New Class of Eigenstates in Generic Hamiltonian Systems

Details New Class of Eigenstates in Generic Hamiltonian Systems New Class of Eigenstates in Generic Hamiltonian Systems

2000-04-04

arxiv.org/abs/nlin/0004005v2

Phys. Rev. Lett 85, 1214 (2000)

Nonlinear Sciences

Chaotic Dynamics

4 pages, 3 figures, Phys. Rev. Lett., to appear

Scientific paper

10.1103/PhysRevLett.85.1214

In mixed systems, besides regular and chaotic states, there are states supported by the chaotic region mainly living in the vicinity of the hierarchy of regular islands. We show that the fraction of these hierarchical states scales as $\hbar^{-\alpha}$ and relate the exponent $\alpha=1-1/\gamma$ to the decay of the classical staying probability $P(t)\sim t^{-\gamma}$. This is numerically confirmed for the kicked rotor by studying the influence of hierarchical states on eigenfunction and level statistics.

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