Semiclassical mechanics of bound chaotic potentials

Abstract

Semiclassical methods for determining quantum eigenvalues in chaotic systems are discussed. A recent calculation for an open scattering system with Axiom-A properties serves as a starting point for the discussion. How deviation from Axiom-A properties, such as intermittency and occurrence of small stability islands, normally arise in bound Hamiltonian systems, and how these deviations complicate the calculation of semiclassical eigenvalues are demonstrated. It is also stressed that since such deviations are typical of bound Hamiltonian systems, they might be of crucial importance for the statistical properties of the energy levels.