Related papers: Sharp estimates of Green function of hyperbolic Br…
We present some results on Bernstein processes which are Brownian diffusions that appear in Euclidean Quantum Mechanics: We express the distributions of these processes with the help of those of Bessel processes. We then determine two…
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…
Quantization of electrodynamics in curved space-time in the Lorenz gauge and with arbitrary gauge parameter makes it necessary to study Green functions of non-minimal operators with variable coefficients. Starting from the integral…
The newly developed Gorkov-Green's function approach represents a promising path to the ab initio description of medium-mass open-shell nuclei. We discuss the implementation of the method at second order with a two-body interaction, with…
Inspired by the recent proposed Legendre orthogonal polynomial representation of imaginary-time Green's functions, we develop an alternate representation for the Green's functions of quantum impurity models and combine it with the…
This is the author Master's Thesis and its main purpose is to demonstrate that it is possible to formulate Einstein's field equations as an initial value problem. The first chapter concerns the hyperbolic equations theory. The definition of…
The possibility is discussed of using straight-line paths of integration in computing the integral representation of the three-body Coulomb Green's function. In our numerical examples two different integration contours are considered. It is…
In this article we use linear algebra to improve the computational time for the obtaining of Green's functions of linear differential equations with reflection (DER). This is achieved by decomposing both the `reduced' equation (the ODE…
A computationally efficient Green's function approach is developed to evaluate the optical properties of nanostructures using a GW formalism applied on top of a tight-binding and mean-field Hubbard model. The use of the GW approximation…
Some elementary algebraic points regarding the Green function for a localised flux tube are developed. A calculation of the effective action density is included.
It is known that a full description of Brownian motion in the entire course of time should incorporate both kinetic and hydrodynamic effects, but a formula accounts for both effects has been established only in three dimension and only for…
We present an original strategy for the calculation of direct and inverse photo-emission spectra from first principles. The main goal is to go beyond the standard Green's function approaches, such as the $GW$ method, in order to find a good…
The thermodynamics of low dimensional spin-1/2 Heisenberg ferromagnets (HFM) in an external magnetic field is investigated within a second-order two-time Green function formalism in the wide temperature and field range. A crucial point of…
In this paper, we discuss estimates of transition densities of subordinate Brownian motions in open subsets of Euclidean space. When $D$ is a $C^{1,1}$ domain, we establish sharp two-sided estimates for the transition densities of a large…
Green function techniques for studying nonequilibrium processes in dirty two-band superconductors are discussed. Perturbation expansions and Green function equations are developed. A time dependent modification of the Usadel equation is…
We explicitly construct a heat kernel as a Neumann series for certain function spaces, such as $L^{1}$, $L^{2}$, and Hilbert spaces, associated to a locally compact Hausdorff space $\mathfrak{X}$ with Borel $\sigma$-algebra $\mathcal{B}$,…
We extend the upper estimates obtained by M. Carlehed and B.-Y. Chen about the ratio of the classical and pluricomplex Green functions to the case of $\mathcal C^2$-smooth locally $\mathbb C$-convexifiable domains of finite type. We also…
We establish two-sided heat kernel estimates for random conductance models with non-uniformly elliptic (possibly degenerate) stable-like jumps on graphs. These are long range counterparts of well known two-sided Gaussian heat kernel…
We prove a conjecture of Lalley and Sellke [Ann. Probab. 15 (1987)] asserting that the empirical (time-averaged) distribution function of the maximum of branching Brownian motion converges almost surely to a double exponential, or Gumbel,…
Following Donaldson's oppenness theorem on deforming a conical K\"ahler-Einstein metric, we prove a parabolic Schauder-type estimate with respect to conical metrics. As a corollary, we show that the conical K\"ahler-Ricci Flow exists for…