Scarring in open chaotic systems: The local density of states
arXiv:1902.00879 · doi:10.1209/0295-5075/126/10003
Abstract
Chaotic Hamiltonians are known to follow Random Matrix Theory (RMT) ensembles in the apparent randomness of their spectra and wavefunction statistics. Deviations form RMT also do occur, however, due to system-specific properties, or as quantum signatures of classical chaos. Scarring, for instance, is the enhancement of wavefunction intensity near classical periodic orbits, and it can be characterized by a local density of states (or local spectrum) that clearly deviates from RMT expectations, by exhibiting a peaked envelope, which has been described semiclassically. Here, the system is connected to an opening, the local density of states is introduced for the resulting non-Hermitian chaotic Hamiltonian, and estimated a priori in terms of the Green's function of the closed system and the open channels. The predictions obtained are tested on quantum maps coupled both to a single-channel opening and to a Fresnel-type continuous opening. The main outcome is that strong coupling to the opening gradually suppresses the energy dependence of the local density of states due to scarring, and restores RMT behavior.
arXiv comment9 pages, 3 figures
References in corpus (46)
- Combining directional light output and ultralow loss in deformed microdisks
- Leaking Chaotic Systems
- Scattering, reflection and impedance of waves in chaotic and disordered systems with absorption
- Scarred eigenstates for quantum cat maps of minimal periods
- Linear and Nonlinear Theory of Eigenfunction Scars
- Universal Impedance Fluctuations in Wave Chaotic Systems
- Chaos-assisted directional light emission from microcavity lasers
- Distribution of the S-matrix in chaotic microwave cavities with direct processes and absorption
- Statistics of resonance width shifts as a signature of eigenfunction non-orthogonality
- Classical wave experiments on chaotic scattering
- Distribution of reflection coefficients in absorbing chaotic microwave cavities
- Statistics of Impedance and Scattering Matrices in Chaotic Microwave Cavities: Single Channel Case
- Power spectrum analysis and missing level statistics of microwave graphs with violated time reversal invariance
- Semiclassical structure of chaotic resonance eigenfunctions
- Non-universality in the spectral properties of time-reversal invariant microwave networks and quantum graphs
- Statistics of Impedance, Local Density of States, and Reflection in Quantum Chaotic Systems with Absorption
- 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
- Universal statistics of the local Green's function in quantum chaotic systems with absorption
- Semiclassical quantization with short periodic orbits
- Intensity Fluctuations in Closed and Open Systems
- Induced Time-Reversal Symmetry Breaking Observed in Microwave Billiards
- Superscars in billiards -- A model for doorway states in quantum spectra
- Localization of resonance eigenfunctions on quantum repellers
- Controllable quantum scars in semiconductor quantum dots
- Photodissociation in Quantum Chaotic Systems: Random Matrix Theory of Cross-Section Fluctuations
- A statistical model for the excitation of cavities through apertures
- Inhomogeneous losses and complexness of wave functions in chaotic cavities
- Scarring in open quantum systems
- Boundary losses and spatial statistics of complex modes in a chaotic microwave cavity
- A model for chaotic dielectric microresonators
- Spectra and spectral correlations of microwave graphs with symplectic symmetry
- Resonance eigenfunction hypothesis for chaotic systems
- Scar and Antiscar Quantum Effects in Open Chaotic Systems
- Distribution of the wave function inside chaotic partially open systems
- Resonance width distribution in RMT: Weak coupling regime beyond Porter-Thomas
- Experimental test of a trace formula for two-dimensional dielectric resonators
- Mesoscopic transport and quantum chaos
- Scarring and the statistics of tunnelling
- Fluctuations in an established transmission in the presence of a complex environment
- Trace formula for chaotic dielectric resonators tested with microwave experiments
- Wavefunction Statistics using Scar States
- Semiclassical basis sets for the computation of molecular vibrational states
- The role of short periodic orbits in quantum maps with continuous openings
- Envelope and phase distribution of a resonance transmission through a complex environment