Related papers: Network models for localisation problems belonging…
The localization properties of electron states in the quantum Hall regime are reviewed. The random Landau model, the random matrix model, the tight-binding Peierls model, and the network model of Chalker and Coddington are introduced.…
An N-channel generalization of the network model of Chalker and Coddington is considered. The model for N = 1 is known to describe the critical behavior at the plateau transition in systems exhibiting the integer quantum Hall effect. Using…
The random magnetic flux problem on a lattice and in a quasi one-dimensional (wire) geometry is studied both analytically and numerically. The first two moments of the conductance are obtained analytically. Numerical simulations for the…
We investigate two-dimensional Wess-Zumino models in the continuum and on spatial lattices in detail. We show that a non-antisymmetric lattice derivative not only excludes chiral fermions but in addition introduces supersymmetry breaking…
We demonstrate from a fundamental perspective the physical and mathematical origins of band warping and band non-parabolicity in electronic and vibrational structures. Remarkably, we find a robust presence and connection with pairs of…
We seek the possibility of a disorder driven transition in a tight-binding lattice with a flat band using complexity parameter approach. Our results indicate the existence of a localized to extended states transition with increasing…
Effects of heterogeneity in the suspected-infected-susceptible model on networks are investigated using quenched mean-field theory. The emergence of localization is described by the distributions of the inverse participation ratio and…
Flat bands imply lack of itinerancy due to some constraints that, in principle, results in anomalous behaviors with randomness. By a molecular orbital (MO) representation of the flat band systems, random MO models are introduced where the…
We use a superspin Hamiltonian defined on an infinite-dimensional Fock space with positive definite scalar product to study localization and delocalization of noninteracting spinless quasiparticles in quasi-one-dimensional quantum wires…
I discuss recent results on the relation between the localisation of low-lying Dirac eigenmodes, the restoration of chiral symmetry, and deconfinement in QCD and QCD-like models, providing evidence of a close connection between the three…
Field-theoretical approach to Anderson localization in 2D disordered fermionic systems of chiral symmetry classes (BDI, AIII, CII) is developed. Important representatives of these symmetry classes are random hopping models on bipartite…
We investigate the dynamic behavior of lattices with disorder introduced through non-local network connections. Inspired by the Watts-Strogatz small-world model, we employ a single parameter to determine the probability of local connections…
The effects of static disorder on the Z_2 quantum spin-Hall effect for non-interacting electrons propagating in two-dimensional space is studied numerically. A two-dimensional time-reversal symmetric network model is constructed to account…
Linear control theory is used to develop an improved localized control scheme for spatially extended chaotic systems, which is applied to a Coupled Map Lattice as an example. The optimal arrangement of the control sites is shown to depend…
We present a model for a class of random binary lattices by introducing a one-dimensional system where impurities are placed in one sublattice while host atoms lie on the other sublattice. The source of disorder is the stochastic…
We study the small-world network model, which mimics the transition between regular-lattice and random-lattice behavior in social networks of increasing size. We contend that the model displays a normal continuous phase transition with a…
We construct the generic phase diagrams encoding the topologically distinct localized and delocalized phases of noninteracting fermionic quasiparticles for any symmetry class from the tenfold way in one, two, and three dimensions. To this…
We study the localization properties of two-dimensional electrons in a weak perpendicular magnetic field. For this purpose we construct weakly chiral network models on the square and triangular lattices, by separating in space the regions…
This paper presents a theory of interaction-induced band-flattening in strongly correlated electron systems. We begin by illustrating an inherent connection between flat bands and index theorems, and presenting a generic prescription for…
We study the emergence of synchronisation in a chiral network of harmonic oscillators. The network consists of a set of locally incoherently pumped harmonic oscillators coupled pairwise in cascade with travelling field modes. Such cascaded…