Abstract
It is shown that, contrary to a common belief, statistical spectral properties of systems that exhibit classically chaotic behaviour may not obey the statistics typical for Random Matrix Theory. In particular, the nearest neighbor statistics for hydrogen atom in a strong static magnetic field does not obey the usual Wigner distribution. A simple model using a set of regular states coupled to a set of chaotic states modeled by a random matrix reproduces correctly the observed distributions both in the bound regime and for resonances above the ionization threshold.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Preview
Unable to display preview. Download preview PDF.
References
O. Bohigas in Chaos and quantum physics, edited by M.-J. Giannoni, A. Voros and J. Zinn-Justin, Les Houches Summer School, Session LII (North-Holland, Amsterdam, 1991).
F. Haake, Quantum Signatures of Chaos (Springer, Berlin 1991).
C. Iu, G.R. Welch, M.M. Kash, K. Hsu, and D. Kleppner, Phys. Rev. Lett. 63, 1133 (1989).
D. Delande and J.C. Gay, Phys. Rev. Lett., 57, 2006 (1986)
D. Wintgen and H. Friedrich, Phys. Rev. Lett., 57, 571 (1986)
G. Wunner, U. Woelk, I. Zech, G. Zeller, T. Ertl, P. Geyer, W. Schweizer and P. Ruder, Phys. Rev. Lett., 57, 3261 (1986).
H. Friedrich and D. Wintgen, Phys. Rep. 183, 37 (1989).
J. Zakrzewski, K. Dupret, and D. Delande, Phys. Rev. Lett. 74, 522 (1995).
D. Delande, A. Bommier and J.C. Gay, Phys. Rev. Lett. 66, 141 (1991).
K. Dupret, D. Delande and J. Zakrzewski, to be published.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1995 Springer-Verlag
About this paper
Cite this paper
Zakrzewski, J., Dupret, K., Delande, D. (1995). Wigner or non-wigner: That is the question. In: Garbaczewski, P., Wolf, M., Weron, A. (eds) Chaos — The Interplay Between Stochastic and Deterministic Behaviour. Lecture Notes in Physics, vol 457. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60188-0_83
Download citation
DOI: https://doi.org/10.1007/3-540-60188-0_83
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-60188-3
Online ISBN: 978-3-540-44722-1
eBook Packages: Springer Book Archive