Related papers: Periodic-Orbit Theory of Anderson Localization on …
Anderson localization is related to exponential localization of a particle in the configuration space in the presence of a disorder potential. Anderson localization can be also observed in the momentum space and corresponds to quantum…
The main goal of the present paper is to convince that it is feasible to construct a `periodic orbit theory' of localization by extending the idea of classical action correlations. This possibility had been questioned by many researchers in…
Anderson localization is a famous wave phenomenon that describes the absence of diffusion of waves in a disordered medium. Here we generalize the landscape theory of Anderson localization to general elliptic operators and complex boundary…
We study a multi-particle quantum graph with random potential. Taking the approach of multiscale analysis we prove exponential and strong dynamical localization of any order in the Hilbert-Schmidt norm near the spectral edge. Apart from the…
We study Schr\"odinger operators on quantum graphs where the number of edges between points is determined by orbits of a "shift of finite type". We prove Anderson localization for these systems.
We establish a deterministic technique to investigate transport moments of arbitrary order. The theory is applied to the analysis of different kinds of intermittent one-dimensional maps and the Lorentz gas with infinite horizon: the typical…
We quantize graphs (networks) which consist of a finite number of bonds and vertices. We show that the spectral statistics of fully connected graphs is well reproduced by random matrix theory. We also define a classical phase space for the…
We present a self-consistent theory of Anderson localization that yields a simple algorithm to obtain \emph{typical local density of states} as an order parameter, thereby reproducing the essential features of a phase-diagram of…
Anderson localization is a quantum phenomenon in which disorder localizes electronic wavefunctions. In this work, we propose a new approach to study Anderson localization based on the density matrix formalism. Drawing an analogy to the…
The self-consistent theory of Anderson localization of quantum particles or classical waves in disordered media is reviewed. After presenting the basic concepts of the theory of Anderson localization in the case of electrons in disordered…
Anderson localization is the ubiquitous phenomenon of inhibition of transport of classical and quantum waves in a disordered medium. In dimension one, it is well known that all states are localized, implying that the distribution of an…
The one parameter scaling theory is a powerful tool to investigate Anderson localization effects in disordered systems. In this paper we show this theory can be adapted to the context of quantum chaos provided that the classical phase space…
We consider methods based on the topological degree theory to compute periodic orbits of area preserving maps. Numerical approximations of the Kronecker integral and the application of Stenger's method allows us to compute the value of the…
We propose a new viewpoint on the study of localization transitions in disordered quantum systems, showing how critical properties can be seen also as a geometric transition in the data space generated by the classically encoded…
We define a class of quantum systems called regular quantum graphs. Although their dynamics is chaotic in the classical limit with positive topological entropy, the spectrum of regular quantum graphs is explicitly computable analytically…
Systems which can spontaneously reveal periodic evolution are dubbed time crystals. This is in analogy with space crystals that display periodic behavior in configuration space. While space crystals are modelled with the help of space…
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…
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 show that Anderson localization in quasi-one dimensional conductors with ballistic electron dynamics, such as an array of ballistic chaotic cavities connected via ballistic contacts, can be understood in terms of classical electron…
The Anderson model in one dimension is a quantum particle on a discrete chain of sites with nearest-neighbor hopping and random on-site potentials. It is a progenitor of many further models of disordered systems, and it has spurred numerous…