Recent Developments in the Theory of Scarring
arXiv:chao-dyn/9810013 · doi:10.1088/0951-7715/12/2/009
Abstract
We review recent progress in attaining a quantitative understanding of the scarring phenomenon, the non-random behavior of quantum wavefunctions near unstable periodic orbits of a classically chaotic system. The wavepacket dynamics framework leads to predictions about statistical long-time and stationary properties of quantum systems with chaotic classical analogues. Many long-time quantum properties can be quantitatively understood using only short-time classical dynamics information; these include wavefunction intensity distributions, intensity correlations in phase space and correlations between wavefunctions, and distributions of decay rates and conductance peaks in weakly open systems. Strong deviations from random matrix theory are predicted and observed in the presence of short unstable periodic orbits.
22 pages, 15 figures, invited review paper for Nonlinearity
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Cited by in corpus (62)
- Quantum Chaos and Thermalization in Isolated Systems of Interacting Particles
- Yrast line for weakly interacting trapped bosons
- Measuring Scars of Periodic Orbits
- Between classical and quantum
- Rotational spectra of weakly interacting Bose-Einstein condensates
- Chaos-driven dynamics in spin-orbit coupled atomic gases
- Orbit bifurcations and the scarring of wavefunctions
- Quantum Lissajous Scars
- Nodal portraits of quantum billiards: Domains, lines, and statistics
- Wave Function Structure in Two-Body Random Matrix Ensembles
- Linear and Nonlinear Rogue Wave Statistics in the Presence of Random Currents
- Scarring by homoclinic and heteroclinic orbits
- Controllable quantum scars in semiconductor quantum dots
- No quantum ergodicity for star graphs
- Chaos and quantum scars in a coupled top model
- Intermediate wave-function statistics
- Localization of Eigenfunctions in the Stadium Billiard
- Semiclassical Construction of Random Wave Functions for Confined Systems
- Chaotic eigenfunctions in momentum space
- Localization properties of groups of eigenstates in chaotic systems
- Holographic Quantum Scars
- Polyatomic trilobite Rydberg molecules in a dense random gas
- Fragmented Condensate Ground State of Trapped Weakly Interacting Bosons in Two Dimensions
- Coherence dynamics of kicked Bose-Hubbard dimers: Interferometric signatures of chaos
- Square billiard with a magnetic flux
- Effects of scarring on quantum chaos in disordered quantum wells
- Hilbert-space localization in closed quantum systems
- Quantization of a billiard model for interacting particles
- Fluctuations of wave functions about their classical average
- Scarring Effects on Tunneling in Chaotic Double-Well Potentials
- Scarring and the statistics of tunnelling
- Localised eigenfunctions in Seba billiards
- Beyond the First Recurrence in Scar Phenomena
- Hyperbolic Scar Patterns in Phase Space
- Semiclassical spatial correlations in chaotic wave functions
- Quasienergy operators and generalized squeezed states for systems of trapped ions
- Disorder enhanced quantum many-body scars in Hilbert crystals
- Wavefunction Statistics using Scar States
- Genuine quantum scars in many-body spin systems
- Scars of the Wigner function
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- Semiclassical theory of strong localization for quantum thermalization
- Chaotic resonance modes in dielectric cavities: Product of conditionally invariant measure and universal fluctuations
- Formation, prevalence, and stability of bouncing-ball quantum scars
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- Characterization of hybrid quantum eigenstates in systems with mixed classical phasespace
- Variational Scarring in Graphene Quantum Dots
- Superscars in the LiNC=LiCN isomerization reaction
- Quantum Scars in Quantum Field Theory
- Correlations of chaotic eigenfunctions: a semiclassical analysis
- Variational Scarring in Open Two-Dimensional Quantum Dots
- Resonance states of the three-disk scattering system
- Orbit bifurcations and wavefunction autocorrelations
- Deterministic many-body dynamics with multifractal response
- Two particles on a chain with disordered interaction: Localization and dissociation of bound states and mapping to chaotic billiards
- The scar mechanism revisited
- Structure of Quantum Chaotic Wavefunctions: Ergodicity, Localization, and Transport
- Quantum birthmarks: Ergodicity breaking beyond scarring
- Quantum Scars and Caustics in Majorana Billiards
- Periodic revivals from supersymmetry in a fermionic kinetically constrained model
- Maximal scarring for eigenfunctions of quantum graphs
- Metastability, chaos and spectrum tomography for Bose-Hubbard rings and chains