Related papers: Nonexistence in Thomas-Fermi-Dirac-von Weizs\"acke…
The classical Maxwell-Dirac and Maxwell-Klein-Gordon theories admit solutions of the field equations where the corresponding electric current vanishes in the causal complement of some bounded region of Minkowski space. This poses the…
We consider the mass-critical nonlinear Schr\"odinger equation on non-compact metric graphs. A quite complete description of the structure of the ground states, which correspond to global minimizers of the energy functional under a mass…
With recent developments in simulating nonadiabatic systems to high accuracy, it has become possible to determine how much energy is attributed to nuclear quantum effects beyond zero-point energy. In this work we calculate the…
We systematically develop a density functional description for the equilibrium properties of a two-dimensional, harmonically trapped, spin-polarized dipolar Fermi gas based on the Thomas-Fermi von Weizs\"acker approximation. We pay…
We prove within the Hartree-Fock theory of pseudo-relativistic atoms that the maximal negative ionization charge and the ionization energy of an atom remain bounded independently of the nuclear charge Z and the fine structure constant…
In this paper we consider the {\it Density Functional Theory} (DFT) framework, where a functional of the form $$F_\eps(\rho)=\eps T(\rho)+bC(\rho)-U(\rho)$$ has to be minimized in the class of non-negative measures $\rho$ which have a…
We study the periodic Hartree-Fock model used for the description of electrons in a crystal. The existence of a minimizer was previously shown by Catto, Le Bris and Lions (Ann. Inst. H. Poincare Anal. Non Lineaire} 18 (2001), no.6,…
We prove a threshold phenomenon for the existence/non-existence of energy minimizing solitary solutions of the diffraction management equation for strictly positive and zero average diffraction. Our methods allow for a large class of…
The "catastrophe" in solving the Dirac equation for an electron in the field of a point electric charge, which emerges for the charge numbers Z > 137, is removed in this work by effective accounting of finite dimensions of nuclei. For this…
We prove an existence theorem for the Boltzmann-Fermi-Dirac equation for integrable collision kernels in possibly bounded domains with specular reflection at the boundaries, using the characteristic lines of the free transport. We then…
We investigate, under a volume constraint and among sets contained in a Euclidean half-space, the minimization problem of an energy functional given by the sum of a capillarity perimeter, a nonlocal interaction term and a gravitational…
We find the low-temperature behavior of the Casimir-Polder free energy and entropy for an atom interacting with real graphene sheet possessing nonzero energy gap and chemical potential. Employing the formalism of the polarization tensor, it…
We study atoms with N electrons, and nuclear charge Z. It is well known that the cationic regime, Z > N is qualitatively described by Thomas-Fermi theory. The anionic regime, Z < N, on the other hand, is characterized by an instability…
The Feynman, Metropolis and Teller treatment of compressed atoms is extended to the relativistic regimes. Each atomic configuration is confined by a Wigner-Seitz cell and is characterized by a positive electron Fermi energy. The…
A general approach to analyze the electrodynamics of nuclear matter in bulk is presented using the relativistic Thomas-Fermi equation generalizing to the case of $N \simeq (m_{\rm Planck}/m_n)^3$ nucleons of mass $m_n$ the approach well…
This paper is concerned with configurations of two-material thermal conductors that minimize the Dirichlet energy for steady-state diffusion equations with nonlinear boundary conditions described mainly by maximal monotone operators. To…
In this paper, we study the existence of minimizers to the following functional related to the nonlinear Choquard equation: $$ E(u)=\frac{1}{2}\ds\int_{\R^N}|\nabla…
The semi-classical approach leading to the Thomas-Fermi (TF) model provides a simple universal thermodynamic description of the electronic cloud surrounding the nucleus in an atom. This model is known to be exact at the limit of…
The effect of strong quantizing magnetic field on the equation of state of matter at the outer crust region of magnetars is studied. The density of such matter is low enough compared to the matter density at the inner crust or outer core…
We consider a Thomas-Fermi mean-field model for large neutral atoms. That is, Schr\"odinger operators $H_Z^{\text{TF}}=-\Delta-\Phi_Z^{\text{TF}}$ in three-dimensional space, where $Z$ is the nuclear charge of the atom and…