Parametric dependent Hamiltonians, wave functions, random matrix theory, and quantal-classical correspondence - art. no. 036203

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 .