Distributions of Off-Diagonal Scattering Matrix Elements: Exact Results
arXiv:1307.4739 · doi:10.1016/j.aop.2013.11.006
Abstract
Scattering is a ubiquitous phenomenon which is observed in a variety of physical systems which span a wide range of length scales. The scattering matrix is the key quantity which provides a complete description of the scattering process. The universal features of scattering in chaotic systems is most generally modeled by the Heidelberg approach which introduces stochasticity to the scattering matrix at the level of the Hamiltonian describing the scattering center. The statistics of the scattering matrix is obtained by averaging over the ensemble of random Hamiltonians of appropriate symmetry. We derive exact results for the distributions of the real and imaginary parts of the off-diagonal scattering matrix elements applicable to orthogonally-invariant and unitarily-invariant Hamiltonians, thereby solving a long standing problem.
29 pages, 5 figures, Published version
References in corpus (11)
- Scattering, reflection and impedance of waves in chaotic and disordered systems with absorption
- Universal Statistics of the Scattering Coefficient of Chaotic Microwave Cavities
- Experimental and numerical investigation of the reflection coefficient and the distributions of Wigner's reaction matrix for irregular graphs with absorption
- Experimental investigation of Wigner's reaction matrix for irregular graphs with absorption
- Distribution of Scattering Matrix Elements in Quantum Chaotic Scattering
- Experimental Test of Universal Conductance Fluctuations by means of Wave-Chaotic Microwave Cavities
- Universal Chaotic Scattering on Quantum Graphs
- Integration of Grassmann variables over invariant functions on flat superspaces
- Observation of Periodic Orbits on Curved Two - dimensional Geometries
- Correlation Widths in Quantum--Chaotic Scattering
- Universal K-matrix distribution in beta=2 Ensembles of Random Matrices
Cited by in corpus (15)
- Statistics of Complex Wigner Time Delays as a counter of S-matrix poles: Theory and Experiment
- Recursion for the smallest eigenvalue density of -Wishart-Laguerre ensemble
- Experimental investigation of distributions of the off-diagonal elements of the scattering and the Wigner's matrices for networks with broken time reversal invariance
- Distribution of Off-Diagonal Cross Sections in Quantum Chaotic Scattering: Exact Results and Data Comparison
- Spin-resolved electron waiting times in a quantum dot spin valve
- On Random Matrix Averages Involving Half-Integer Powers of GOE Characteristic Polynomials
- Fluctuations in an established transmission in the presence of a complex environment
- Full-dimensional quantum scattering calculations on ultracold atom-molecule collisions in magnetic fields: The role of molecular vibrations
- A Physical Interpretation of Imaginary Time Delay
- Joint probability distributions for projection probabilities of random orthonormal states
- Investigation of the enhancement factor in the regime of semi-Poisson statistics in a singular microwave cavity
- Envelope and phase distribution of a resonance transmission through a complex environment
- Fluctuations and correlations in scattering on a resonance coupled to a chaotic background
- Time Domain Generalization of the Random Coupling Model and Experimental Verification in a Complex Scattering System
- Universality Emerging in a Universality: Derivation of the Ericson Transition in Stochastic Quantum Scattering and Experimental Validation