Leaking Chaotic Systems
arXiv:1208.0254 · doi:10.1103/RevModPhys.85.869
Abstract
There are numerous physical situations in which a hole or leak is introduced in an otherwise closed chaotic system. The leak can have a natural origin, it can mimic measurement devices, and it can also be used to reveal dynamical properties of the closed system. In this paper we provide an unified treatment of leaking systems and we review applications to different physical problems, both in the classical and quantum pictures. Our treatment is based on the transient chaos theory of open systems, which is essential because real leaks have finite size and therefore estimations based on the closed system differ essentially from observations. The field of applications reviewed is very broad, ranging from planetary astronomy and hydrodynamical flows, to plasma physics and quantum fidelity. The theory is expanded and adapted to the case of partial leaks (partial absorption/transmission) with applications to room acoustics and optical microcavities in mind. Simulations in the lima .con family of billiards illustrate the main text. Regarding billiard dynamics, we emphasize that a correct discrete time representation can only be given in terms of the so- called true-time maps, while traditional Poincar é maps lead to erroneous results. We generalize Perron-Frobenius-type operators so that they describe true-time maps with partial leaks.
Review article, 54 pages, final published version
References in corpus (56)
- Dynamics of Loschmidt echoes and fidelity decay
- Long-Time Correlations in the Stochastic Regime
- Combining directional light output and ultralow loss in deformed microdisks
- Decoherence, Entanglement and Irreversibility in Quantum Dynamical Systems with Few Degrees of Freedom
- Scattering, reflection and impedance of waves in chaotic and disordered systems with absorption
- Chaos-assisted directional light emission from microcavity lasers
- Fractal Weyl laws for chaotic open systems
- Quantum-to-classical crossover of quasi-bound states in open quantum systems
- Dynamical Energy Analysis - determining wave energy distributions in complex vibro-acoustical structures
- Dynamics of Anderson localization in open 3D media
- On universality of algebraic decays in Hamiltonian systems
- Semiclassical structure of chaotic resonance eigenfunctions
- Correcting ray optics at curved dielectric microresonator interfaces: Phase-space unification of Fresnel filtering and the Goos-Haenchen shift
- Stickiness in mushroom billiards
- Open circular billiards and the Riemann hypothesis
- Fractal Weyl law for chaotic microcavities: Fresnel's laws imply multifractal scattering
- Poincare recurrences and transient chaos in systems with leaks
- Universality of algebraic laws in Hamiltonian systems
- Hypothesis of strong chaos and anomalous diffusion in coupled symplectic maps
- Recurrence Time Statistics for Finite Size Intervals
- Fractal Weyl law for quantum fractal eigenstates
- Directional emission of stadium-shaped micro-lasers
- Noise-enhanced trapping in chaotic scattering
- Peeping at chaos: Nondestructive monitoring of chaotic systems by measuring long-time escape rates
- Non-Hamiltonian dynamics in optical microcavities resulting from wave-inspired corrections to geometric optics
- Weyl asymptotics: From closed to open systems
- Poincare recurrences from the perspective of transient chaos
- Classical Phase Space Revealed by Coherent Light
- Emission from dielectric cavities in terms of invariant sets of the chaotic ray dynamics
- Instability statistics and mixing rates
- Prevalence of marginally unstable periodic orbits in chaotic billiards
- Spectral statistics in an open parametric billiard system
- Inhomogeneous losses and complexness of wave functions in chaotic cavities
- First experimental evidence for quantum echoes in scattering systems
- Fractal Weyl law for three-dimensional chaotic hard-sphere scattering systems
- Boundary losses and spatial statistics of complex modes in a chaotic microwave cavity
- Chaos-assisted emission from asymmetric resonant cavity microlasers
- Resonance distribution in open quantum chaotic systems
- Sensing Small Changes in a Wave Chaotic Scattering System
- Semiclassical Mechanism for the Quantum Decay in Open Chaotic Systems
- Distribution of resonances in the quantum open baker map
- Avoided level crossing statistics in open chaotic billiards
- Stochastic perturbations in open chaotic systems: random versus noisy maps
- Loschmidt echo in quantum maps: the elusive nature of the Lyapunov regime
- Experimental test of a trace formula for two-dimensional dielectric resonators
- Quasimodes of a chaotic elastic cavity with increasing local losses
- Nonperiodic echoes from mushroom billiard hats
- Faster than expected escape for a class of fully chaotic maps
- Escape time statistics for mushroom billiards
- Leaking method approach to surface transport in the Mediterranean Sea from a numerical ocean model
- Quantum decay of an open chaotic system: a semiclassical approach
- Effect of noise in open chaotic billiards
- Fidelity decay for local perturbations: microwave evidence for oscillating decay exponents
- Transient features of quantum open maps
- Weyl law for fat fractals
- Relativistic echo dynamics and the stability of a beam of Landau electrons
Cited by in corpus (92)
- Quantum and Wave Dynamical Chaos in Superconducting Microwave Billiards
- Route to extreme events in excitable systems
- Survivability of Deterministic Dynamical Systems
- Experimental control of transport resonances in a coherent quantum rocking ratchet
- Self-induced switchings between multiple space-time patterns on complex networks of excitable units
- Topological Invariant and Anomalous Edge Modes of Strongly Nonlinear Systems
- Resonances in open quantum maps
- Classifying orbits in the restricted three-body problem
- Fractal basins of escape and the formation of spiral arms in a galactic potential with a bar
- Mitigating long transient time in deterministic systems by resetting
- Spatial structure of lasing modes in wave-chaotic semiconductor microcavities
- Hierarchical Fractal Weyl Laws for Chaotic Resonance States in Open Mixed Systems
- Resonance eigenfunction hypothesis for chaotic systems
- Resonance width distribution in RMT: Weak coupling regime beyond Porter-Thomas
- Chaotic Systems with Absorption
- 3D billiards: visualization of regular structures and trapping of chaotic trajectories
- Multimode Lasing in Wave-Chaotic Semiconductor Microlasers
- Formation and interaction of resonance chains in the open 3-disk system
- Statistics of time delay and scattering correlation functions in chaotic systems II. Semiclassical Approximation
- Quantum signatures of classical multifractal measures
- Chaotic transport of navigation satellites
- Structure of resonance eigenfunctions for chaotic systems with partial escape
- Localization of Chaotic Resonance States due to a Partial Transport Barrier
- How does the oblateness coefficient influence the nature of orbits in the restricted three-body problem?
