2000/01/31 by Doron Cohen, Tsampikos Kottos · 2 citations
Chemistry · Mathematics · Physics and Astronomy · #Classical limit #Eigenvalues and eigenvectors #Hamiltonian (control theory) #Kernel (algebra) #Limit (mathematics) #Mathematical analysis #Mathematical physics #Mathematics #Molecular spectroscopy and chirality #Parametric statistics #Physics #Pure mathematics #Quantum #Quantum chaos and dynamical systems #Quantum mechanics #Random matrix #Statistical physics #Theoretical and Computational Physics #Wave function #cond-mat #nlin.CD
paper · pdf · doi:10.1103/physreve.63.036203
published as Phys. Rev. E 63, 36203 (2001). · 7 pages, 5 figures, long detailed version
arxiv created 2000/09/21 · openalex publication_date 2001/02/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 two-dimensional 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 delta(x)[triple bond](x-x(0)). This kernel, regarded as a function of n-m, 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 well-defined classical limit, and the study addresses the issue of quantum-classical correspondence. Both the perturbative and the nonperturbative regimes are explored. The limitations of the random matrix theory approach are demonstrated.