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The paper reviews some parts of classical potential theory with applications to two dimensional fluid dynamics, in particular vortex motion. Energy and forces within a system of point vortices are similar to those for point charges when the…
This is a supplementary material of our recent paper\cite{yangPRB}, where a class of exactly solvable S=1 quantum Ising spin models were studied based on the hole decomposition scheme. Here we provide some details for the Green functions,…
We provide Green's function estimates for parabolic operators on polyhedrons and polyhedral cones in $\mathbb{R}^3$. These estimates incorporate mixed weights, which include appropriate powers of the distances to the vertices, the edges,…
A relaxed factorization is used to obtain many of the properties obeyed by the confluent hypergeometric functions. Their implications on the analytical solutions of some interesting physical problems are also studied. It is quite remarkable…
We introduce a Green function and analogues of other related kernels for finite and infinite networks whose edge weights are complex-valued admittances with positive real part. We provide comparison results with the same kernels associated…
We provide quantitative inductive estimates for Green's functions of matrices with (sub)expoentially decaying off diagonal entries in higher dimensions. Together with Cartan's estimates and discrepancy estimates, we establish explicit…
Problems with topological uncertainties appear in many fields ranging from nano-device engineering to the design of bridges. In many of such problems, a part of the domains boundaries is subjected to random perturbations making inefficient…
The properties of the gauge invariant two-point quark Green's function are studied in the large-Nc limit of two-dimensional QCD. The analysis is done by means of an exact integrodifferential equation. The Green's function is found infrared…
For a chordal SLE$_\kappa$ ($\kappa\in(0,8)$) curve in a domain $D$, the $n$-point Green's function valued at distinct points $z_1,\dots,z_n\in D$ is defined to be $$G(z_1,\dots,z_n)=\lim_{r_1,\dots,r_n\downarrow 0} \prod_{k=1}^n r_k^{d-2}…
In Green's function theory, the total energy of an interacting many-electron system can be expressed in a variational form using the Klein or Luttinger-Ward functionals. Green's function theory also naturally addresses the case where the…
Closed expressions are derived for resonant multidimensional X-ray spectroscopy using the quasiparticle nonlinear exciton representation of optical response. This formalism is applied to predict coherent four wave mixing signals which probe…
Green function (which can be called the q-analogous of the Hankel function) on the quantum plane E_q^2= E_q(2)/U(1) is constructed.
We calculate the multipoint Green functions in 1+1 dimensional integrable quantum field theories. We use the crossing formula for general models and calculate the 3 and 4 point functions taking in to account only the lower nontrivial…
The spectral properties of the quantum mechanical system consisting of a quantum dot with a short-range attractive impurity inside the dot are investigated in the zero-range limit. The Green function of the system is obtained in an explicit…
A local-orbital based ab initio approach to obtain the Green function for large heterogeneous systems is developed. First a Green function formalism is introduced based on exact diagonalization. Then the self energy is constructed from an…
The Green's function has been an indispensable tool to study many-body systems that remain one of the biggest challenges in modern quantum physics for decades. The complicated calculation of Green's function impedes the research of…
Thermodynamic functions of ionic systems were evaluated analytically using the Green's Function for Body Centered Cubic Lattices. The free energy density, chemical potential, pressure, spinodals, and coulomb ionic potentials are expressed…
The main purpose of the present paper is to introduce the notion of squeezing functions of bounded domains and study some properties of them. The relation to geometric and analytic structures of bounded domains will be investigated.…
We compute the Green's functions for scalars, fermions and vectors in the color field associated with the infinite momentum frame wavefunction of a large nucleus. Expectation values of this wavefunction can be computed by integrating over…
Light transport in superdiffusive media of finite size is studied theoretically. The intensity Green's function for a slab geometry is found by discretizing the fractional diffusion equation and employing the eigenfunction expansion method.…