Failure of random matrix theory to correctly describe quantum dynamics Academic Article uri icon

abstract

  • Consider a classically chaotic system that is described by a Hamiltonian ${\mathcal{H}}_{0}.$ At $t=0$ the Hamiltonian undergoes a sudden change ${\mathcal{H}}_{0}\ensuremath{\mapsto}\mathcal{H}.$ We consider the quantum-mechanical spreading of the evolving energy distribution, and argue that it cannot be analyzed using a conventional random-matrix theory (RMT) approach. Conventional RMT can be trusted only to the extent that it gives trivial results that are implied by first-order perturbation theory. Nonperturbative effects are sensitive to the underlying classical dynamics, and therefore the $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\Elzxh}}0$ behavior for effective RMT models is strikingly different from the correct semiclassical limit.

publication date

  • January 1, 2001