Fluctuations and correlations in scattering on a resonance coupled to a chaotic background
arXiv:1712.07178 · doi:10.12693/APhysPolA.132.1688
Abstract
We discuss and briefly overview recent progress with studying fluctuations in scattering on a resonance state coupled to the background of many chaotic states. Such a problem arises naturally, e.g., when dealing with wave propagation in the presence of a complex environment. Using a statistical model based on random matrix theory, we obtain a number of nonperturbative results for various statistics of scattering characteristics. This includes the joint and marginal distributions of the reflection and transmission intensities and phases, which are derived exactly at arbitrary coupling to the background with finite absorption. The intensities and phases are found to exhibit highly non-trivial statistical correlations, which remain essential even in the limit of strong absorption. In the latter case, we also consider the relevant approximations and their accuracy. As an application, we briefly discuss the statistics of the phase rigidity (or mode complexness) in such a scattering situation.
arXiv comment7 pages, 4 figures (in the Proceedings of 8th Workshop on Quantum Chaos and Localisation Phenomena, Warsaw, Poland: May 19-21, 2017)
References in corpus (29)
- Random Matrix Theories in Quantum Physics: Common Concepts
- Scattering, reflection and impedance of waves in chaotic and disordered systems with absorption
- Distribution of the S-matrix in chaotic microwave cavities with direct processes and absorption
- Quantum Chaotic Scattering in Microwave Resonators
- Classical wave experiments on chaotic scattering
- Statistics of Impedance, Local Density of States, and Reflection in Quantum Chaotic Systems with Absorption
- Universal Properties of 2-Port Scattering, Impedance and Admittance Matrices of Wave Chaotic Systems
- A Simple Mode on a Highly Excited Background: Collective Strength and Damping in the Continuum
- Delay times and reflection in chaotic cavities with absorption
- Distribution of Scattering Matrix Elements in Quantum Chaotic Scattering
- Universal statistics of the local Green's function in quantum chaotic systems with absorption
- Fluctuating "order parameter" for a quantum chaotic system with partially broken time-reversal symmetry
- Intensity Fluctuations in Closed and Open Systems
- Correlation functions of scattering matrix elements in microwave cavities with strong absorption
- Wavefunction statistics in open chaotic billiards
- Measurement of long-range wavefunction correlations in an open microwave billiard
- A first-principles model of time-dependent variations in transmission through a fluctuating scattering environment
- Superscars in billiards -- A model for doorway states in quantum spectra
- Interfering Doorway States and Giant Resonances. I: Resonance Spectrum and Multipole Strengths
- Decay out of a Superdeformed Band
- Inhomogeneous losses and complexness of wave functions in chaotic cavities
- Interfering Doorway States and Giant Resonances. II: Transition Strengths
- Microwave fidelity studies by varying antenna coupling
- Statistics of eigenfunctions in open chaotic systems: a perturbative approach
- Distributions of Off-Diagonal Scattering Matrix Elements: Exact Results
- Boundary losses and spatial statistics of complex modes in a chaotic microwave cavity
- Eigenfunctions of electrons in weakly disordered quantum dots: Crossover between orthogonal and unitary symmetries
- Fluctuations in an established transmission in the presence of a complex environment
- Ballistic Electron Quantum Transport in Presence of a Disordered Background