Ergodic semiclassical quantum mechanics Academic Article uri icon

abstract

  • After major progress in the last years, chaotic phenomena in classical systems are fairly well understood (Lichtenberg and Lieberman, 1983). On the other hand, many questions regarding the behavior of the quantized version of chaotic systems are still open (Berry, 1983). Moreover, the predictive ability in the field of quantum chaos is mostly qualitative. For time independent Hamiltonian systems, the few quantitative results are based either on semiclassical arguments (Berry, 1977; Berry and Tabor, 1977; Gutzwiller, 1967, 1969, 1970, 1971 1980; Pechukas, 1983) or on the random matrix theory (Mehta, 1967; Brody, Flores, French, Mello, Pandey and Wong, 1981). Regarding the former, we have no working scheme by which non-integrable systems can be semiclassically quantized. The Einstein- Brillouin-Keller (van Vleck, 1928; Keller, 1958) method is bound to break down in those …

publication date

  • January 1, 1987