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Last update: 23/03/2003

 Houches March 2003

École de physique des Houches

E Bogomolny
Quantum and arithmetic chaos


Abstract:

The lectures are focused on the investigation of statistical properties of energy levels of quantum systems. We adopt an approach based on the trace formulas which relate quantum eigenvalue densities with classical periodic orbits. The main attention is given to the structure of classical periodic orbits for different models. The following questions are discussed: Construction of trace formulas. Number-theoretical zeta functions. Semiclassical expressions of correlation functions. Structure of periodic orbits for generic integrable and chaotic models. Sum rules. Non-diagonal terms. Arithmetical systems. Diffractive models.

lecture: