Open AccessSTOCHASTICITY OF THE EFFECTIVE SUBSPACE TAKEN UP BY A COHERENT STATE IN QUANTUM SYSTEM CORRESPONDING TO CLASSICAL CHAOTIC ONE
Author(s) -
Yaowen Xing,
Guowen Xu
Publication year - 1999
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.48.769
Subject(s) - subspace topology , physics , hamiltonian (control theory) , chaotic , quantum chaos , random matrix , quantum , statistical physics , coherent states , quantum mechanics , integrable system , mathematical physics , mathematics , quantum dynamics , mathematical analysis , computer science , artificial intelligence , mathematical optimization , eigenvalues and eigenvectors
It is well known that all torus are destroyed in the Poincare' section with a certain energy E0 when a classical system is in completely chaotic state. But in its quantum counterpart, the features of the subspace taken up by a coherent state with central energy E0=E0 is not yet clear. In the present paper, taking nuclear Lipkin model as an example, we study the properties of such a subspace taken up by the coherent state of SU(3) group. An effective subspace is obtained by using a new renormalization approach. Our results show that in such an effective subspace the distribution of the nearest level spacings, the elements of effective Hamiltonian matrix, and the one-to-one correspondent map from the subspace of an integrable system to that of nonintegrable one are all consistent with predictions of random matrix theory.