# Multifractal wave functions of simple quantum maps.

@article{Martin2010MultifractalWF, title={Multifractal wave functions of simple quantum maps.}, author={John Martin and Ignacio Garc{\'i}a-Mata and Olivier Giraud and Bertrand Georgeot}, journal={Physical review. E, Statistical, nonlinear, and soft matter physics}, year={2010}, volume={82 4 Pt 2}, pages={ 046206 } }

We study numerically multifractal properties of two models of one-dimensional quantum maps: a map with pseudointegrable dynamics and intermediate spectral statistics and a map with an Anderson-like transition recently implemented with cold atoms. Using extensive numerical simulations, we compute the multifractal exponents of quantum wave functions and study their properties, with the help of two different numerical methods used for classical multifractal systems (box-counting and wavelet…

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## References

SHOWING 1-10 OF 69 REFERENCES

Theory and Applications

- 2009

Infinitary rewriting generalises usual finitary rewriting by providing infinite reduction sequences with a notion of convergence. The idea of – at least conceptually – assigning a meaning to infinite…

Journal of Geophysical Research

- Nature
- 1949

FROM March 1949 the journal Terrestrial Magnetism and Almespheric Electricity will appear under the new title Journal of Geophysical Research. The change the name marks the transfer of editorship…

"J."

- 1890

however (for it was the literal soul of the life of the Redeemer, John xv. io), is the peculiar token of fellowship with the Redeemer. That love to God (what is meant here is not God’s love to men)…

Phys

- Rev. E 77, 035201(R)
- 2008

Rev

- Mod. Phys. 80, 1355
- 2008

Phys

- Rev. Lett. 93, 254102
- 2004

Phys

- Rev. B 62, 7920
- 2000

Phys

- Rev. Lett. 79, 1913
- 1997

Phys

- Rev. Lett. 101, 255702 (2008); G. Lemarié, J. Chabé, P. Szriftgiser, J.-C. Gar- reau, B. Grémaud, and D. Delande, Phys. Rev. A 80, 043626
- 2009

Rev. Mod. Phys

- Rev. Mod. Phys
- 2008