Related papers: Conserving approximations vs Two-Particle Self-Con…
I introduce several simplified schemes for the approximation of the self-consistency condition of the dynamical cluster approximation. The applicability of the schemes is tested numerically using the fluctuation-exchange approximation as a…
The two-dimensional n-body problem of classical mechanics is a non-integrable Hamiltonian system for n > 2. Traditional numerical integration algorithms, which are polynomials in the time step, typically lead to systematic drifts in the…
This paper concerns the construction and analysis of a numerical scheme for a mixed discrete-continuous fragmentation equation. A finite volume scheme is developed, based on a conservative formulation of a truncated version of the…
The equilibration of two coupled reservoirs is studied using a Green function approach which is suitable for future development with the closed time path method. The problem is solved in two parameterizations, in order to demonstrate the…
Nonconservative evolution problems describe irreversible processes and dissipative effects in a broad variety of phenomena. Such problems are often characterised by a conservative part, which can be modelled as a Hamiltonian term, and a…
The conformal method developed in the 1970s and the more recent Lagrangian and Hamiltonian conformal thin-sandwich methods are techniques for finding solutions of the Einstein constraint equations. We show that they are manifestations of a…
A new methodology is developed to integrate numerically the equations of motion for classical many-body systems in molecular dynamics simulations. Its distinguishable feature is the possibility to preserve, independently on the size of the…
The two-dimensional Hubbard model is studied using the variational quantum Monte Carlo technique with Gutzwiller-type variational wave functions. In addition to the simple one-site correlated Gutzwiller wave function, we use a form with…
The problem of reconstructing functions from their asymptotic expansions in powers of a small variable is addressed by deriving a novel type of approximants. The derivation is based on the self-similar approximation theory, which presents…
Two approaches for the efficient rational approximation of the Fermi-Dirac function are discussed: one uses the contour integral representation and conformal mapping and the other is based on a version of the multipole representation of the…
In the framework of quantum thermodynamics, we propose a method to quantitatively describe thermodynamic quantities for out-of-equilibrium interacting many-body systems. The method is articulated in various approximation protocols which…
We propose a general method for optimization with semi-infinite constraints that involve a linear combination of functions, focusing on the case of the exponential function. Each function is lower and upper bounded on sub-intervals by…
We present a novel implicit scheme for the numerical solution of time-dependent conservation laws. The core idea of the presented method is to exploit and approximate the mixed spatial-temporal derivative of the solution that occurs…
In this paper we propose a new approach to least squares approximation problems. This approach is based on partitioning and Schur function. The nature of this approach is combinatorial, while most existing approaches are based on algebra…
Radiation hydrodynamics simulations based on the one-fluid two-temperature model may violate the law of energy conservation because the governing equations are expressed in a nonconservative formulation. Here, we maintain the important…
Using a theorem of partial differential equations, we present a general way of deriving the conserved quantities associated with a given classical point mechanical system, denoted by its Hamiltonian. Some simple examples are given to…
The formalism of Kohn and Sham uses a specific (model) hamiltonian which highly simplifies the many-electron problem to that of noninteracting fermions. The theorem of Hohenberg and Kohn tells us that, for a given ground state density, this…
A computationally efficient Green's function approach is developed to evaluate the optical properties of nanostructures using a GW formalism applied on top of a tight-binding and mean-field Hubbard model. The use of the GW approximation…
We present a unified many-body perturbation theory for open quantum systems, that treats dissipation, correlations, and external driving on equal footing. Using a Keldysh-Lindblad formalism, we introduce diagrammatic treatment of…
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…