Semiclassical limit for a truncated Hamiltonian.
In the numerical calculation of the eigenenergies of a polynomial Hamiltonian, the majority of the levels depend on the cutoff of the basis used. By analyzing the finite Hamiltonian matrix as corresponding to a classical "Action Billiard" we are able to explain several features of the full spectrum using semiclassical periodic orbit theory. There are a large number of low-period orbits which interfere at the higher energies contained in the billiard. In this range the billiard becomes more regular than the untruncated Hamiltonian, as reflected by the Berry-Robnik level spacing distribution. (c) 1996 American Institute of Physics.
Castilho
Cesar
C
Mathematics Department, University of California at Santa Cruz, Santa Cruz, California 95064Centro Brasileiro de Pesquisas Fisicas, Rua Dr. Xavier Sigaud, 150, Rio de Janeiro, RJ 22290-180, Brazil.
Ozorio De Almeida
A. M.
AM