Probing the eigenfunction fractality with a stop watch

Abstract

We study numerically the distribution of scattering phases $\mathcal{P}(\Phi )$ and of Wigner delay times $\mathcal{P}({\tau }_W)$ for the power-law banded random matrix (PBRM) model at criticality with one channel attached to it. We find that $\mathcal{P}(\Phi )$ is insensitive to the position of the channel and undergoes a transition towards uniformity as the bandwidth $b$ of the PBRM model increases. The inverse moments of Wigner delay times scale as $<{\tau }_W^{-q}>\sim L^{-q{D}_{q+1}}$, where $D_q$ are the multifractal dimensions of the eigenfunctions of the corresponding closed system and $L$ is the system size. The latter scaling law is sensitive to the position of the channel.

5 pages, 4 figures

References in corpus (10)

• Statistical Signatures of Photon Localization
• Dimensionality dependence of the wave function statistics at the Anderson transition
• Fluctuations of the correlation dimension at metal-insulator transitions
• Fluctuation of the Correlation Dimension and the Inverse Participation Number at the Anderson Transition
• Distribution of proper delay times in quantum chaotic scattering: A crossover from ideal to weak coupling
• Induced vs Spontaneous Breakdown of S-matrix Unitarity: Probability of No Return in Quantum Chaotic and Disordered Systems
• Statistics of delay times in mesoscopic systems as a manifestation of eigenfunction fluctuations
• Fingerprints of classical diffusion in open 2D mesoscopic systems in the metallic regime
• Statistics of Dynamics of Localized Waves
• Statistics of resonances and delay times: A criterion for Metal-Insulator transitions

Cited by in corpus (26)

• Anderson Transitions
• Light fields in complex media: mesoscopic scattering meets wave control
• Exact relations between multifractal exponents at the Anderson transition
• Scattering, reflection and impedance of waves in chaotic and disordered systems with absorption
• Statistics of Resonances and Delay Times in Random Media: Beyond Random Matrix Theory
• Avalanches of Bose-Einstein Condensates in Leaking Optical Lattices
• Signatures of photon localization
• Boundary multifractality in critical 1D systems with long-range hopping
• Resonance width distribution for high-dimensional random media
• Scattering at the Anderson transition: Power--law banded random matrix model
• Critical Fidelity
• Anderson localization transition with long-ranged hoppings : analysis of the strong multifractality regime in terms of weighted Levy sums
• Statistics of the two-point transmission at Anderson localization transitions
• A critical Dyson hierarchical model for the Anderson localization transition
• Joint moments of proper delay times
• Multifractality in random networks with power-law decaying bond strengths
• Multifractality of open quantum systems
• Parametric invariant Random Matrix Model and the emergence of multifractality
• Multifractal fluctuations in the survival probability of an open quantum system
• On the multifractal dimensions and statistical properties of critical ensembles characterized by the three classical Wigner-Dyson symmetry classes
• Scattering and transport statistics at criticality
• Scattering and transport properties of the three classical Wigner-Dyson ensembles at the Anderson transition
• Anderson transitions : multifractal or non-multifractal statistics of the transmission as a function of the scattering geometry
• Scaling properties of delay times in one-dimensional random media
• Time delay matrix at the spectrum edge and the minimal chaotic cavities
• Short-Time Loschmidt Gap in Dynamical Systems with Critical Chaos