CLASSICAL HAMILTONIAN-DYNAMICS OF RESCALED QUANTUM LEVELS

Extending previous work of Pechukas and Yukawa, we map the eigenvalue problem of a quantum Hamiltonian H = g(A)(Ho + AV) onto the classical Hamiltonian dynamics of a fictitious gas. The rescaling factor g(A) is chosen so as to prevent the level density of H from thinning out indefinitely as A * 03; for the fictitious gas g(A) gives rise to a harmonic binding potential not present for g = 1, i.e. for Pechukas' gas. The confining potential makes equilibrium statistical mechanics applicable to the gas. The canonical ensemble of our gas turns out to be equivalent to the Gaussian ensembles of random Hermitian matrices. © 1990 IOP Publishing Ltd.