Dynamical Chaos and Many-Body Quantum Systems

摘要: Recent developments in quantum chaology and, specially this last year, have shown how to quantize bounded or scattering classically chaotic systems [1–8]. These semiclassical methods proved be most powerful not only billiards [2, 4] but also realistic atomic like the hydrogen atom a magnetic field [6], anisotropic Kepler system [1, 7], and helium [8]. Scattering resonances energy levels are obtained terms of classical periodic orbits. Depending on problem version method, they calculated as zeros function involving Selberg zeta function, poles Ruelle functions, half-integers integrated Gutzwiller trace function. impressive results solve 74-year-old raised 1917 by Einstein who criticized Bohr-Sommerfeld quantization being inapplicable non-integrable [9]. The new appear complementary EBK rules completely integrable systems.