Related papers: The Spectrum of the Almost Mathieu Operator
In this article we consider a class of integrable operators and investigate its connections with the following theories:the spectral theory of non-self-adjoint operators, the Riemann-Hilbert problem, the canonical differential systems and…
Quasiperiodic systems are an intermediate class of systems between periodic crystals and disordered systems, famously exhibiting metal-insulator transitions (MITs) even in one dimension. While their transport properties have been studied…
This work explores a simple approximation to describe isolated impurity scattering in a strongly correlated metal. The approximation combines conventional one electron scattering theory and the Dynamic Mean Field Theory to describe strong…
These notes are based on lecture courses I gave to third year mathematics students at Cambridge. They could form a basis of an elementary one--term lecture course on integrable systems covering the Arnold-Liouville theorem, inverse…
Quasi-periodic Schr\"odinger-type operators naturally arise in solid state physics, describing the influence of an external magnetic field on the electrons of a crystal. In the late 1970s, numerical studies for the most prominent model, the…
In this note we present and briefly discuss results, which include as a particular case the theorem announced in [L. Biasco, and L. Chierchia. On the measure of Lagrangian invariant tori in nearly-integrable mechanical systems. Atti Accad.…
Two phenomena have been recently observed in high-mobility Si MOS structures: (1) strong enhancement of the metallic conduction at low temperatures, T < 2K, and (2) the scaling behavior of the temperature and electric field dependences of…
The dynamics of charge carriers close to the Mott transition is explored theoretically and experimentally in the quasi two-dimensional organic charge-transfer salt $\kappa$-(BEDT-TTF)$_2$Cu[N(CN)$_2$]Br$_x$Cl$_{1-x}$, with varying Br…
The insulator-to-metal transition in dense fluid hydrogen is an essential phenomenon to understand gas giant planetary interiors and the physical and chemical behavior of highly compressed condensed matter. Using fast laser spectroscopy…
A new two-pole approximation, which allows to describe the transition from an insulating state to a metallic one at increase of bandwidth, and also the observable in some compounds transition from a metalic state to an insulating one with…
We have varied the disorder in a two-dimensional electron system in silicon by applying substrate bias. When the disorder becomes sufficiently low, we observe the emergence of the metallic phase, and find evidence for a metal-insulator…
These are introductory lecture notes on Mather's theory for Tonelli Lagrangian and Hamiltonian systems. They are based on a series of lectures given by the author at Universit\`a degli Studi di Napoli "Federico II" (April 2009), at…
The strong coupling diagram technique is used for investigating states near the metal-insulator transition in the half-filled two-dimensional repulsive Hubbard model. The nonlocal third-order term is included in the irreducible part along…
We describe a list of open problems in random matrix theory and the theory of integrable systems that was presented at the conference Asymptotics in Integrable Systems, Random Matrices and Random Processes and Universality, Centre de…
We study the metal-insulator transition in two sets of amorphous Si_{1-x}Ni_x films. The sets were prepared by different, electron-beam-evaporation-based technologies: evaporation of the alloy, and gradient deposition from separate Ni and…
The talk contains a short introduction to mesonic Chiral Perturbation Theory (ChPT). In addition four disparate areas where some progress has been made in recent years are discussed. These are the last fit of the order $p^4$…
Magnetic clock transitions (CTs), defined by vanishing first-order sensitivity of the transition frequency to magnetic field fluctuations, provide a powerful route to suppress decoherence in donor spin systems. Here, we present the…
Summary of a talk given at the International Seminar "Analysis of spectral invariants and related operator theory", Tokyo University of Science, Unga Campus, 5-6 Oct. 2009
The theory of almost commuting matrices can be used to quantify topological obstructions to the existence of localized Wannier functions with time-reversal symmetry in systems with time-reversal symmetry and strong spin-orbit coupling. We…
In these expository notes we draw together and develop the ideas behind some recent progress in two directions: the treatment of finite type partial differential operators by prolongation, and a class of differential complexes known as…