Universal intensity statistics of multifractal resonance states
arXiv:2012.02541 · doi:10.1103/PhysRevE.103.042204
Abstract
We conjecture that in chaotic quantum systems with escape the intensity statistics for resonance states universally follows an exponential distribution. This requires a scaling by the multifractal mean intensity which depends on the system and the decay rate of the resonance state. We numerically support the conjecture by studying the phase-space Husimi function and the position representation of resonance states of the chaotic standard map, the baker map, and a random matrix model, each with partial escape.
References in corpus (39)
- Random Matrix Theories in Quantum Physics: Common Concepts
- Statistics of resonance poles, phase shifts and time delays in quantum chaotic scattering for systems with broken time reversal invariance
- Combining directional light output and ultralow loss in deformed microdisks
- Ergodicity breaking in a model showing many-body localization
- Formation of long-lived, scarlike modes near avoided resonance crossings in optical microcavities
- Leaking Chaotic Systems
- Truncations of random unitary matrices
- Quasi-Scarred Resonances in a Spiral-Shaped Microcavity
- Fractal Weyl laws for chaotic open systems
- Quantum-to-classical crossover of quasi-bound states in open quantum systems
- Multifractal dimensions for random matrices, chaotic quantum maps, and many-body systems
- Quantum Mechanics and Semiclassics of Hyperbolic n-Disk Scattering Systems
- Semiclassical structure of chaotic resonance eigenfunctions
- On the rate of quantum ergodicity in Euclidean billiards
- Fractal Weyl law for chaotic microcavities: Fresnel's laws imply multifractal scattering
- Spectra of Random Contractions and Scattering Theory for Discrete-Time Systems
- Numerical Study of Quantum Resonances in Chaotic Scattering
- Statistical properties of eigenstate amplitudes in complex quantum systems
- Ulam method and fractal Weyl law for Perron--Frobenius operators
- From scattering theory to complex wave dynamics in non-hermitian PT-symmetric resonators
- Quantization of generic chaotic 3D billiard with smooth boundary II: structure of high-lying eigenstates
- Localization of resonance eigenfunctions on quantum repellers
- Amplitude distribution of eigenfunctions in mixed systems
- Quantum chaotic resonances from short periodic orbits
- Fractal Weyl law behavior in an open, chaotic Hamiltonian system
- Scarring in open quantum systems
- Spatial structure of lasing modes in wave-chaotic semiconductor microcavities
- Fractal Weyl law for three-dimensional chaotic hard-sphere scattering systems
- Resonance distribution in open quantum chaotic systems
- Resonance eigenfunction hypothesis for chaotic systems
- On the resonance eigenstates of an open quantum baker map
- Short periodic orbit approach to resonances and the fractal Weyl law
- Formation and interaction of resonance chains in the open 3-disk system
- Quantum billiards and constrained random wave correlations
- Quantum signatures of classical multifractal measures
- Structure of resonance eigenfunctions for chaotic systems with partial escape
- Short periodic orbits theory for partially open quantum maps
- Localization of Chaotic Resonance States due to a Partial Transport Barrier
- Phase-space correlations of chaotic eigenstates
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- Husimi dynamics generated by non-Hermitian Hamiltonians
- Chaotic resonance modes in dielectric cavities: Product of conditionally invariant measure and universal fluctuations
- Semiclassical Husimi distributions for non-Hermitian quantum systems
- Local random vector model for semiclassical fractal structure of chaotic resonance states
- Resonance states of the three-disk scattering system
- Semiclassical Limit of Resonance States in Chaotic Scattering
- Self-Similarity Among Energy Eigenstates
- Left-Right Husimi Representation of Chaotic Resonance States: Invariance and Factorization