Related papers: On Mott's formula for the ac-conductivity in the A…
The low-frequency dynamical response of an Anderson insulator is dominated by so-called Mott resonances: hybridization of pairs of states close in energy, but separated spatially. We study the effect of interaction on Mott resonances in the…
We study the Anderson model as a description of the quantum RC circuit for spin-1/2 electrons and a single level connected to a single lead. Our analysis relies on the Fermi liquid nature of the ground state which fixes the form of the low…
We prove lower bounds on the localization length of eigenfunctions in the three-dimensional Anderson model at weak disorders. Our results are similar to those obtained by Schlag, Shubin and Wolff for dimensions one and two. We prove that…
Results of large-scale numerical simulations are reported on the Anderson localization in a two-dimensional square lattice tight-binding model with random flux. Localization lengths, fluctuations of the conductance, and the density of…
The transport coefficients of the Anderson model require knowledge of both the temperature and frequency dependence of the single--particle spectral densities and consequently have proven difficult quantities to calculate. Here we show how…
We discuss a semiclassical calculation of low energy charge transport in one-dimensional (1d) insulators with a focus on Mott insulators, whose charge degrees of freedom are gapped due to the combination of short range interactions and a…
Anderson localization has been studied extensively for more than half a century. However, while our understanding has been greatly enhanced by calculations based on a small epsilon expansion in d = 2 + epsilon dimensions in the framework of…
We present a theory of the DC electron transport in insulators near Anderson-Mott transitions under the influence of coexisting electron correlation and randomness. At sufficiently low temperatures, the DC electron transport in…
We introduce a conceptual reformulation of the Mott-Berezinski\u{i} (MB) theory of low-frequency AC conductivity in disordered systems based on localization landscape theory. Instead of assuming uniform localization and fixed hopping…
Using our recently developed Chebyshev expansion technique for finite-temperature dynamical correlation functions we numerically study the AC conductivity $\sigma(\omega)$ of the Anderson model on large cubic clusters of up to $100^3$…
We consider a class of unbounded quasiperiodic Schr\"odinger-type operators on $\ell^2(\mathbb Z^d)$ with monotone potentials (akin to the Maryland model) and show that the Rayleigh--Schr\"odinger perturbation series for these operators…
We consider periodically driven Anderson insulators. The short time behavior for weak, monochromatic, uniform electric fields is given by linear response theory and was famously derived by Mott. We go beyond this to consider both long…
In the theory of ergodic one-dimensional Schrodinger operators, ac spectrum has been traditionally expected to be very rigid. Two key conjectures in this direction state, on one hand, that ac spectrum demands almost periodicity of the…
We conclude our analysis of the linear response of charge transport in lattice systems of free fermions subjected to a random potential by deriving general mathematical properties of its conductivity at the macroscopic scale. The present…
The phenomenon of Anderson localization is studied for a class of one-particle Schr\"odinger operators with random Zeeman interactions. These operators arise as follows: Static spins are placed randomly on the sites of a simple cubic…
We study temperature induced metal-insulator transition in doped ferromagnetic semiconductors, described by s-d exchange model. The transition is a result of the mobility edge movement, the disorder being due to magnetic ions spin density…
We consider a two dimensional magnetic Schroedinger operator with a spatially stationary random magnetic field. We assume that the magnetic field has a positive lower bound and that it has Fourier modes on arbitrarily short scales. We prove…
We consider the change in electron localization due to the presence of electron-electron repulsion in the \HA model. Taking into account local Mott-Hubbard physics and static screening of the disorder potential, the system is mapped onto an…
Time-dependent Schroedinger's equation is integrated for a one-dimensional strongly-correlated electron system driven by large electric fields. For larger electric fields, many-body Landau-Zener tunneling takes place at anti-crossings of…
We pinpoint the spectral decomposition for the Anderson tight-binding model with an unbounded random potential on the Bethe lattice of sufficiently large degree. We prove that there exist a finite number of mobility edges separating…