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This article is devoted to deduce the expression of the Green's function related to a general constant coefficients fractional difference equation coupled to Dirichlet conditions. In this case, due to the points where some of the fractional…
If h is a ring-valued function on a simplicial complex G we can define two matrices L and g, where the matrix entries are the h energy of homoclinic intersections. We know that the sum over all h values on G is equal to the sum of the Green…
The Hubbard model, a cornerstone in the field of condensed matter physics, serves as a fundamental framework for investigating the behavior of strongly correlated electron systems. This paper presents a novel perspective on the model,…
We propose two ways for determining the Green's matrix for problems admitting Hamiltonians that have infinite symmetric tridiagonal (i.e. Jacobi) matrix form on some basis representation. In addition to the recurrence relation comming from…
The asymmetric Hubbard model is used in investigating the lattice gas of the moving particles of two types. The model is considered within the dynamical mean-field method. The effective single-site problem is formulated in terms of the…
We use the moment approach of Nolting (exact sum rules) (Z. Physik 255, 25 (1972)) for the attractive Hubbard model in the superconducting phase. Our diagonal and off - diagonal spectral functions are constructed and evaluated with the sum…
The quantum Hall conductivity in the presence of constant magnetic field may be represented as the topological TKNN invariant. Recently the generalization of this expression has been proposed for the non - uniform magnetic field. \rev{The…
Diagrammatic analysis for normal state of Hubbard model proposed in our previous paper [1] is generalized and used to investigate superconducting state of this model. We use the notion of charge quantum number to describe the irreducible…
This is a sequel to arXiv:2401.02087. We prove the Green function rigidity conjecture in arXiv:2401.02087 for conformal Laplacian in dimension $n\geq 3$. For the Paneitz operator, we prove the Green function rigidity conjecture when $n\neq…
The Green functions of the partial differential operators of even order acting on smooth sections of a vector bundle over a Riemannian manifold are investigated via the heat kernel methods. We study the resolvent of a special class of…
We consider a general one-particle Hamiltonian H = - \Delta_r + u(r) defined in a d-dimensional domain. The object of interest is the time-independent Green function G_z(r,r') = < r | (z-H)^{-1} | r' >. Recently, in one dimension (1D), the…
We develop a new structure of the Green's function of a second-order elliptic operator in divergence form in a 2D bounded domain. Based on this structure and the theory of rearrangement of functions, we construct concentrated…
We have applied the Fast Fourier transform (FFT), which allows to compute efficiently convolution sums, to solve the set of self-consistent T-matrix equations to get the Green function of the two dimensional attractive-U Hubbard modelbelow…
We propose an algorithm for determining the zeros of the electric conductivity in large molecular nanonstructures such as graphene sheets. To this end, we employ the inverse graph method, whereby non-zeros of the Green's functions are…
Using the description in terms of the Hubbard operators hole and spin Green's functions of the two-dimensional t-J model are calculated in an approximation which retains the rotation symmetry of the spin susceptibility in the paramagnetic…
Green's function zeros, which can emerge only if correlation is strong, have been for long overlooked and believed to be devoid of any physical meaning, unlike Green's function poles. Here, we prove that Green's function zeros instead…
We compute the Green's function for the Hodge Laplacian on the symmetric spaces M\times\Sigma, where M is a simply connected n-dimensional Riemannian or Lorentzian manifold of constant curvature and \Sigma is a simply connected Riemannian…
We introduce a performance-optimized method to simulate localization problems on bipartite tight-binding lattices. It combines an exact renormalization group step to reduce the sparseness of the original problem with the recursive Green's…
The lattice Green function, i.e., the resolvent of the discrete Laplace operator, is fundamental in probability theory and mathematical physics. We derive its long-distance behaviour via a detailed analysis of an integral representation…
Transport properties of 2D materials especially close to their boundary has received much attention after the successful fabrication of graphene and other fascinating materials afterwards. While most previous work is devoted to the…