Related papers: Generating functionals method of N.N.Bogolyubov an…
The Gross-Pitaevskii equation and its generalisations to dissipative and dipolar gases have been very useful in describing dynamics of cold atomic gases, as well as polaritons and other nonlinear systems. For some of these applications the…
Functional covariates arise in many scientific and engineering applications when model inputs take the form of time-dependent or spatially distributed profiles, such as varying boundary conditions or changing material behaviours. In…
Thermal Bogoliubov transformation is an essential ingredient of the thermo field dynamics -- the real time formalism in quantum field and many-body theories at finite temperatures developed by H. Umezawa and coworkers. The approach to study…
Gaussian processes (GPs) are pervasive in functional data analysis, machine learning, and spatial statistics for modeling complex dependencies. Modern scientific data sets are typically heterogeneous and often contain multiple known…
Following the idea of the density functional approach, we develop a generalized Bogoliubov theory of an interacting Bose gas confined in a one-dimensional harmonic trap, by using a local chemical potential - calculated with the Lieb-Liniger…
We introduce Generator Matching, a modality-agnostic framework for generative modeling using arbitrary Markov processes. Generators characterize the infinitesimal evolution of a Markov process, which we leverage for generative modeling in a…
In [Grenier-Nguyen], we introduced so called {\em generators} functions to precisely follow the regularity of analytic solutions of Navier Stokes equations. In this short note, we give a presentation of these generator functions and use…
Complex processes in perforated domains occur in many real-world applications. These problems are typically characterized by physical processes in domains with multiple scales (see Figure 1 for the illustration of a perforated domain).…
Functional graphs (FGs) model the graph structures used to analyse the behaviour of functions from a discrete set to itself. In turn, such functions are used to study real complex phenomena evolving in time. As the systems involved can be…
The understanding of complex quantum many-body systems has been vastly boosted by tensor network (TN) methods. Among others, excitation spectrum and long-range interacting systems can be studied using TNs, where one however confronts the…
Diffusion generative models have recently been applied to domains where the available data can be seen as a discretization of an underlying function, such as audio signals or time series. However, these models operate directly on the…
Despite recent advances, systematic quantitative treatment of the electron correlation problem in extended systems remains a formidable task. Systematically improvable Green's function methods capable of quantitatively describing weak and…
The generator coordinate (GC) method is a variational approach to the quantum many-body problem in which interacting many-body wave functions are constructed as superpositions of (generally nonorthogonal) eigenstates of auxiliary…
The theory of Self-Consistent Green's Function (SCGF) is reformulated in an explicit Nambu-covariant fashion for applications to many-body systems at non-zero temperature in symmetry-broken phases. This is achieved by extending the…
Combinatorial harmonic analysis techniques are used to develop new functional analysis methods based on Bogoliubov functionals. Concrete applications of the methods are presented, namely, the study of a non-equilibrium stochastic dynamics…
We derive the main equations of irreversible thermodynamic including the expression for the Glansdorff-Prigogine extremal principle from stochastic thermodynamics. To this end, we analyze a system that is subject to gradients of temperature…
Quantum generative modeling is emerging as a powerful tool for advancing data analysis in high-energy physics, where complex multivariate distributions are common. However, efficiently learning and sampling these distributions remains…
The method of many-body Green's functions is developed for arbitrary systems of electrons and nuclei starting from the full (beyond Born-Oppenheimer) Hamiltonian of Coulomb interactions and kinetic energies. The theory presented here…
We provide a general methodology to directly determine the validity of the meanfield Bogoliubov-de Gennes equation. In particular we apply this methodology to the case of two component interacting ultracold Fermi gases. As an example, we…
The nuclear energy density functional method at finite temperature is a useful tool for studies of nuclear structure at high excitation, and also for researches of nuclear matter involved in explosive stellar phenomena and neutron stars.…