Experimental study of the distributions of off-diagonal scattering-matrix elements of quantum graphs with symplectic symmetry

Abstract

We report on experimental studies of the distribution of the off-diagonal elements of the scattering matrix of open microwave networks with symplectic symmetry and a chaotic wave dynamics. These consist of two geometrically identical subgraphs with unitary symmetry described by complex conjugate Hamiltonians, that are coupled by a pair of bonds. The results are compared to random-matrix theory predictions obtained on the basis of the Heidelberg approach for the scattering matrix of open quantum-chaotic systems. We demonstrate that deviations from random-matrix theory predictions observed in the distributions may be attributed to the fact that the subgraphs are not fully connected.

References in corpus (54)

• Random-Matrix Theory of Quantum Transport
• Random Matrix Theories in Quantum Physics: Common Concepts
• The Statistical Theory of Quantum Dots
• Periodic Orbit Theory and Spectral Statistics for Quantum Graphs
• Kirchhoff's Rule for Quantum Wires
• Quantum Graphs: Applications to Quantum Chaos and Universal Spectral Statistics
• Random Matrices and Chaos in Nuclear Physics
• Quantum Chaos in Ultracold Collisions of Erbium
• Random Matrices and Chaos in Nuclear Physics: Nuclear Reactions
• Experimental simulation of quantum graphs by microwave networks
• Periodic-Orbit Theory of Level Correlations
• Scattering, reflection and impedance of waves in chaotic and disordered systems with absorption
• Chaotic Scattering on Individual Quantum Graphs
• Chaotic Scattering on Graphs
• Quantum Graphs: A simple model for Chaotic Scattering
• Distribution of the S-matrix in chaotic microwave cavities with direct processes and absorption
• Quantum Chaotic Scattering in Microwave Resonators
• Distribution of reflection coefficients in absorbing chaotic microwave cavities
• Quantum Experiments and Graphs: Multiparty States as coherent superpositions of Perfect Matchings
• Are Scattering Properties of Graphs Uniquely Connected to Their Shapes?
• Power spectrum analysis and missing level statistics of microwave graphs with violated time reversal invariance
• Experimental and numerical investigation of the reflection coefficient and the distributions of Wigner's reaction matrix for irregular graphs with absorption
• A microwave realization of the Gaussian symplectic ensemble
• Resonance widths in open microwave cavities studied by harmonic inversion
• Universal spectral statistics in quantum graphs
• Non-universality in the spectral properties of time-reversal invariant microwave networks and quantum graphs
• Statistics of Impedance, Local Density of States, and Reflection in Quantum Chaotic Systems with Absorption
• Classical 1D maps, quantum graphs and ensembles of unitary matrices
• Universal Properties of 2-Port Scattering, Impedance and Admittance Matrices of Wave Chaotic Systems
• Universal Quantum Graphs
• Induced Violation of Time-Reversal Invariance in the Regime of Weakly Overlapping Resonances
• Crossover from Orthogonal to Unitary Symmetry for Ballistic Electron Transport in Chaotic Microstructures
• Scattering theory on graphs
• Distribution of Scattering Matrix Elements in Quantum Chaotic Scattering
• Non-Weyl Microwave Graphs
• Investigation of nodal domains in the chaotic microwave ray-splitting rough billiard
• Universal Chaotic Scattering on Quantum Graphs
• A first-principles model of time-dependent variations in transmission through a fluctuating scattering environment
• Chaotic Scattering in the Regime of Weakly Overlapping Resonances
• Ericson fluctuations in an open, deterministic quantum system: theory meets experiment
• Transparent Quantum Graphs
• Cross-Section Fluctuations in Chaotic Scattering
• 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
• Spectra and spectral correlations of microwave graphs with symplectic symmetry
• Distributions of the Wigner reaction matrix for microwave networks with symplectic symmetry in the presence of absorption
• Transition from Gaussian-orthogonal to Gaussian-unitary ensemble in a microwave billiard with threefold symmetry
• Experimental investigation of distributions of the off-diagonal elements of the scattering and the Wigner's $\hat{K}$ matrices for networks with broken time reversal invariance
• Distribution of Off-Diagonal Cross Sections in Quantum Chaotic Scattering: Exact Results and Data Comparison
• Nonperiodic echoes from quantum mushroom billiard hats
• Correlation Widths in Quantum--Chaotic Scattering
• Microwave graphs analogs for the voltage drop in three-terminal devices with orthogonal, unitary and symplectic symmetry
• Experimental study of closed and open microwave waveguide graphs with preserved and partially violated time-reversal invariance
• Eigenfunction and eigenmode-spacing statistics in chaotic photonic crystal graphs