Parametric dependent Hamiltonians, wavefunctions, random-matrix-theory, and quantal-classical correspondence

Details Parametric dependent Hamiltonians, wavefunctions, random-matrix-theory, and quantal-classical correspondence Parametric dependent Hamiltonians, wavefunctions, random-matrix-theory, and quantal-classical correspondence

2000-01-13

arxiv.org/abs/nlin/0001026v2

Phys. Rev. E 63, 36203 (2001).

Nonlinear Sciences

Chaotic Dynamics

7 pages, 5 figures, long detailed version

Scientific paper

10.1103/PhysRevE.63.036203

We study a classically chaotic system which is described by a Hamiltonian $H(Q,P;x)$ where $(Q,P)$ are the canonical coordinates of a particle in a 2D 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 $P(n|m)= ||^2$ evolves as a function of $x-x0$. This kernel, regarded as a function of $n-m$, characterizes the shape of the wavefunctions, and it also can be interpreted as the local density of states (LDOS). The kernel $P(n|m)$ has a well defined classical limit, and the study addresses the issue of quantum-classical correspondence (QCC). We distinguish between restricted QCC and detailed QCC. Both the perturbative and the non-perturbative regimes are explored. The limitations of the random-matrix-theory (RMT) approach are demonstrated.

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