D. Cohen et T. Kottos, Parametric dependent Hamiltonians, wave functions, random matrix theory, and quantal-classical correspondence - art. no. 036203, PHYS REV E, 6303(3), 2001, pp. 6203
We study a classically chaotic system that is described by a Hamiltonian H(
Q,P;x), when (Q,P) are the canonical coordinates of a particle in a two-dim
ensional well, and x is a parameter. By changing x we can deform the ''shap
e" of the well. The quantum eigenstates of the system are \n(x)). We analyz
e numerically how the parametric kernel P(n/m)=\(n(x)\m(x(o)))\(2) evolves
as a function of deltax=(x-x(o)). This kernel, regarded as a function of n-
m, characterizes the shape of the wave functions, and it also can be interp
reted as the local density of states. The kernel P(n\m) has a well-defined
classical limit, and the study addresses the issue of quantum-classical cor
respondence. Both the perturbative and the nonperturbative regimes are expl
ored. The limitations of the random matrix theory approach are demonstrated
.