Return probability and scaling exponents in the critical random matrix ensemble

Abstract

We study an asymptotic behavior of the return probability for the critical random matrix ensemble in the regime of strong multifractality. The return probability is expected to show critical scaling in the limit of large time or large system size. Using the supersymmetric virial expansion we confirm the scaling law and find analytical expressions for the fractal dimension of the wave functions $d_2$ and the dynamical scaling exponent $\mu$. By comparing them we verify the validity of the Chalker's ansatz for dynamical scaling.

14 pages, submitted to J. Phys. A

References in corpus (17)

• Transition from localized to extended eigenstates in the ensemble of power-law random banded matrices
• Multifractality and critical fluctuations at the Anderson transition
• Eigenfunction fractality and pseudogap state near superconductor-insulator transition
• Fractal superconductivity near localization threshold
• Relation between the Correlation Dimensions of Multifractal Wavefunctions and Spectral Measures in Integer Quantum Hall Systems
• Two-eigenfunction correlation in a multifractal metal and insulator
• Anderson localization transition and eigenfunction multifractality in ensemble of ultrametric random matrices
• Dynamical scaling for critical states: is Chalker's ansatz valid for strong fractality?
• Strong eigenfunction correlations near the Anderson localization transition
• Virial expansion for almost diagonal random matrices
• Supersymmetry Approach to Almost Diagonal Random Matrices
• Critical Metal Phase at the Anderson Metal-Insulator Transition with Kondo Impurities
• Level compressibility in a critical random matrix ensemble: The second virial coefficient
• Universal and non-universal features of the multifractality exponents of critical wave-functions
• Density of states for almost diagonal random matrices
• Supersymmetric Virial Expansion for Time-Reversal Invariant Disordered Systems
• Correlation of eigenstates in the critical regime of quantum Hall systems

Cited by in corpus (22)

• Dynamics at the Many-Body Localization Transition
• Return probability for the Anderson model on the random regular graph
• Inevitable Power-law Behavior of Isolated Many-Body Quantum Systems and How It Anticipates Thermalization
• Power-law decay exponents: a dynamical criterion for predicting thermalization
• Recurrent scattering and memory effect at the Anderson localization transition
• Multifractal dimensions for all moments for certain critical random matrix ensembles in the strong multifractality regime
• Kondo-Anderson Transitions
• Levy flights and multifractality in quantum critical diffusion and in classical random walks on fractals
• Scale-Invariant Survival Probability at Eigenstate Transitions
• Scale-invariant critical dynamics at eigenstate transitions
• Statistical properties of the Green function in finite size for Anderson Localization models with multifractal eigenvectors
• Multifractality in the generalized Aubry-Andre quasiperiodic localization model with power-law hoppings or power-law Fourier coefficients
• Localization, fractality, and ergodicity in a monitored qubit
• Time-dependent reflection at the localization transition
• Localization transition in random Levy matrices : multifractality of eigenvectors in the localized phase and at criticality
• Exponential Orthogonality Catastrophe at the Anderson Metal-Insulator Transition
• Towards a Comprehensive Theory of Metal-Insulator Transitions in Doped Semiconductors
• Critical dynamics of long-range quantum disordered systems
• Quantum logarithmic multifractality
• Level number variance and spectral compressibility in a critical two-dimensional random matrix model
• Dynamics of Anderson localization in disordered wires
• Quantum Fidelity of the Aubry-André Model and the Exponential Orthogonality Catastrophe