A Fredholm determinant for semiclassical quantization

1993/07/26 by Predrag Cvitanović, Per E. Rosenqvist, Gábor Vattay +1 · 4 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #chao-dyn #nlin.CD

paper · pdf · doi:10.1063/1.165992

published as CHAOS 3 (4), 619 (1993) · Revtex, Ask for figures from [email protected]

arxiv created 1993/07/26 · openalex publication_date 1993/10/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Periodic orbits as the skeleton of classical and quantum chaos

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