Related papers: Green's functions for magnetic Dirac operators and…
In calculating Green functions for interacting quantum systems numerically one often has to resort to finite systems which introduces a finite size level spacing. In order to describe the limit of system size going to infinity correctly,…
We use finite field-dependent BRS transformations (FFBRS) to connect the Green functions in a set of two otherwise unrelated gauge choices. We choose the Lorentz and the axial gauges as examples. We show how the Green functions in axial…
Given a sequence of regular planar domains converging in the sense of kernel, we prove that the corresponding Green's functions converge uniformly on the complex sphere, provided the limit domain is also regular, and the connectivity is…
We consider Dirac-like operators with piecewise constant mass terms on spin manifolds, and we study the behaviour of their spectra when the mass parameters become large. In several asymptotic regimes, effective operators appear: the…
A dynamic 3D Green's function for the homogeneous, isotropic and viscoelastic (of the Zener type) half-space is derived in a closed form. The results obtained here can be used as either stand-alone solutions for simple problems or in…
In this paper, we establish sharp two-sided estimates for the Green functions of non-symmetric diffusions with measure-valued drifts in bounded Lipschitz domains. As consequences of these estimates, we get a 3G type theorem and a…
Let $(\overline M,\overline g)$ be a time- and space-oriented Lorentzian spin manifold, and let $M$ be a compact spacelike hypersurface of $\overline M$ with induced Riemannian metric $g$ and second fundamental form $K$. If $(\overline…
In this paper we consider the reproducing kernel thesis for boundedness and compactness for operators on $\ell^2$--valued Bergman-type spaces. This paper generalizes many well--known results about classical function spaces to their…
We study Dirac-type operators on incomplete cusp edge spaces with invertible boundary families. In particular, we construct the heat kernel for the associated Laplace-type operator and prove that the Dirac operators are essentially…
We develop a new algebraic setting for treating piecewise functions and distributions together with suitable differential and Rota-Baxter structures. Our treatment aims to provide the algebraic underpinning for symbolic computation systems…
We consider second-order elliptic partial differential operators acting on sections of vector bundles over a compact Riemannian manifold without boundary, working without the assumption of Laplace-like principal part $-\N^\mu\N_\mu$. Our…
An electronic orbital of a dihedral angle of a molecular chain is introduced. A tight-binding Hamiltonian on the basis of the dihedral orbitals is defined. This yields the Green's function between two dihedral angles of the chain. It is…
Structure and coordinate dependence of the reflected wave, as well as boundary conditions for quasi-particles of graphene and the two dimensional electron gas in sheets with abrupt lattice edges are obtained and analyzed by the Green's…
We obtain simple formulas for the matrix elements of the resolvent operator (the Green's function) in any finite set of square integrable basis. These formulas are suitable for numerical computations whether the basis elements are…
We consider the radial Dirac operator with compactly supported potentials. We study resonances as the poles of scattering matrix or equivalently as the zeros of modified Fredholm determinant. We obtain the following properties of the…
Massive Dirac fermions break the chiral symmetry explicitly and also make the Berry curvature of the band structure non-Abelian. By utilizing the Green's function technique, we develop a microscopic theory to establish a set of quantum…
We investigate a first boundary value problem for a second-order partial differential equation involving the Prabhakar fractional derivative in time. Using structural properties of the Prabhakar kernel and generalized Mittag-Leffler…
A nonzero non-Hermitian winding number indicates that a gapped system is in a nontrivial topological class due to the non-Hermiticity of its Hamiltonian. While for Hermitian systems nontrivial topological quantum numbers are reflected by…
This introduction to Green's functions is based on their role as kernels of differential equations. The procedures to construct solutions to a differential equation with an external source or with an inhomogeneity term are put together to…
Green's functions are highly useful in analyzing the dynamical behavior of polynomials in their escaping set. The aim of this paper is to construct an analogue of Green's functions for planar quasiregular mappings of degree two and constant…