Quantization rules for strongly chaotic systems

Sep, 1992
28 pages
Published in:
  • Mod.Phys.Lett.B 6 (1992) 1691-1720
Report number:
  • DESY-92-132

Citations per year

19931994199523
Abstract: (WSP)
We discuss the quantization of strongly chaotic systems and apply several quantization rules to a model system given by the unconstrained motion of a particle on a compact surface of constant negative Gaussian curvature. We study the periodic-orbit theory for distinct symmetry classes corresponding to a parity operation which is always present when such a surface has genus two. Recently, several quantization rules based on periodic orbit theory have been introduced. We compare quantizations using the dynamical zeta function Z(s) with the quantization condition cos(πN(E))=0,\cos(\pi {\mathcal N} (E)) = 0 \,, where a periodic-orbit expression for the spectral staircase N(E) is used. A general discussion of the efficiency of periodic-orbit quantization then allows us to compare the different methods. The system dependence of the efficiency, which is determined by the topological entropy τ and the mean level density dˉ(E)\bar{d} (E), is emphasized.
  • chaos
  • quantization: zeta function
  • orbit