Universal intensity statistics of multifractal resonance states

Clauß, Konstantin; Kunzmann, Felix; Bäcker, Arnd; Ketzmerick, Roland

doi:10.1103/physreve.103.042204

Cited by 8 publications

(12 citation statements)

References 76 publications

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“…Within each subregion the resonance state visually fluctuates as in closed chaotic quantum maps and we expect an exponential distribution around the average, as studied in Ref. [50] for quantum maps with escape and without randomization. The subregion structure remains the same for increasing N and the Planck cell becomes arbitrarily small compared to it, giving a well-defined semiclassical limit.…”

Section: Resonance Statesmentioning

confidence: 61%

“…This leads to a straightforward derivation of the analytic expressions for their structure and its dependence on γ, given in Ref. [50,App. D].…”

Section: Appendix a Substructure Of Randomization Regionsmentioning

confidence: 99%

“…Such models are defined as the composition of a random matrix and an escape operator [69,78,79,80,50],…”

Section: Appendix a Substructure Of Randomization Regionsmentioning

confidence: 99%

“…Here we focus on the semiclassical structure of resonance states in chaotic systems with escape. They are described by multifractal measures on phase space [37,38,39,40,41,42,43,44,45,46,47,48,49] with exponentially distributed intensity fluctuations [50]. These measures are conditionally invariant under the classical dynamics with escape [51,19] and strongly depend on the corresponding quantum decay rate γ [40,47,48].…”

Section: Introductionmentioning

confidence: 99%

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

Clauß,

Ketzmerick

2021

Preprint

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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 wave 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. Comparison to the baker map without randomization shows very good agreement of the multifractal structures. Quantitative differences indicate that a semiclassical description for systems without randomization must take into account that the multifractal structures persist down to the Planck scale.

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Section: Resonance Statesmentioning

confidence: 61%

“…This leads to a straightforward derivation of the analytic expressions for their structure and its dependence on γ, given in Ref. [50,App. D].…”

Section: Appendix a Substructure Of Randomization Regionsmentioning

confidence: 99%

“…Such models are defined as the composition of a random matrix and an escape operator [69,78,79,80,50],…”

Section: Appendix a Substructure Of Randomization Regionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Clauß,

Ketzmerick

2021

Preprint

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“…Recently, a factorization conjecture for fully chaotic open systems was introduced, that applies to resonance states with arbitrary decay rate [38,71]: one factor is given by universal exponentially distributed intensity fluctuations corresponding to a complex random wave model. The other factor depends on the decay rate and is given by some classical conditionally-invariant measure that is suitably smoothed.…”

Section: Introductionmentioning

confidence: 99%

Resonance states of the three-disk scattering system

Schmidt,

Ketzmerick

2023

New J. Phys.

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For the paradigmatic three-disk scattering system, we confirm a recent conjecture for open chaotic systems, which claims that resonance states are composed of two factors. In particular, we demonstrate that one factor is given by universal exponentially distributed intensity fluctuations. The other factor, supposed to be a classical density depending on the lifetime of the resonance state, is found to be very well described by a classical construction. Furthermore, ray-segment scars, recently observed in dielectric cavities, dominate every resonance state at small wavelengths also in the three-disk scattering system. We introduce a new numerical method for computing resonances, which allows for going much further into the semiclassical limit. As a consequence we are able to confirm the fractal Weyl law over a correspondingly large range.

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