Abstract
Energy levels of a square well containing δ-function barriers on a Cantor set are analysed. According to the standard tests the spectrum has the characteristics of quantum chaotic behaviour. A discussion on the connection between the spectrum, the wave functions and the exceptional points in the case of quantum chaos is given.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Casati, G. (ed.) Chaotic behaviour in quantum systems. New York: Plenum Press 1985
Heiss, W.D.: Z. Phys. A — Atomic Nuclei329, 133 (1988); Heiss, W.D., Kotzé, A.A.: Z. Phys. A — Atomic Nuclei331, 223 (1988)
Heiss, W.D., Steeb, W.-H.: Phys. Rev. A39, 6018 (1989)
Bohigas, O., Giannoni, M.-J.: Mathematical and computational methods in nuclear physics. Dehesa, J.S., Gomez, J.M.J., Polls, A. (eds.) Lecture Notes in Physics 209. Berlin, Heidelberg, New York: Springer 1984
Wintgen, D., Friedrich, H.: Phys. Rev. Lett.57, 571 (1986); Delande, D., Gay, J.C.: Phys. Rev. Lett.57, 2006 (1986)
Brody, T.A., Flores, J., French, J.B., Mello, P.A., Panday, A., Wong, S.S.M.: Rev. Mod. Phys.53, 385 (1981)
Haq, R.U., Pandey, A., Bohigas, O.: Phys. Rev. Lett.48, 1086 (1982)
Eckhardt, B.: Phys. Rep.163, 205 (1988)
Heller, E.J.: In: Quantum chaos and statistical nuclear physics. Seligman, T.H., Nishioka, H. (eds.) Lecture Notes in Physics 263. Berlin, Heidelberg, New York: Springer 1986; O'Connor, P.W. Heller, E.J.: Phys. Rev. Lett.61, 2288 (1988)
Berry, M.V.: Chaotic behaviour in quantum systems. Casati, G. (ed.) New York: Plenum Press 1985
Kato, T.: Perturbation theory of linear operators. Berlin, Heidelberg, New York: Springer 1966
Heiss, W.D., Sannino, A.L.: J. Phys. A (to appear)
Zirnbauer, M.R., Verbaarschot, J.J.M., Weidenmüller, H.A.W.: Nucl. Phys.411, 161 (1983)
Adachi, S., Toda, M. and Ikeda, K., Phys. Rev. Lett.61, 655 (1988)
Author information
Authors and Affiliations
Additional information
This work was carried out while one of the authors (W.D.H.) enjoyed and gratefully acknowledges the hospitality at the Kellogg Radiation Laboratory of the California Institute of Technology. Partial support was given by National Science Foundation Grants No. PHY85-05682 and PHY86-04197.