A Fredholm Determinant for Semi-classical Quantization

Copenhagen; Denmark); Ecole Normale Sup\'erieure de Lyon; France); G\'abor Vattay (Niels Bohr Institute; Hans Henrik Rugh (Unit\'e de Math\'ematiques Pures et Appliqu\'ees; Per E. Rosenqvist; Predrag Cvitanovi\'c

arxiv: chao-dyn/9307014 · v1 · submitted 1993-07-26 · chao-dyn · nlin.CD

A Fredholm Determinant for Semi-classical Quantization

Predrag Cvitanovi\'c , Per E. Rosenqvist , G\'abor Vattay (Niels Bohr Institute , Copenhagen , Denmark) , Hans Henrik Rugh (Unit\'e de Math\'ematiques Pures et Appliqu\'ees , Ecole Normale Sup\'erieure de Lyon , France) This is my paper

classification chao-dyn nlin.CD

keywords conjecturedeterminantsmodelanalyticityapproximationaxiombetterconvergence

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We investigate a new type of approximation to quantum determinants, the ``\qFd", and test numerically the conjecture that for Axiom A hyperbolic flows such determinants have a larger domain of analyticity and better convergence than the \qS s derived from the \Gt. 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.

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A Fredholm Determinant for Semi-classical Quantization

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