Scattering, reflection and impedance of waves in chaotic and disordered systems with absorption

Abstract

We review recent progress in analysing wave scattering in systems with both intrinsic chaos and/or disorder and internal losses, when the scattering matrix is no longer unitary. By mapping the problem onto a nonlinear supersymmetric sigma-model, we are able to derive closed form analytic expressions for the distribution of reflection probability in a generic disordered system. One of the most important properties resulting from such an analysis is statistical independence between the phase and the modulus of the reflection amplitude in every perfectly open channel. The developed theory has far-reaching consequences for many quantities of interest, including local Green functions and time delays. In particular, we point out the role played by absorption as a sensitive indicator of mechanisms behind the Anderson localisation transition. We also provide a random-matrix-based analysis of S-matrix and impedance correlations for various symmetry classes as well as the distribution of transmitted power for systems with broken time-reversal invariance, completing previous works on the subject. The results can be applied, in particular, to the experimentally accessible impedance and reflection in a microwave or ultrasonic cavity attached to a system of antennas.

30 pages, 2 figures; review in the Special Issue of J. Phys. A: Math. Gen. on "Trends in Quantum Chaotic Scattering" (published version with updated refs)

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• Universal statistics of the local Green's function in quantum chaotic systems with absorption
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• Boundary losses and spatial statistics of complex modes in a chaotic microwave cavity
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Cited by in corpus (50)

• Exact relations between multifractal exponents at the Anderson transition
• Beyond mean-field dynamics in open Bose-Hubbard chains
• Quantum and Wave Dynamical Chaos in Superconducting Microwave Billiards
• Experimental and numerical investigation of the reflection coefficient and the distributions of Wigner's reaction matrix for irregular graphs with absorption
• Nonlinear statistics of quantum transport in chaotic cavities
• In-situ Broadband Cryogenic Calibration for Two-port Superconducting Microwave Resonators
• Experimental Examination of the Effect of Short Ray Trajectories in Two-port Wave-Chaotic Scattering Systems
• Resonances in open quantum maps
• Efficient semiclassical approach for time delays
• Inhomogeneous losses and complexness of wave functions in chaotic cavities
• Microwave fidelity studies by varying antenna coupling
• Statistics of eigenfunctions in open chaotic systems: a perturbative approach
• Missing-level statistics in classically chaotic quantum systems with symplectic symmetry
• Statistics of Complex Wigner Time Delays as a counter of S-matrix poles: Theory and Experiment
• Distributions of the Wigner reaction matrix for microwave networks with symplectic symmetry in the presence of absorption
• Resonance width distribution in RMT: Weak coupling regime beyond Porter-Thomas
• Distribution of Off-Diagonal Cross Sections in Quantum Chaotic Scattering: Exact Results and Data Comparison
• On Random Matrix Averages Involving Half-Integer Powers of GOE Characteristic Polynomials
• Experimental investigation of the elastic enhancement factor in a transient region between regular and chaotic dynamics
• Chaotic Scattering with Localized Losses: S-Matrix Zeros and Reflection Time Difference for Systems with Broken Time Reversal Invariance
• Implementing Non-Universal Features with a Random Matrix Theory Approach: Application to Space-to-Configuration Multiplexing
• Elastic enhancement factor as a quantum chaos probe
• Quartic multifractality and finite-size corrections at the spin quantum Hall transition
• Generalized multifractality at spin quantum Hall transition
• Nonstationary random acoustic and electromagnetic fields as wave diffusion processes
• A Physical Interpretation of Imaginary Time Delay
• Microwave graphs analogs for the voltage drop in three-terminal devices with orthogonal, unitary and symplectic symmetry
• Wave systems with direct processes and localized losses or gains: the non-unitary Poisson kernel
• Experimental study of closed and open microwave waveguide graphs with preserved and partially violated time-reversal invariance
• Chaotic scattering with direct processes: A generalization of Poisson's kernel for non-unitary scattering matrices
• Effective chiral magnetic currents, topological magnetic charges, and microwave vortices in a cavity with an enclosed ferrite disk
• Experimental determination of the absorption strength in absorbing chaotic cavities
• Poynting's theorem for planes waves at an interface: a scattering matrix approach
• Elastic Enhancement Factor: from Mesoscopic Systems to Macroscopic Analogous Devices
• Nonlinear Wave Chaos: Statistics of Second Harmonic Fields
• Scattering Statistics in Nonlinear Wave Chaotic Systems
• Superuniversal Statistics of Complex Time-Delays in Non-Hermitian Scattering Systems
• Closed and open superconducting microwave waveguide networks as a model for quantum graphs
• Asymmetric Transmission Through a Classical Analogue of the Aharonov-Bohm Ring
• Investigation of the enhancement factor in the regime of semi-Poisson statistics in a singular microwave cavity
• Coupled unidirectional chaotic microwave graphs
• Scaling properties of delay times in one-dimensional random media
• Time Domain Generalization of the Random Coupling Model and Experimental Verification in a Complex Scattering System
• Semiclassical calculation of time delay statistics in chaotic quantum scattering
• Fluctuations and correlations in scattering on a resonance coupled to a chaotic background
• Chaotic scattering through coupled cavities
• Experimental study of the distributions of off-diagonal scattering-matrix elements of quantum graphs with symplectic symmetry
• Scarring in open chaotic systems: The local density of states
• Universal Frequency Correlations and Recurrence Statistics of Complex Impedance Matrices
• Diffuse field cross-correlations: scattering theory and electromagnetic experiments