Related papers: Finite elements and the discrete variable represen…
A new version of application Pauli-Villars regularized Green functions in the quantum field theory using higher derivatives is proposed. In this version the regularizing mass $M$ is large but finite. Our approach is demonstrated and…
We derive a general expression for the electron nonequilibrium (NE) distribution function in the context of steady state quantum transport through a two-terminal nanodevice with interaction. The central idea for the use of NE distributions…
In this work, we develop a highly efficient representation of functions and differential operators based on Fourier analysis. Using this representation, we create a variational hybrid quantum algorithm to solve static, Schr\"odinger-type,…
The non-equilibrium Green's function formalism for infinitely extended reservoirs coupled to a finite system can be derived by solving the equations of motion for a tight-binding Hamiltonian. While this approach gives the correct density…
In this paper, both semidiscrete and completely discrete finite volume element methods (FVEMs) are analyzed for approximating solutions of a class of linear hyperbolic integro- differential equations in a two-dimensional convex polygonal…
We describe the non-equilibrium dynamics of the Sachdev-Ye-Kitaev models of fermions with all-to-all interactions. These provide tractable models of the dynamics of quantum systems without quasiparticle excitations. The Kadanoff-Baym…
We propose a finite element discretisation approach for the incompressible Euler equations which mimics their geometric structure and their variational derivation. In particular, we derive a finite element method that arises from a…
We describe an ab initio method for calculating the electronic structure, electronic transport, and forces acting on the atoms, for atomic scale systems connected to semi-infinite electrodes and with an applied voltage bias. Our method is…
Nonequilibrium Green's functions represent underutilized means of studying the time evolution of quantum many-body systems. In view of a rising computer power, an effort is underway to apply the Green's functions formalism to the dynamics…
The pair distribution function (PDF) is a key quantity for the analysis of correlation effects of a quantum system both in equilibrium and far from equilibrium. We derive an expression for the PDF in terms of the single-particle Green's…
Green's functions characterize the fundamental solutions of partial differential equations; they are essential for tasks ranging from shape analysis to physical simulation, yet they remain computationally prohibitive to evaluate on…
The nonequilibrium Dyson (or Kadanoff-Baym) equation, which is an equation of motion with long-range memory kernel for real-time Green functions, underlies many numerical approaches based on the Keldysh formalism. In this paper we map the…
The two-particle problem within a nonequilibrium many-particle system is investigated in the framework of real-time Green's functions. Starting from the dynamically screened ladder approximation of the nonequlibrium Bethe-Salpeter equation,…
A generalized quantum kinetic equation (RKE) of the Kadanoff-Baym type is obtained on the basis of the Heisenberg equations of motion where the time evolution and space translation are separated from each other by means of the covariant…
The discrete variable representation (DVR) basis is nearly optimal for numerically representing wave functions in nuclear physics: Suitable problems enjoy exponential convergence, yet the Hamiltonian remains sparse. We show that one can…
Nonperturbative dynamic theory has a particular advantage in studying the transport in a quantum impurity system in a steady state. Here, we develop a new approach for obtaining the retarded Green's function expressed in resolvent form. We…
We construct a new functional for the single particle Green's function, which is a variant of the standard Baym Kadanoff functional. The stability of the stationary solutions to the new functional is directly related to aspects of the…
Time-dependent nonequilibrium Green's functions (TDNEGF) are shown to provide a flexible, effective tool for the description of quantum mechanical single particle scattering on a spatially localized, time-dependent potential. Focusing on…
This paper is concerned with mixed finite element method (FEM) for solving the two-dimensional, nonlinear fourth-order active fluid equations. By introducing an auxiliary variable $w=-\Delta u$, the original fourth problem is transformed…
We discuss the application of the Discrete Variable Representation to Schr\"odinger problems which involve singular Hamiltonians. Unlike recent authors who invoke transformations to rid the eigenvalue equation of singularities at the cost…