Related papers: Multiplicity of solutions to GW-type approximation…
We apply verified numerics to the Nirenberg problem, proving that a genuine solution exists near two given computer-generated approximate solutions. This proves existence of a solution for a particular prescribed curvature that was…
Ab initio many-body perturbation theory within the $GW$ approximation is a Green's function formalism widely used in the calculation of quasiparticle excitation energies of solids. In what has become an increasingly standard approach,…
We review the exact solutions in modified gravity. It is one of the main problems of mathematical physics for the gravity theory. One can obtain an exact solution if the field equations reduce to a system of ordinary differential equations.…
The parquet formalism and Hedin's $GW\gamma$ approach are unified into a single theory of vertex corrections, corresponding to an exact reformulation of the parquet equations in terms of boson exchange. The method has no drawbacks compared…
We report unphysical irregularities and discontinuities in some key experimentally-measurable quantities computed within the GW approximation of many-body perturbation theory applied to molecular systems. In particular, we show that the…
Multiple solutions exist in various experimental situations whenever the sum of several amplitudes is used to fit the experimentally measured distributions, such as the cross section, the mass spectrum, or the angular distribution. We show…
Many-body perturbation theory in the GW approximation is a useful method for describing electronic properties associated with charged excitations. A hierarchy of GW methods exists, starting from non-self-consistent G0W0, through partial…
Many combinatorial problems can be formulated as a polynomial optimization problem that can be solved by state-of-the-art methods in real algebraic geometry. In this paper we explain many important methods from real algebraic geometry, we…
We propose a new algorithm to the problem of polygonal curve approximation based on a multiresolution approach. This algorithm is suboptimal but still maintains some optimality between successive levels of resolution using dynamic…
In many-body perturbation theory (MBPT) the self-energy \Sigma=iGW\Gamma plays the key role since it contains all the many body effects of the system. The exact self-energy is not known; as first approximation one can set the vertex…
New stochastic approaches for the computation of electronic excitations are developed within the many-body perturbation theory. Three approximations to the electronic self-energy are considered: $G_0W_0$, $G_0W_0^tc$, and…
A global picture is drawn tying together most exact cosmological solutions of gravitational theories in four or more spacetime dimensions.
A unified approach, for solving a wide class of single and many-body quantum problems, commonly encountered in literature is developed based on a recently proposed method for finding solutions of linear differential equations. Apart from…
Understanding, finding, or even deciding on the existence of real solutions to a system of equations is a very difficult problem with many applications. While it is hopeless to expect much in general, we know a surprising amount about these…
A method of solving Maxwell equations in a vicinity of a multipole particle (moving along an arbitrary trajectory) is proposed. The method is based on a geometric construction of a trajectory-adapted coordinate system, which simplifies…
Using continuation methods and bifurcation theory, we study the exact multiplicity of periodic solutions, and the global solution structure, for periodic problems of first order. The results are applied to a population model with fishing,…
We have developed a new type of self-consistent scheme within the $GW$ approximation, which we call quasiparticle self-consistent $GW$ (QS$GW$). We have shown that QS$GW$ rather well describes energy bands for a wide-range of materials,…
Approximate solutions to functional evolution equations are constructed through a combination of series and conjugation methods, and relative errors are estimated. The methods are illustrated, both analytically and numerically, by…
We study some aspects of linearized gravity as gauge theory, with massive deformation. Recently it has been shown that there are two distinct solutions, which represent physical massive gravity. The purpose of the present work is to show…
Hedin's scheme is solved with the inclusion of the vertex function ($GW\Gamma$) for a set of small molecules. The computational scheme allows for the consistent inclusion of the vertex both at the polarizability level and in the…