Related papers: The fractional saturable impurity
Flexible boundary condition methods couple an isolated defect to bulk through the bulk lattice Green's function. The inversion of the force-constant matrix for the lattice Green's function requires Fourier techniques to project out the…
We investigate the particle and kinetic-energy densities for $N$ non-interacting fermions confined in a local potential. Using Gutzwiller's semi-classical Green function, we describe the oscillating parts of the densities in terms of closed…
In this paper we study the scattering length for positive additive functionals of symmetric stable processes on ${\bf R}^d$. The additive functionals considered here are not necessarily continuous. We prove that the semi-classical limit of…
The aim of this paper is to deduce a discrete version of the fractional Laplacian in matrix form defined on the 1D periodic (cyclically closed) linear chain of finite length.We obtain explicit expressions for this fractional Laplacianmatrix…
This book is intended as a self-contained introduction to selected topics in the fractional world, focusing particularly on aspects that arise in the study of equations driven by the fractional Laplacian. The scope of this work is not…
We study impurity-induced particle growth and scrambling in clean one-dimensional free-fermion systems. We show that a single local impurity can act as a branching source: particle or operator weight propagates coherently into the free…
We study qualitative properties of solutions to the fractional Lane-Emden-Fowler equations with slightly subcritical exponents where the associated fractional Laplacian is defined in terms of either the spectra of Dirichlet Laplacian or the…
In this work we study the crystal symmetry fractionalization in chiral spin liquids with the chiral-semion topological order. We show that if such a chiral spin liquid is realized in a two-dimensional lattice model with odd number of…
We present the results of detailed theoretical investigations of changes in local density of total electronic surface states in 2D anisotropic atomic semiconductor lattice in vicinity of impurity atom for a wide range of applied bias…
It is demonstrated that there is a characteristic impurity concentration, at which variation with concentration and overall appearance of the local density of states at the impurity site in graphene are changing their behavior. Features…
The manipulation of locked intrinsic localized modes/discrete breathers is studied experimentally in nonlinear electric transmission line arrays. Introducing a static lattice impurity in the form of a capacitor, resistor or inductor has…
The Hubbard model with geometrical frustration is investigated in a metallic phase close to half-filling. We calculate the single particle spectral function for the triangular lattice within dynamical cluster approximation, which is further…
We theoretically investigate how quasi-particle properties of an attractive Fermi polaron are affected by nonzero temperature and finite impurity concentration. By applying both non-self-consistent and self-consistent many-body $T$-matrix…
We present simple proofs of a discrete fractional and non-fractional Hardy inequality, Our constants are explicit, but not optimal. In the class of power weights, we get a complete picture of when the non-fractional Hardy inequality holds,…
The functional integral method can be used in quantum mechanics to find the scattering amplitude for particles in the external field. We will obtain the potential scattering amplitude form the complete Green function in the corresponding…
We develop the impurity lattice Monte Carlo formalism, for the case of two distinguishable impurities in a bath of polarized fermions. The majority particles are treated as explicit degrees of freedom, while the impurities are described by…
We study the effects of an integrable impurity in a periodic t-J chain. The impurity couples to both spin and charge degrees of freedom and has the interesting feature that the interaction with the bulk can be varied continuously without…
We study anisotropic fractional discrete Laplacians $\Delta_{\mathbb{Z}^d}^{\vec{\mathbf{r}}}$ with exponents $\vec{\mathbf{r}}\in\mathbb{R}^d\setminus\{0\}$ on $\ell^2(\mathbb{Z}^d)$. We establish a Mourre estimate on compact energy…
In this paper we consider approximations of Neumann problems for the integral fractional Laplacian by continuous, piecewise linear finite elements. We analyze the weak formulation of such problems, including their well-posedness and…
We propose a two-dimensional time-reversal invariant system of essentially non-interacting electrons on a square lattice that exhibits configurations with fractional charges e/2. These are vortex-like topological defects in the dimerization…