Phys. Rev. Lett. 85, 1214–1217 (2000)New Class of Eigenstates in Generic Hamiltonian SystemsReceived 10 March 2000; revised 28 April 2000; published in the issue dated 7 August 2000 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 ħα and we relate the exponent α = 1-1/γ to the decay of the classical staying probability P(t)∼t-γ. This is numerically confirmed for the kicked rotor by studying the influence of hierarchical states on eigenfunction and level statistics. © 2000 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevLett.85.1214
DOI:
10.1103/PhysRevLett.85.1214
PACS:
05.45.Mt, 03.65.Sq
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