Fractal potentials from energy levels
Abstract
We analyze the reconstruction by Wu and Sprung [Phys. Rev. E 48, 2595 (1993)] of a fractal one-dimensional potential, the quantum spectrum of which reproduces the first 500 nontrivial zeros of the Riemann ζ function. Our construction is based on a spectrum with Gaussian unitary ensemble statistics as far as the nearest-neighbor spacing distribution is concerned. Our results show that a reliable estimate of the fractal dimension of the potential necessitates a very large number of levels.
- Publication:
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Physical Review E
- Pub Date:
- June 1995
- DOI:
- 10.1103/PhysRevE.51.6323
- Bibcode:
- 1995PhRvE..51.6323R
- Keywords:
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- 05.40.+j