A Fredholm determinant for semiclassical quantization
Copyright policy )A Fredholm determinant for semiclassical quantization
We investigate a new type of approximation to quantum determinants, the ‘‘quantum Fredholm determinant,’’ and test numerically the conjecture that for Axiom A hyperbolic flows such determinants have a larger domain of analyticity and better convergence than the Gutzwiller–Voros zeta functions derived from the Gutzwiller trace formula. The conjecture is supported by numerical investigations of the 3-disk repeller, a normal-form model of a flow, and a model 2-D map.
- École Normale Supérieure de Lyon France
- University of Copenhagen Denmark
- École Normale Supérieure de Lyon France
- Niels Bohr Institute Denmark
- Eötvös Loránd University Hungary
Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics, Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc., Spectral problems; spectral geometry; scattering theory on manifolds, FOS: Physical sciences, Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory, Chaotic Dynamics (nlin.CD), Nonlinear Sciences - Chaotic Dynamics, Quantum chaos
Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics, Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc., Spectral problems; spectral geometry; scattering theory on manifolds, FOS: Physical sciences, Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory, Chaotic Dynamics (nlin.CD), Nonlinear Sciences - Chaotic Dynamics, Quantum chaos
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