Related papers: Universal conductance distribution in three dimens…
We report a finite size scaling study of the Anderson transition. Different scaling functions and different values for the critical exponent have been found, consistent with the existence of the orthogonal and unitary universality classes…
The Anderson transitions in a random magnetic field in three dimensions are investigated numerically. The critical behavior near the transition point is analyzed in detail by means of the transfer matrix method with high accuracy for…
The Anderson transition in three dimensions in a randomly varying magnetic flux is investigated in detail by means of the transfer matrix method with high accuracy. Both, systems with and without an additional random scalar potential are…
We study numerically the metal - insulator transition in the Anderson model on various lattices with dimension $2 < d \le 4$ (bifractals and Euclidian lattices). The critical exponent $\nu$ and the critical conductance distribution are…
Using a modification of the Shapiro scaling approach, we derive the distribution of conductance in the magnetic field applicable in the vicinity of the Anderson transition. This distribution is described by the same equations as in the…
The boundary condition dependence of the critical behavior for the three dimensional Anderson transition is investigated. A strong dependence of the scaling function and the critical conductance distribution on the boundary conditions is…
Anderson localization is fundamentally controlled by dimensionality, yet the nature of the Anderson transition in continuously tunable noninteger dimensions remains largely unexplored. Here, we introduce a family of three-dimensional…
We use multifractal finite-size scaling to perform a high-precision numerical study of the critical properties of the Anderson localization-delocalization transition in the unitary symmetry class, considering the Anderson model including a…
The statistics of critical wave functions at the Anderson transition in three and four dimensions are studied numerically. The distribution of the inverse participation ratios (IPR) $P_q$ is shown to acquire a scale-invariant form in the…
In quantum systems, signatures of multifractality are rare. They have been found only in the multiscaling of eigenfunctions at critical points. Here we demonstrate multifractality in the magnetic-field-induced universal conductance…
We generalize universal relations between the multifractal exponent \alpha_0 for the scaling of the typical wave function magnitude at a (Anderson) localization-delocalization transition in two dimensions and the corresponding critical…
We propose an Ansatz for Universal conductance fluctuations in continuous dimensions from 0 up to 4. The Ansatz agrees with known formulas for integer dimensions 1, 2 and 3, both for hard wall and periodic boundary conditions. The method is…
Disordered non-interacting systems are classified into ten symmetry classes, with the unitary class being the most fundamental. The three and four dimensional unitary universality classes are attracting renewed interest because of their…
The disorder induced metal--insulator transition is investigated in a three-dimensional simple cubic lattice and compared for the presence and absence of time-reversal and spin-rotational symmetry, i.e. in the three conventional symmetry…
The universal conductance fluctuations of quasi-two-dimensional systems are analyzed with experimental considerations in mind. The traditional statistical metrics of these fluctuations (such as variance) are shown to have large statistical…
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…
We study Anderson transition for light in three dimensions by performing large-scale ab-initio simulations of electromagnetic wave transport in disordered ensembles of conducting spheres. A mobility edge that separates diffusive transport…
Numerical studies of the Anderson transition are based on the finite-size scaling analysis of the smallest positive Lyapunov exponent. We prove numerically that the same scaling holds also for higher Lyapunov exponents. This scaling…
We propose a generalization of multifractal analysis that is applicable to the critical regime of the Anderson localization-delocalization transition. The approach reveals that the behavior of the probability distribution of wavefunction…
We obtain an analytic expression for the full distribution of conductance for a strongly disordered three dimensional conductor within a perturbative approach based on the transfer-matrix formulation. Our results confirm numerical evidence…