Levy flights and multifractality in quantum critical diffusion and in classical random walks on fractals

Abstract

We employed the method of virial expansion in order to compute the retarded density correlation function (generalized diffusion propagator) in the critical random matrix ensemble in the limit of strong multifractality. We found that the long-range nature of the Hamiltonian is a common root of both multifractality and Levy flights which show up in the power-law intermediate- and long-distance behavior, respectively, of the density correlation function. We review certain models of classical random walks on fractals and show the similarity of the density correlation function in them to that for the quantum problem described by the random critical long-range Hamiltonians.

12 pages, 9 figures, v2: several typos corrected; submitted to PRB

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Cited by in corpus (20)

• One-dimensional quasicrystals with power-law hopping
• Critical thermalization of a disordered dipolar spin system in diamond
• Return probability for the Anderson model on the random regular graph
• Multifractality of eigenstates in the delocalized non-ergodic phase of some random matrix models : Wigner-Weisskopf approach
• Quantum Levy flights and multifractality of dipolar excitations in a random system
• Dynamical evolution in a one-dimensional incommensurate lattice with $\mathcal{P}\mathcal{T}$ symmetry
• Spread of wave packets in disordered hierarchical lattices
• Scale-Invariant Survival Probability at Eigenstate Transitions
• Scale-invariant critical dynamics at eigenstate transitions
• Nonequilibrium phase transition in an open quantum spin system with long-range interaction
• Statistical properties of the Green function in finite size for Anderson Localization models with multifractal eigenvectors
• Enhanced Amplitude for Superconductivity due to Spectrum-wide Wave Function Criticality in Quasiperiodic and Power-law Random Hopping Models
• 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
• Localization transition in random Levy matrices : multifractality of eigenvectors in the localized phase and at criticality
• Critical dynamics of long-range quantum disordered systems
• Quantizing Lévy flights
• Quantum logarithmic multifractality
• Magnetic instability and spin-glass order beyond the Anderson-Mott transition in interacting power-law random banded matrix fermions
• Quantum walkers in a disordered lattice with power-law hopping