- A boundary integral formalism for stochastic ray tracing in billiards
- Odd thermodynamic limit for the Loschmidt echo
- Escape through a time-dependent hole in the doubling map
- Universal intensity statistics of multifractal resonance states
- Impact of cavity geometry on microlaser dynamics
- Multifractality of open quantum systems
- Eigenfunctions of the Perron-Frobenius operator and the finite-time Lyapunov exponents in uniformly hyperbolic area-preserving maps
- Husimi dynamics generated by non-Hermitian Hamiltonians
- Follow the fugitive: an application of the method of images to open dynamical systems
- Semiclassical Husimi distributions for non-Hermitian quantum systems
- Chaotic resonance modes in dielectric cavities: Product of conditionally invariant measure and universal fluctuations
- On the classification of orbits in the three-dimensional Copenhagen problem with oblate primaries
- Slim Fractals: The Geometry of Doubly Transient Chaos
- Decay of semiclassical massless Dirac fermions from integrable and chaotic cavities
- Importance Sampling of Rare Events in Chaotic Systems
- Separation of particles leading to decay and unlimited growth of energy in a driven stadium-like billiard
- Chaotic Explosions
- Lagrangian descriptors for the Bunimovich stadium billiard
- Bill2d - a software package for classical two-dimensional Hamiltonian systems
- Slow and fast escape for open intermittent maps
- Local random vector model for semiclassical fractal structure of chaotic resonance states
- Probabilistic description of dissipative chaotic scattering
- Fractal and Wada escape basins in the chaotic particle drift motion in tokamaks
- Fractal structures for the Jacobi Hamiltonian of restricted three-body problem
- Chaotic saddles in a generalized Lorenz model of magnetoconvection
- Resonance spectra for quantum maps of kicked scattering systems by complex scaling
- Measure, dimension, and complexity of the transient motion in Hamiltonian systems
- Leaking from the phase space of the Riemann-Liouville fractional standard map
- Rotating Leaks in the Stadium Billiard
- Transient chaos and fractal structures in planetary feeding zones
- Resonance states of the three-disk scattering system
- Algebraic statistics of Poincaré recurrences in DNA molecule
- Asymptotic escape rates and limiting distributions for multimodal maps
- Why Escape Is Faster Than Expected
- Escape dynamics and fractal basin boundaries in Seyfert galaxies
- Transition from normal to ballistic diffusion in a one-dimensional impact system
- Optimal interdependence enhances robustness of complex systems
- Multimodal distribution of transient time of predator extinction in a three-species food chain
- Escape rate scaling in infinite measure preserving systems
- Two-Particle Circular Billiards Versus Randomly Perturbed One-Particle Circular Billiards
- Weak Nanoscale Chaos And Anomalous Relaxation in DNA
- Semiclassical Limit of Resonance States in Chaotic Scattering
- Diffusion Phenomena in a Mixed Phase Space
- Transport properties of diffusive particles conditioned to survive in trapping environments
- Taming chaos to sample rare events: the effect of weak chaos
- On Transfer Operators and Maps with Random Holes
- Chaos and the Flow Capture Problem: Polluting is Easy, Cleaning is Hard
- Stochastic boundary approaches to many-particle systems coupled to a particle reservoir
- Leaky Fermi accelerators
- Sub-diffusive behavior in the Standard Map
- Temporal-varying failures of nodes in networks
- Correspondence principle, dissipation, and Ginibre ensemble
- Unidirectionally Coupled Map Lattices with Non-Linear Coupling: Unbinding Transitions and Super-Long Transients
- Chaos and Parrondo's paradox: An overview
- Orbital dynamics in galactic potentials under mass transfer
- Escape-rate response to noise of all amplitudes in leaky chaos
- Chaotic fields out of equilibrium are observable independent
- Does an intermittent dynamical system remain (weakly) chaotic after drilling in a hole?
- Escape rates for the Farey map with approximated holes
- Quantum particle escape from a time-dependent confining potential
- Diffusion and escape times in the open-leaky standard map
- Escape dynamics through a continuously growing leak
- Escape Dynamics of Many Hard Disks
- Scarring in open chaotic systems: The local density of states
- Stochastic Web Map: Survival probability and escape frequency
- Fractals in rate-induced tipping
- Left-Right Husimi Representation of Chaotic Resonance States: Invariance and Factorization
- Atom scattering off a vibrating surface: An example of chaotic scattering with three degrees of freedom