Related papers: The Spectrum of the Almost Mathieu Operator
Lecture notes from 1993 Park City lectures and 1994 Trento lectures. The focus of these lectures is on giving a mathematical description of the A-model and B-model correlation functions on a Calabi--Yau manifold, and a precise mathematical…
For the immediate vicinity of the metal-insulator transition (MIT), data on the dependence of the resistivity rho on the charge carrier concentration n from an Si MOSFET experiment by Kravchenko et al. and from an AlAs quantum well study by…
Non-standard .sty file `equations.sty' now included inline. The critical exponents of the metal--insulator transition in disordered systems have been the subject of much published work containing often contradictory results. Values ranging…
Experimental evidence for the possible universality classes of the metal-insulator transition (MIT) in two dimensions (2D) is discussed. Sufficiently strong disorder, in particular, changes the nature of the transition. Comprehensive…
We focus on the central problem of discriminating between metallic and insulating behaviour in amorphous alloys formed between a semiconductor and a metal. For this, the logarithmic temperature derivative of the conductivity, w = d ln sigma…
We introduce self-similar versions of the one-dimensional almost Mathieu operators. Our definition is based on a class of self-similar Laplacians instead of the standard discrete Laplacian, and includes the classical almost Mathieu…
We examine the metal-insulator transition in a half-filled Hubbard model of electrons with random and all-to-all hopping and exchange, and an on-site non-random repulsion, the Hubbard $U$. We argue that recent numerical results of Cha et…
It is shown that the spectacular metal-insulator transition in Eu-rich EuO can be simulated within an extended Kondo lattice model. The different orders of magnitude of the jump in resistivity in dependence on the concentration of oxygen…
In the framework of the tight binding approximation, we study a non-interacting model on the three-component dice lattice with real nearest-neighbor and complex next-nearest-neighbor hopping subjected to $\Lambda$- or V-type sublattice…
For about twenty years, it has been the prevailing view that there can be no metallic state or metal-insulator transition in two dimensions in zero magnetic field. In the last several years, however, unusual behavior suggestive of such a…
Lecture note topics: 1. Some tools from real and complex analysis, 2. Hilbert spaces, 3. Banach spaces, 4. Compact operators and their spectra, 5. Intermezzo: reproducing kernel Hilbert spaces, 6. Banach algebras ,7. Spectral theory of…
We investigate the dynamics of correlated charge carriers in the vicinity of the Mott metal-to-insulator transition in various of the title quasi-two-dimensional organic charge-transfer salts by means of fluctuation (noise) spectroscopy.…
The single-particle dynamics close to a metal-to-insulator transition induced by strong repulsive interaction between the electrons is investigated. The system is described by a half-filled Hubbard model which is treated by dynamic…
Using a cold atomic gas exposed to laser pulses -- a realization of the chaotic quasiperiodic kicked rotor with three incommensurate frequencies -- we study experimentally and theoretically the Anderson metal-insulator transition in three…
We introduce a systematic low-energy approach to strongly correlated electron systems in infinite dimensions, and apply it to the problem of the correlation-induced metal-insulator transition in the half-filled Hubbard model. We determine…
A recently found metal-insulator transition in a model for cyclotron resonance in a two-dimensional periodic potential is investigated by means of spectral properties of the time evolution operator. The previously found dynamical signatures…
This talk is dedicated to various aspects of Mirror Symmetry. It summarizes some of the mathematical developments that took place since M. Kontsevich's report at the Z\"urich ICM and provides an extensive, although not exhaustive,…
Transition metal dichalcogenide superlattices provide an exciting new platform for exploring and understanding a variety of phases of matter. The moir\'e continuum Hamiltonian, of two-dimensional jellium in a modulating potential, provides…
We investigate a disordered two-dimensional lattice model for noninteracting electrons with long-range power-law transfer terms and apply the method of level statistics for the calculation of the critical properties. The eigenvalues used…
We investigate the metal insulator transitions at finite temperature for the Hubbard model with diagonal alloy disorder. We solve the dynamical mean field theory equations with the non crossing approximation and we use the coherent…