Related papers: Generating functionals method of N.N.Bogolyubov an…
The Bogoliubov method for the excitation spectrum of a Bose-condensed gas is generalized to apply to a gas with an exact large number $ N$ of particles. This generalization yields a description of the Schr\"odinger picture field operators…
This work is concerned with the development of a family of Galerkin finite element methods for the classical Kolmogorov's equation. Kolmogorov's equation serves as a sufficiently rich, for our purposes, model problem for kinetic-type…
Theory of non-equilibrium Green's function (NGF) provides a practical framework for studying quantum many-body systems out of equilibrium. Extending the previous mean field approach developed for nuclear systems in one dimension with NGF,…
Correlated classical and quantum many-particle systems out of equilibrium are of high interest in many fields, including dense plasmas, correlated solids, and ultracold atoms. Accurate theoretical description of these systems is challenging…
In this work we investigate the advantages of multiscale methods in Petrov-Galerkin (PG) formulation in a general framework. The framework is based on a localized orthogonal decomposition of a high dimensional solution space into a low…
The concept of time correlation functions is a very convenient theoretical tool in describing relaxation processes in multiparticle systems because, on one hand, correlation functions are directly related to experimentally measured…
The coupling effects in multiphysics processes are often neglected in designing multiscale methods. The coupling may be described by a non-positive definite operator, which in turn brings significant challenges in multiscale simulations. In…
Condensed Fermi systems with an odd number of particles can be described by means of polarizing external fields having a time-odd character. We illustrate how this works for Fermi gases and atomic nuclei treated by density functional theory…
A stochastic method is described for estimating Green's functions (GF's), appropriate to linear advection-diffusion-reaction transport problems, evolving in arbitrary geometries. By allowing straightforward construction of approximate,…
In this paper, we study the problem of massless particle creation in a flat, homogeneous and isotropic universe in the framework of $f(G)$ gravity. The Bogolyubov coefficients are calculated for the accelerating power-law solutions of the…
We review the stochastic Gross-Pitaevskii approach for non-equilibrium finite temperature Bose gases, focussing on the formulation of Stoof; this method provides a unified description of condensed and thermal atoms, and can thus describe…
We propose a novel many-body truncation for Gorkov self-consistent Green's function (SCGF) theory where pairing correlations are handled at first order, while dynamical correlations are described using the particle-number-conserving…
We propose a numerical method to efficiently compute quantum generating functions (QGF) for a wide class of observables in one-dimensional quantum systems at high temperature. We obtain high-accuracy estimates for the cumulants and…
We present a real-time second-order Green's function (GF) method for computing excited states in molecules and nanostructures, with a computational scaling of $O(N_{\rm e}^3$), where $N_{\rm e}$ is the number of electrons. The cubic scaling…
The task of deducing three-dimensional molecular configurations from their two-dimensional graph representations holds paramount importance in the fields of computational chemistry and pharmaceutical development. The rapid advancement of…
We study the form factors of local operators of integrable QFT's between states with finite energy density. These states arise, for example, at finite temperature, or from a generalized Gibbs ensemble. We generalize Smirnov's form factor…
A common problem in physics and engineering is the calculation of the minima of energy functionals. The theory of Sobolev gradients provides an efficient method for seeking the critical points of such a functional. We apply the method to…
State-of-the-art multi-reference energy density functional calculations require the computation of norm overlaps between different Bogoliubov quasiparticle many-body states. It is only recently that the efficient and unambiguous calculation…
The generating function method that we had developing has various applications in physics and not only interress undergraduate students but also physicists. We solve simply difficult problems or unsolved commonly used in quantum, nuclear…
We propose an efficient stochastic method to implement numerically the Bogolubov approach to study finite-temperature Bose-Einstein condensates. Our method is based on the Wigner representation of the density matrix describing the non…