Singular Bohr-Sommerfeld Rules For 2D Integrable Systems

Singular Bohr-Sommerfeld Rules For 2D Integrable Systems

Singular Bohr-sommerfeld Rules for 2d Integrable Systems

In this paper, we describe Bohr-Sommerfeld rules for semi-classical completely integrable systems with 2 degrees of freedom with non degenerate singularities (Morse-Bott singularities) under the assumption that the energy level of the first Hamiltonian is non singular. The more singular case of focus-focus singularities is studied in [27] and [26]. The case of 1 degree of freedom has been studi...

Singular Bohr–sommerfeld Rules for 2d Integrable Systems

– This article gives Bohr–Sommerfeld rules for semiclassical completely integrable systems with two degrees of freedom with non-degenerate singularities (Morse–Bott singularities) under the assumption that the energy level of the first Hamiltonian is non-singular. The more singular case of focus– focus singularities was treated in previous works by San Vũ Ngo. c. The case of one degree of freed...

Quantum monodromy and Bohr-Sommerfeld rules

This article is based on a talk given in Dijon for the 2000 summer school “Topological and Geometrical Methods: Applications to Dynamical Systems”. The standard definitions of the monodromy invariant for completely integrable classical systems are reviewed, and the link to the quantum monodromy observed in the joint spectrum of commuting operators is explained. The mathematical treatment relies...

Bohr-Sommerfeld quantization of periodic orbits.

We show, that the canonical invariant part of h̄ corrections to the Gutzwiller trace formula and the Gutzwiller-Voros spectral determinant can be computed by the Bohr-Sommerfeld quantization rules, which usually apply for integrable systems. We argue that the information content of the classical action and stability can be used more effectively than in the usual treatment. We demonstrate the imp...