Related papers: On the Kohn-Sham equations with periodic backgroun…
This paper addresses the well-posedness of a general class of bulk-surface convective Cahn--Hilliard systems with singular potentials. For this model, we first prove the existence of a global-in-time weak solution by approximating the…
The purpose of this article is to extend the work by Anantharaman and Canc\`es [1], and prove the existence of minimizers for the spin-polarized Kohn-Sham model in the presence of a magnetic field within the local spin density…
We analyze the effect of a finite volume on the thermodynamic potentials of a relativistic quantum field theory defined on a hypertorus at vanishing chemical potential. Using the symmetries of the Euclidean partition function, we interpret…
Finite temperature density functional theory requires representations for the internal energy, entropy, and free energy as functionals of the local density field. A central formal difficulty for an orbital-free representation is…
Within exact electron density-functional theory, we investigate Kohn-Sham (KS) potentials, orbital energies, and non-interacting kinetic energies of the fractional ions of Li, C and F. We use quantum Monte Carlo densities as input, which…
The gas of the interacted electrons is usually described within Kohn-Sham approximation by the set of Poisson and Schr\"{o}dinger equations with an effective potential for the single-particle wave functions. The solution of these equations…
It is known that smooth solutions to the non-isentropic Navier-Stokes equations without heat-conductivity may lose their regularities in finite time in the presence of vacuum. However, in spite of the recent progress on such blowup…
In this notes, we illustrate why the infinite volume scattering amplitude is in fact dispensable when it comes to formulating few-body quantization condition in finite volume. Only subprocess interactions or interactions associated…
We present a finite-volume based numerical scheme for a nonlocal Cahn-Hilliard equation which combines ideas from recent numerical schemes for gradient flow equations and nonlocal Cahn-Hilliard equations. The equation of interest is a…
In this paper we study the convergence rate of a finite volume approximation of the compressible Navier--Stokes--Fourier system. To this end we first show the local existence of a highly regular unique strong solution and analyse its global…
A solution to the linear Boltzmann equation satisfies an energy bound, which reflects a natural fact: The energy of particles in a finite volume is bounded in time by the energy of particles initially occupying the volume augmented by the…
We aim to study a finite volume scheme to solve the two dimensional inviscid primitive equations of the atmosphere with humidity and saturation, in presence of topography and subject to physically plausible boundary conditions to the system…
Quantum resonances, i.e., metastable states with a finite lifetime, play an important role in nuclear physics and other domains. Describing this phenomenon theoretically is generally a challenging task. In this work, we combine two…
We present a method for evaluating the partition function in a varying external field. Specifically, we look at the case of a non-interacting, charged, massive scalar field at finite temperature with an associated chemical potential in the…
In this paper it is shown that unique solutions to the relativistic Boltzmann equation exist for all time and decay with any polynomial rate towards their steady state relativistic Maxwellian provided that the initial data starts out…
We consider the binding energy of a two-body system with a repulsive Coulomb interaction in a finite periodic volume. We define the finite-volume Coulomb potential as the usual Coulomb potential, except that the distance is defined as the…
The one-loop effective potential for non-relativistic bosons with a delta function repulsive potential is calculated for a given chemical potential using functional methods. After renormalization and at zero temperature it reproduces the…
In this work we study in a formal way the density dependent hadron field theory at finite temperature for nuclear matter. The thermodynamical potential and related quantities, as energy density and pressure are derived in two different…
\begin{abstract} We consider the following poly-harmonic equations with critical exponents: \begin{equation}\label{P} (-\Delta)^m u =K(y)u^{\frac{N+2m}{N-2m}},\;\;\; u>0\;\;\;\hbox{in} \mathbb{R}^N, \end{equation} where $N>…
With the Schwinger's proper-time formalism of the Nambu-Jona-Lasinio model, we investigate the finite volume effects in the presence of magnetic fields. Since the coupling constant $G$ can be influenced by strong magnetic fields, the model…