Estimating the spectral density of unstable scars
arXiv:2112.15554 · doi:10.1088/1751-8121/ac7e0c
Abstract
In quantum chaos, the spectral statistics generally follows the predictions of Random Matrix Theory (RMT). A notable exception is given by scar states, that enhance probability density around unstable periodic orbits of the classical system, therefore causing significant deviations of the spectral density from RMT expectations. In this work, the problem is considered of both RMT-ruled and scarred chaotic systems coupled to an opening. In particular, predictions are derived for the spectral density of a chaotic Hamiltonian scattering into a single- or multiple channels. The results are tested on paradigmatic quantum chaotic maps on a torus. The present report develops the intuitions previously sketched in [D. Lippolis, EPL 126 (2019) 10003].
arXiv comment25 pages, 10 figures
References in corpus (23)
- Chaos and Quantum Thermalization
- Quantum Many-Body Scars and Weak Breaking of Ergodicity
- Quantum scarred eigenstates in a Rydberg atom chain: entanglement, breakdown of thermalization, and stability to perturbations
- Periodic orbits, entanglement and quantum many-body scars in constrained models: matrix product state approach
- Scarred eigenstates for quantum cat maps of minimal periods
- Linear and Nonlinear Theory of Eigenfunction Scars
- Observation of Scarred Modes in Asymmetrically Deformed Microcylinder Lasers
- Quantum chaos and effective thermalization
- Slow quantum thermalization and many-body revivals from mixed phase space
- Statistics of resonance width shifts as a signature of eigenfunction non-orthogonality
- Statistics of Impedance and Scattering Matrices in Chaotic Microwave Cavities: Single Channel Case
- A Simple Mode on a Highly Excited Background: Collective Strength and Damping in the Continuum
- First Experimental Observation of Superscars in a Pseudointegrable Barrier Billiard
- Wavefunction Intensity Statistics from Unstable Periodic Orbits
- A Matrix Element for Chaotic Tunnelling Rates and Scarring Intensities
- Localization of resonance eigenfunctions on quantum repellers
- Superscars in billiards -- A model for doorway states in quantum spectra
- A model for chaotic dielectric microresonators
- Scar and Antiscar Quantum Effects in Open Chaotic Systems
- Scarring and the statistics of tunnelling
- Short periodic orbits theory for partially open quantum maps
- The short periodic orbit method for excited chaotic eigenfunctions
- Scarring in classical chaotic dynamics with noise