相关论文: Green's matrix from Jacobi-matrix Hamiltonian

The parqueting-reflection principle is shown to also work for constructing harmonic Green functions and harmonic Neumann functions for a class of domains, which are bounded by two arcs in $\mathbb{C}$ with a special intersecting angle…

We lift the constraint of a diagonal representation of the Hamiltonian by searching for square integrable bases that support a tridiagonal matrix representation of the wave operator. Doing so results in exactly solvable problems with a…

A unified theory of orthogonal polynomials of a discrete variable is presented through the eigenvalue problem of hermitian matrices of finite or infinite dimensions. It can be considered as a matrix version of exactly solvable Schr\"odinger…

The boundary value of the resolvent of a generic periodic tight-binding Hamiltonian with matrix symbols is shown to satisfy a limit absorption principle which is continuous in energy in dimensions $d=3$, and in dimension $d=2$ away from…

We consider the free space Helmholtz Green's function and split it into the sum of oscillatory and non-oscillatory (singular) components. The goal is to separate the impact of the singularity of the real part at the origin from the…

Hamiltonians are 2-by-2 positive semidefinite real symmetric matrix-valued functions satisfying certain conditions. In this paper, we solve the inverse problem for which recovers a Hamiltonian from the solution of a first-order system…

The Hubbard model is exactly solved for two particles with opposite spins on d-dimensional hypercubes. It is shown that the spectrum can be separated into two parts: a trivial (U-independent) part resulting from symmetries of hypercubes and…

In this short article, we non-perturbatively derive a recursive formula for the Green's function associated with finitely many point Dirac delta potentials in one dimension. We also extend this formula to the case for the Dirac delta…

Previous work in the literature has studied gravitational radiation in black-hole collisions at the speed of light. In particular, it had been proved that the perturbative field equations may all be reduced to equations in only two…

We derive formulas for the matrix elements of the two dimensional square lattice Green function along the diagonal, and along the coordinate axes. We also give an asymptotic formula for the diagonal elements.

The basic mathematical properties of Green's functions used in statistical mechanics as well as the equations defining these functions and the techniques of solving these equations are reviewed. An approach is presented called the…

In this paper, we discuss some results on integrable Hamiltonian systems with two degrees of freedom. We revisit the much-studied problem of the two-dimensional harmonic oscillator and discuss its (super)integrability in the light of a…

Hamiltonian formulation of N=3 systems is considered in general. The Jacobi equation is solved in three classes. Compatible Poisson structures in these classes are determined and explicitly given. The corresponding bi-Hamiltonian systems…

We present a simple recipe to construct the Green's function associated with a Hamiltonian of the form H=H_0+V, where H_0 is a Hamiltonian for which the associated Green's function is known and V is a delta-function potential. We apply this…

We study the orthogonal polynomials associated with the equilibrium measure, in logarithmic potential theory, living on the attractor of an Iterated Function System. We construct sequences of discrete measures, that converge weakly to the…

Orthogonal polynomials on the real line always satisfy a three-term recurrence relation. The recurrence coefficients determine a tridiagonal semi-infinite matrix (Jacobi matrix) which uniquely characterizes the orthogonal polynomials. We…

This work proposes a higher-order iterative framework for solving matrix equations, inspired by the structure and functionality of neural networks. A modification of the classical Jacobi iterative method is introduced to compute…

It is known that the equation $x'(t)=Ax(t)+f(t)$, where $A$ is a bounded linear operator, has a unique bounded solution $x$ for any bounded continuous free term~$f$ if and only if the spectrum of the coefficient $A$ does not intersect the…

Natural modes of helical structures are treated by using the periodic dyadic Green's functions in cylindrical coordinates. The formulation leads to an infinite system of one-dimensional integral equations in reciprocal (Fourier) space. Due…

We develop Green's function formalism to describe continuous multi-layered quasi-one-dimensional setups described by piece-wise constant single-particle Hamiltonians. The Hamiltonians of the individual layers are assumed to be quadratic…