Related papers: Constructive Fractional-Moment Criteria for Locali…
A technically convenient signature of localization, exhibited by discrete operators with random potentials, is exponential decay of the fractional moments of the Green function within the appropriate energy ranges. Known implications…
A technically convenient signature of Anderson localization is exponential decay of the fractional moments of the Green function within appropriate energy ranges. We consider a random Hamiltonian on a lattice whose randomness is generated…
Mathematical analysis of the Anderson localization has been facilitated by the use of suitable fractional moments of the Green function. Related methods permit now a readily accessible derivation of a number of physical manifestations of…
One of the fundamental results in the theory of localization for discrete Schr\"odinger operators with random potentials is the exponential decay of Green's function and the absence of continuous spectrum. In this paper we provide a new…
We give a proof of dynamical localization in the form of exponential decay of spatial correlations in the time evolution for the one-dimensional continuum Anderson model via the fractional moments method. This follows via exponential decay…
We present a new, short, self-contained proof of localization properties of multi-dimensional continuum random Schr\"odinger operators in the fluctuation boundary regime. Our method is based on the recent extension of the fractional moment…
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…
A simple quantum mechanical model consisting of a discrete level resonantly coupled to a continuum of finite width, where the coupling can be varied from perturbative to strong (Fano-Anderson model), is considered. The particle is initially…
We consider the spectral and dynamical properties of quantum systems of $n$ particles on the lattice $\Z^d$, of arbitrary dimension, with a Hamiltonian which in addition to the kinetic term includes a random potential with iid values at the…
The fractional moment method, which was initially developed in the discrete context for the analysis of the localization properties of lattice random operators, is extended to apply to random Schr\"odinger operators in the continuum. One of…
We consider recurrent diffusive random walks on a strip. We present constructive conditions on Green functions of finite sub-domains which imply a Central Limit Theorem with polynomial error bound, a Local Limit Theorem, and mixing of…
We prove spectral and dynamical localization for Anderson models on locally finite graphs using the fractional moment method. Our theorems extend earlier results on localization for the Anderson model on $\ZZ^d$. We establish geometric…
The Green's function contains much information about physical systems. Mathematically, the fractional moment method (FMM) developed by Aizenman and Molchanov connects the Green's function and the transport of electrons in the Anderson…
The non-Fermi liquid physics at the edge of fractional quantum Hall systems is described by specific chiral Conformal Field Theories with central charge c=1. The charged quasi-particles in these theories have fractional charge and obey a…
We construct a density functional theory for two-dimension electron (hole) gases subjected to both strong magnetic fields and external potentials. In particular, we are focused on regimes near even-denominator filling factors, in which the…
Exponentially-localized Wannier functions are a basis of the Fermi projection of a Hamiltonian consisting of functions which decay exponentially fast in space. In two and three spatial dimensions, it is well understood for periodic…
In this work we introduce a procedure to find localized structures with finite energy. We start dealing with global monopoles, and add a new contribution to the potential of the scalar fields, to balance the contribution of the angular…
Determining functionals are tools to describe the finite dimensional long-term dynamics of infinite dimensional dynamical systems. There also exist several applications to infinite dimensional {\em random} dynamical systems. In these…
A rational expansion of the Fermi density operator is proposed. This approach allows to calculate efficiently physical properties of fermionic systems at finite temperatures without solving an eigenvalue problem. Using N evaluations of the…
We employ the Green's function technique to investigate the vacancy-induced quasi-localized magnetic moment formation in mono-layer graphene starting with the Dirac Hamiltonian, which focuses on the {\pi}- orbitals only, involving the…