Related papers: Hyperfunction formulation of many body Green's fun…
The ill-posed analytic continuation problem for Green's functions or self-energies can be done using the Pad\'e rational polynomial approximation. However, to extract accurate results from this approximation, high precision input data of…
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 evaluate the one-particle and double-occupied Green functions for the Hubbard model at half-filling using the moment approach of Nolting. Our starting point is a self-energy, $\Sigma(\vec{k},\omega)$, which has a single pole,…
This article generalizes the notion of the local density of a many-body system to introduce collective coordinates as explicit degrees of freedom. It is shown that the energy of the system can be expressed as a functional of this object.…
Two types of one-body functions extracted from microscpic models of the 8B ground state are compared with one another and with a potential-model wave function. The one-body overlap function seems to have the strongest physical meaning.
We provide an in-depth examination of the $GW$ approximation of Green's function many-body perturbation theory by detailing both its theoretical and practical aspects in the realm of quantum chemistry. First, the quasiparticle context is…
Unique transformation properties under the hyperspherical inversion of a partial differential equation describing a stationary scalar wave in an $N$-dimensional ($N\geqslant2$) Maxwell fish-eye medium are exploited to construct a closed…
By exploiting the analyticity and boundary value properties of the thermal Green functions that result from the KMS condition in both time and energy complex variables, we treat the general (non-perturbative) problem of recovering the…
Two measures of how near an arbitrary function between groups is to being a homomorphism are considered. These have properties similar to conjugates and commutators. The authors show that there is a rich theory based on these structures,…
We show that under quite general conditions, various multifractal spectra may be obtained as Legendre transforms of functions $T\colon \RR\to \RR$ arising in the thermodynamic formalism. We impose minimal requirements on the maps we…
We generate the perturbative expansion of the single-particle Green's function and related self-energy for a half-filled single-band Hubbard model on a square lattice. We invoke algorithmic Matsubara integration to evaluate single-particle…
Green's functions of non-Hermitian systems play a fundamental role in various dynamical processes. Because non-Hermitian systems are sensitive to boundary conditions due to the non-Hermitian skin effect, open-boundary Green's functions are…
This paper introduces a new generalized superfactorial function (referable to as $n^{th}$- degree superfactorial: $sf^{(n)}(x)$) and a generalized hyperfactorial function (referable to as $n^{th}$- degree hyperfactorial: $H^{(n)}(x)$), and…
In this paper, we give a formula for the number of rational points on the Dwork hypersurfaces of degree six over finite fields by using Greene's finite-field hypergeometric function, which is a generalization of Goodson's formula for the…
The nonequilibrium Green's function formalism provides a versatile and powerful framework for numerical studies of nonequilibrium phenomena in correlated many-body systems. For calculations starting from an equilibrium initial state, a…
The problem of the microscopic description of excited states of the even-even open-shell atomic nuclei is considered. A model is formulated which allows one to go beyond the quasiparticle random phase approximation. The physical content of…
This series presents an approach to mathematical biology which makes precise the function of biological molecules. Because biological systems compute, the theory is a general purpose computer language. I build a language for efficiently…
Non-equilibrium Green's functions provide an efficient way to describe the evolution of the energy-momentum tensor during the early time pre-equilibrium stage of high-energy heavy ion collisions. Besides their practical relevance they also…
The electromagnetic Green's function is a crucial ingredient for the theoretical study of modern photonic quantum devices, but is often difficult or even impossible to calculate directly. We present a numerically efficient framework for…
Linear and nonlinear optical effect has been widely discussed in large quantity of materials using theoretical or experimental methods. Except linear optical conductivity, higher-order nonlinear responses are not studied fully. Starting…