Do Spectral Trace Formulae Converge?

Details Do Spectral Trace Formulae Converge? Do Spectral Trace Formulae Converge?

1995-03-02

arxiv.org/abs/chao-dyn/9502025v2

Nonlinear Sciences

Chaotic Dynamics

10 pages REVTeX and 2 Postscript figures in uuencoded TAR'ed compressed format, figures reformatted for Legal size paper, Emai

Scientific paper

We evaluate the Gutzwiller trace formula for the level density of classically chaotic systems by considering the level density in a bounded energy range and truncating its Fourier integral. This results in a limiting procedure which comprises a convergent semiclassical approximation to a well defined spectral quantity at each stage. We test this result on the spectrum of zeros of the Riemann zeta function, obtaining increasingly good approximations to the level density. The Fourier approach also explains the origin of the convergence problems encountered by the orbit truncation scheme.

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