Anomalous diffusion at the Anderson transitions
arXiv:cond-mat/9701013 · doi:10.1143/JPSJ.66.314
Abstract
Diffusion of electrons in three dimensional disordered systems is investigated numerically for all the three universality classes, namely, orthogonal, unitary and symplectic ensembles. The second moment of the wave packet $<\vv{r}^2(t)>$ at the Anderson transition is shown to behave as . From the temporal autocorrelation function , the fractal dimension is deduced, which is almost half the value of space dimension for all the universality classes.
Revtex, 2 figures, to appear in J. Phys. Soc. Jpn.(1997) Feb
References in corpus (1)
Cited by in corpus (58)
- Experimental observation of the Anderson transition with atomic matter waves
- The Ergodic Side of the Many-Body Localization Transition
- Thouless time analysis of Anderson and many-body localization transitions
- Fast Algorithm for Finding the Eigenvalue Distribution of Very Large Matrices
- Observation of anomalous diffusion and fractional self-similarity in one dimension
- What determines the spreading of a wave packet?
- Density of States Scaling at the Semimetal to Metal Transition in Three Dimensional Topological Insulators
- Many-Body Localization in the Age of Classical Computing
- Between a metal and an insulator: the critical state of the Anderson transition
- Anomalous Thouless energy and critical statistics on the metallic side of the many-body localization transition
- Observation of the Anderson Metal-Insulator Transition with Atomic Matter Waves: Theory and Experiment
- Boundary conditions at the mobility edge
- Sub-diffusion in the Anderson model on random regular graph
- Dimensionality dependence of the wave function statistics at the Anderson transition
- Energy spectra, wavefunctions and quantum diffusion for quasiperiodic systems
- Multifractality and its role in anomalous transport in the disordered XXZ spin-chain
- Slow Dynamics in a Two-Dimensional Anderson-Hubbard Model
- Fractality in nonequilibrium steady states of quasiperiodic systems
- Unconditionally Stable Algorithms to Solve the Time-Dependent Maxwell Equations
- Drawing Phase Diagrams of Random Quantum Systems by Deep Learning the Wave Functions
- A semiclassical theory of the Anderson transition
- Electrical properties of isotopically enriched neutron-transmutation-doped ^{70} Ge:Ga near the metal-insulator transition
- Wave-packet dynamics at the mobility edge in two- and three-dimensional systems
- Distribution of fractal dimensions at the Anderson transition
- Universality of the Anderson transition with the quasiperiodic kicked rotor
- Approach to equilbrium in nano-scale systems at finite temperatur
- Detecting delocalization-localization transitions from full density distributions
- Phase diagram of the Anderson transition with atomic matter waves
- Kondo-Anderson Transitions
- Critical Metal Phase at the Anderson Metal-Insulator Transition with Kondo Impurities
- Scale-Invariant Survival Probability at Eigenstate Transitions
- Coherent backscattering reveals the Anderson transition
- Scale-invariant critical dynamics at eigenstate transitions
- Critical dynamics at the Anderson localization mobility edge
- Application of Convolutional Neural Network to Quantum Percolation in Topological Insulators
- One-parameter Superscaling at the Metal-Insulator Transition in Three Dimensions
- Anomalous diffusion and localization in a positionally disordered quantum spin array
- Probing the topological Anderson transition with quantum walks
- Dynamic scaling relation in quantum many-body systems
- Diffusion in the Anderson model in higher dimensions
- Borel-Padé re-summation of the -functions describing Anderson localisation in the Wigner-Dyson symmetry classes
- Periodically and aperiodically Thue-Morse driven long-range systems: from dynamical localization to slow dynamics
- Critical dynamics of long-range quantum disordered systems
- Machine learning the dynamics of quantum kicked rotor
- Dynamical Tunneling in Many-Dimensional Chaotic Systems
- Spectral Properties of Three Dimensional Layered Quantum Hall Systems
- Anderson localization of emergent quasiparticles: Spinon and vison interplay at finite temperature in a gauge theory in three dimensions
- Level Curvature Distribution and the Structure of Eigenfunctions in Disordered Systems
- Quantum logarithmic multifractality
- Dynamics of Anderson localization in disordered wires
- Quantum transport properties of two-dimensional systems in disordered magnetic fields with a fixed sign
- Characterizing dynamical criticality of many-body localization transitions from the Fock-space perspective
- Superconductivity in systems exhibiting the Altshuler-Aronov anomaly
- Critical quantum dynamics of observables at eigenstate transitions
- Survival Probability, Particle Imbalance, and Their Relationship in Quadratic Models
- Anomalous diffusion in quantum system driven by heavy-tailed stochastic processes
- Universal conductance distribution in three dimensional systems in high magnetic fields
- Critical Dynamics of the Anderson Transition on Small-World Graphs