Local random vector model for semiclassical fractal structure of chaotic resonance states

Research output: Contribution to journalResearch articleContributedpeer-review



The semiclassical structure of resonance states of classically chaotic scattering systems with partial escape is investigated. We introduce a local randomization on phase space for the baker map with escape, which separates the smallest multifractal scale from the scale of the Planck cell. This allows for deriving a semiclassical description of resonance states based on a local random vector model and conditional invariance. We numerically demonstrate that the resulting classical measures perfectly describe resonance states of all decay rates γ for the randomized baker map. By decreasing the scale of randomization these results are compared to the deterministic baker map with partial escape. This gives the best available description of its resonance states. Quantitative differences indicate that a semiclassical description for deterministic chaotic systems must take into account that the multifractal structures persist down to the Planck scale.


Original languageEnglish
Article number204006
Pages (from-to)1-25
Number of pages25
JournalJournal of Physics A: Mathematical and Theoretical
Issue number20
Publication statusPublished - 21 Apr 2022

External IDs

unpaywall 10.1088/1751-8121/ac62b9
Scopus 85131142135
Mendeley a72e2226-eeb3-3a9e-b59f-e850d113661f
WOS 000787181600001


DFG Classification of Subject Areas according to Review Boards


  • local randomization, quantum chaos, random vector model, resonance states, semiclassical limit

Library keywords