Related papers: Anderson localization from the replica formalism
The localization of one-electron states in the large (but finite) disorder limit is investigated. The inverse participation number shows a non--monotonic behavior as a function of energy owing to anomalous behavior of few-site localization.…
Precision is a virtue throughout science in general and in optics in particular where carefully fabricated nanometer-scale devices hold great promise for both classical and quantum photonics [1-6]. In such nanostructures, unavoidable…
We study a lattice field model which qualitatively reflects the phenomenon of Anderson localization and delocalization for real symmetric band matrices. In this statistical mechanics model, the field takes values in a supermanifold based on…
Using recent results on uniform large deviation estimates for random matrix products obtained by S. Raman and the author, we prove localization for one dimensional Anderson models with heavy tails.
An ac field, tuned exactly to resonance with the Stark ladder in an ideal tight binding lattice under strong dc bias, counteracts Wannier-Stark localization and leads to the emergence of extended Floquet states. If there is random disorder,…
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…
We elucidate the different mechanisms of wave localisation in disordered finite systems of subwavelength resonators, where the disorder is in the spatial arrangement of the resonators. To do so, we employ the capacitance matrix formalism…
The electronic transport properties in the presence of a temperature gradient in disordered systems near the metal-insulator transition [MIT] are considered. The d.c. conductivity $\sigma$, the thermoelectric power $S$, the thermal…
We show that Anderson localization is possible in waveguide arrays with periodically-spaced defect waveguides having lower refractive index. Such localization is mediated by Bragg reflection, and it takes place even if diagonal or…
We expose an interesting connection between the distribution of local spectral density of states arising in the theory of disordered systems and the notion of superstatistics introduced by Beck and Cohen and recently incorporated in random…
We study the thermal transport properties in three-dimensional disordered systems close to the metal-insulator transition within linear response. Using a suitable form for the energy-dependent conductivity $\sigma$, we show that the value…
We study transport of interacting electrons in a low-dimensional disordered system at low temperature $T$. In view of localization by disorder, the conductivity $\sigma(T)$ may only be non-zero due to electron-electron scattering. For weak…
Within the framework of tight binding models, aperiodic systems are mapped to a renormalized lattice with a dimer defect. In models exhibiting metal-insulator transition, the dimer acts like a resonant cavity and explains the existence of…
We establish, through numerical calculations and comparisons with a recursive Green's function based implementation of the Landauer-B\"uttiker formalism, an efficient method for studying Anderson localization in quasi-one-dimensional and…
We investigate the electronic structure of gap and band tail states in amorphous silicon. Starting with two 216-atom models of amorphous silicon with defect concentration close to the experiments, we systematically study the dependence of…
A mixture of two fermionic species with different masses is studied in an optical lattice. The heavy fermions are subject only to thermal fluctuations, the light fermions also to quantum fluctuations. We derive the Ising-like distribution…
We study the affinities between the shape of the bright soliton of the one-dimensional nonlinear Schroedinger equation and that of the disorder induced localization in the presence of a Gaussian random potential. With emphasis on the…
An ensemble of quasi-periodic discrete Schr\"{o}dinger operators with an arbitrary number of basic frequencies is considered, in a lattice of arbitrary dimension, in which the hull function is a realisation of a stationary Gaussian process…
These lectures present some basic ideas and techniques in the spectral analysis of lattice Schrodinger operators with disordered potentials. In contrast to the classical Anderson tight binding model, the randomness is also allowed to…
Anderson has recently proposed a theory of the strange metal state above Tc in the high Tc superconductors. [arXiv:cond-mat/0512471] It is based on the idea that the unusual transport properties and spectral functions are caused by the…