctuations emerge as average behavior of a family of quantum dynamics drawn from a control parameter interval which becomes vanishingly small in the classical limit; the family thus corresponds to a single classical syst em. We also argue that classically integrable dynamics cannot produce unive rsal spectral fluctuations since their level dynamics resembles a nearly id eal Pechukas-Yukawa gas.