A Fredholm determinant for semiclassical quantization
- 1 October 1993
- journal article
- research article
- Published by AIP Publishing in Chaos: An Interdisciplinary Journal of Nonlinear Science
- Vol. 3 (4) , 619-636
- https://doi.org/10.1063/1.165992
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.Keywords
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This publication has 23 references indexed in Scilit:
- The correlation spectrum for hyperbolic analytic mapsNonlinearity, 1992
- Mixing rates and exterior forms in chaotic systemsJournal of Physics A: General Physics, 1990
- Determination of correlation spectra in chaotic systemsPhysical Review Letters, 1990
- The spectrum of the period-doubling operator in terms of cyclesJournal of Physics A: General Physics, 1990
- Recycling of strange sets: I. Cycle expansionsNonlinearity, 1990
- Invariant Measurement of Strange Sets in Terms of CyclesPhysical Review Letters, 1988
- Unstable periodic orbits and semiclassical quantisationJournal of Physics A: General Physics, 1988
- Fractal measures and their singularities: The characterization of strange setsPhysical Review A, 1986
- Zeta-functions for expanding maps and Anosov flowsInventiones Mathematicae, 1976
- Differentiable dynamical systemsBulletin of the American Mathematical Society, 1967