Summary: Complexity, tunneling, and geometrical symmetry
L. P. Horwitz,1,2,3
and Y. Ashkenazy2
School of Natural Sciences, Institute for Advanced Study, Princeton, New Jersey 08540
Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel
School of Physics, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel-Aviv University, Ramat-Aviv, Israel
The Research Institute, The College of Judea and Samaria, Kedumim and Ariel, P.O.B. 3 Ariel, 44837 Israel
Received 21 October 1996
It is demonstrated in the context of the simple one-dimensional example of a barrier in an infinite well that
highly complex behavior of the time evolution of a wave function is associated with the near degeneracy of
levels in the process of tunneling. Degenerate conditions are obtained by shifting the position of the barrier.
The complexity strength depends on the number of almost degenerate levels which depend on geometrical
symmetry. The presence of complex behavior is studied to establish correlation with spectral degeneracy.
S1063-651X 97 09902-9
PACS number s : 05.45. b, 03.65.Ge, 73.40.Gk