
Click here for full text:
Quantum Energy Levels and Classical Periodic Orbits: Discreteness and Statistical Duality
Connors, R.D.; Keating, J.P.
HPLBRIMS200106
Keyword(s): trace formula; periodic orbit statistics; spectral statistics
Abstract: It is shown that both universal and nonuniversal correlations must exist between classical periodic orbits in order that Gutzwiller's semiclassical trace formula is consistent with a real, discrete quantum energy spectrum. Formulae for the twopoint correlations are derived. The universal correlations are consistent with those conjectured by Argaman et al. (1993). Likewise, both universal and nonuniversal correlations must exist between quantum energy levels in order that the trace formula be consistent with the fact that periodic orbit actions are real and discrete. In this case, the twopoint correlations implied are consistent with random matrix theory and previous semiclassical calculations. These ideas are illustrated with reference to the primes and the Riemann zeros. Notes: R.D. Connors, School of Mathematics, University of Bristol, Bristol, BS8 1TW, UK
25 Pages
Back to Index
