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I review the quantum theory of the electron moving in a random environment. First, the quantum mechanics of individual particles scattered on a random potential is discussed. The quantum-mechanical description is extended to many-body…
An end-to-end strategy for hybrid quantum-classical computations of Green's functions in many-body systems is presented and applied to the pairing model. The scheme makes explicit use of the spectral representation of the Green's function,…
We apply a promising new method from the field of representations of Lie groups to calculate integrals over unitary groups, which are important for multi-antenna communications. To demonstrate the power and simplicity of this technique, we…
We introduce an efficient general method for calculating the self-energies, collective modes, and dispersion relations of quarks and gluons in a momentum-anisotropic high-temperature quark-gluon plasma. The method introduced is applicable…
In the present paper we show how obtain the energy distribution f(E) in our vicinity starting from WIMP density profiles in a self consistent way by employing the Eddington approach and adding reasonable angular momentum dependent terms in…
The linear response description for impurity diffusion in a granular fluid undergoing homogeneous cooling is developed in the preceeding paper. The formally exact Einstein and Green-Kubo expressions for the self-diffusion coefficient are…
A modified $GW$ approximation to many - body systems is developed. The approximation has the same computational complexity as the traditional $GW$ approach, but uses a different truncation scheme. This scheme neglects high order connected…
The $GW$ approximation is considered to be the simplest approximation with Hedin's formulation of many-body perturbation theory. It is expected that some of the deficiencies of the $GW$ approximation can be overcome by adding the so-called…
We present a stochastic description of a model of N mutually repelling active spheres in the presence of external fields and characterize its steady state behavior. To reproduce the effects of the experimentally observed persistence of the…
This work reports the conditions under which weak scattering assumptions can be applied in a beam loaded by multiple resonators supporting both longitudinal and flexural waves. The work derives the equations of motion of a one-dimensional…
The single particle energies obtained in a Kohn--Sham density functional theory (DFT) calculation are generally known to be poor approximations to electron excitation energies that are measured in transport, tunneling and spectroscopic…
Recent high resolution Compton scattering experiments clearly reveal that there are fundamental limitations to the conventional local density approximation (LDA) based description of the ground state electron momentum density (EMD) in…
We investigate different correlation mechanisms for two-electron systems and compare their respective effects on various electron distributions. The simplicity of the wave functions used allows for the derivation of closed-form analytical…
We present a diagrammatic approach to construct self-energy approximations within many-body perturbation theory with positive spectral properties. The method cures the problem of negative spectral functions which arises from a…
In computational and applied statistics, it is of great interest to get fast and accurate calculation for the distributions of the quadratic forms of Gaussian random variables. This paper presents a novel approximation strategy that…
We show how to evaluate mobility profiles, characterizing the transport of confined fluids under a perturbation, from equilibrium molecular simulations. The correlation functions derived with the Green-Kubo formalism are difficult to sample…
The GW Approximation is an ab initio approach to calculating electronic structure which avoids using the Local Density (LDA) Approximation, the Generalized Gradient (GGA) Approximation, or similar density functionals. It goes beyond the…
We establish a general relation between the statistics of the local Green's function for systems with chaotic wave scattering and a uniform energy loss (absorption) and its two-point correlation function for the same system without…
Aims. Numerical test-particle simulations are a reliable and frequently used tool to test analytical transport theories and to predict mean-free paths. The comparison between solutions of the diffusion equation and the particle flux is used…
We report an implementation of self-consistent Green's function many-body theory within a second-order approximation (GF2) for application with molecular systems. This is done by iterative solution of the Dyson equation expressed in matrix…