Parametric dependent Hamiltonians, wave functions, random matrix theory, and quantalclassical correspondence
Abstract
We study a classically chaotic system that is described by a Hamiltonian H(Q,P;x), where (Q,P) are the canonical coordinates of a particle in a twodimensional well, and x is a parameter. By changing x we can deform the ``shape'' of the well. The quantum eigenstates of the system are \n(x)>. We analyze numerically how the parametric kernel P(n\m)=\<n(x)\m(x_{0})>\^{2} evolves as a function of δx≡(xx_{0}). This kernel, regarded as a function of nm, characterizes the shape of the wave functions, and it also can be interpreted as the local density of states. The kernel P(n\m) has a welldefined classical limit, and the study addresses the issue of quantumclassical correspondence. Both the perturbative and the nonperturbative regimes are explored. The limitations of the random matrix theory approach are demonstrated.
 Publication:

Physical Review E
 Pub Date:
 March 2001
 DOI:
 10.1103/PhysRevE.63.036203
 arXiv:
 arXiv:nlin/0001026
 Bibcode:
 2001PhRvE..63c6203C
 Keywords:

 05.45.Mt;
 03.65.Sq;
 Quantum chaos;
 semiclassical methods;
 Semiclassical theories and applications;
 Nonlinear Sciences  Chaotic Dynamics;
 Condensed Matter
 EPrint:
 7 pages, 5 figures, long detailed version