Related papers: Localization for quasi-one-dimensional Dirac opera…
The transmission poles of $N$ number of identical Dirac delta potentials placed periodically in one-dimension are examined in the complex-energy plane. The numerical results show that the imaginary part of the poles scales with 1/N. An…
We construct a microlocalization of the rational Cherednik algebras $H$ of type $S_n$. This is achieved by a quantization of the Hilbert scheme $\Hilb^n\C^2$ of $n$ points in $\C^2$. We then prove the equivalence of the category of…
A model of localization based on the Witten Hamiltonian of supersymmetric quantum mechanics is considered. The case where the superpotential $\phi(x)$ is a random telegraph process is solved exactly. Both the localization length and the…
Quasiperiodic systems serve as fertile ground for studying localisation, due to their propensity already in one dimension to exhibit rich phase diagrams with mobility edges. The deterministic and strongly-correlated nature of the…
We give conditions for local diagonalization of an analytic operator family to a diagonal operator polynomial. The families are acting between real or complex Banach spaces. The basic assumption is given by stabilization of the Jordan…
The Lyapunov exponent, serving as an indicator of the localized state, is commonly utilized to identify localization transitions in disordered systems. In non-Hermitian quasicrystals, the non-Hermitian effect induced by non-reciprocal…
Matrix type operators with the off-diagonal decay of polynomial or sub-exponential types are revisited with weaker assumptions concerning row or column estimates, still giving the continuity results for the frame type operators. Such…
The theoretical description of transport in a wide class of novel materials is based upon quantum percolation and related random resistor network (RRN) models. We examine the localization properties of electronic states of diverse…
We determine the free field hypercubic Dirac operator which is optimally close to satisfying the Ginsparg-Wilson relation. Inserting this operator into the overlap formula, we show that the analytic locality bound on the resulting overlap…
We show that the Dirac factorization method can be successfully employed to treat problems involving operators raised to a fractional power. The technique we adopt is based on an extension of the Pauli matrices and the properties of the…
This paper establishes dynamical localization properties of certain families of unitary random operators on the d-dimensional lattice in various regimes. These operators are generalizations of one-dimensional physical models of quantum…
We derive exact quantum expressions for the localization length $L_c$ for weak disorder in two- and three chain tight-binding systems coupled by random nearest-neighbour interchain hopping terms and including random energies of the atomic…
Starting with an operator in the universal enveloping algebra of a semi-simple, complex Lie group the nearest neighbor statistics of the spectra of this operator along a sequence of representations are discussed. After a short introduction…
We present a theory of electronic transport in graphene in the presence of randomly placed adsorbates. Our analysis predicts a marked asymmetry of the conductivity about the Dirac point, as well as a negative weak-localization…
The rigidity problem for uniform Roe algebras was recently positively solved. Before its solution was found, there were positive solutions under the assumption of certain technical geometric conditions. In this paper, we introduce weaker…
Localization properties of random-mass Dirac fermions for a realization of mass disorder, commonly referred to as Cho-Fisher model, is studied on the D-class chiral network. We show that a simple RG description captures accurately three…
An 1D tight-binding version of the Dirac equation is considered; after checking that it recovers the usual discrete Schr?odinger equation in the nonrelativistic limit, it is found that for two-valued Bernoulli potentials the zero mass case…
It is reported a combined numerical approach to study the localization properties of the one-dimensional tight-binding model with potential modulated along the prime numbers. A localization-delocalization transition was found as function of…
A transfer matrix method is presented for solving the scattering problem for the quasi one-dimensional massless Dirac equation applied to graphene in the presence of an arbitrary inhomogeneous electric and perpendicular magnetic field. It…
Delone operators are Schr\"odinger operators in multi-dimensional Euclidean space with a potential given by the sum of all translates of a given "single-site potential" centred at the points of a Delone set. In this paper, we use…