Related papers: A closed-form energy-minimization basis for gravit…
The regularized vacuum energy (or energy density) of a quantum field subjected to static external conditions is shown to satisfy a certain partial differential equation with respect to two variables, the mass and the "time" (ultraviolet…
In a recent paper [J. Math. Phys. 47 082303 (2006)], Quantum Energy Inequalities were used to place simple geometrical bounds on the energy densities of quantum fields in Minkowskian spacetime regions. Here, we refine this analysis for…
We have recently developed a geometric formulation of the stress field for an interacting quantum system within the local density approximation (LDA) of density functional theory (DFT). We obtain a stress field which is invariant with…
We present evidence that a special class of gravitationally-coupled hidden sectors, in which conformal invariance is dynamically broken in a controlled way, exhibit the properties of dark energy. Such quantum field theories may appear while…
The purpose of this paper is to derive sharp asymptotics of the ground state energy for the heavy atoms and molecules in the relativistic settings, with the self-generated magnetic field, and, in particular, to derive relativistic Scott…
In a previous paper, a bound on the negative energy density seen by an arbitrary inertial observer was derived for the free massless, quantized scalar field in four-dimensional Minkowski spacetime. This constraint has the form of an…
When a Hamiltonian density is bounded by below, we know that the lowest-energy state must be stable. One is often tempted to reverse the theorem and therefore believe that an unbounded Hamiltonian density always implies an instability. The…
Deformations of minimal surfaces lying in constant time slices in static space-times are studied. An exact and universal formula for a change of the area of a minimal surface under shifts of nearby point-like particles is found. It allows…
Locating the global minimum of a complex potential energy surface is facilitated by considering a homotopy, namely a family of surfaces that interpolate continuously from an arbitrary initial potential to the system under consideration.…
In this paper, we study a few theoretical issues in the discretized Kohn-Sham (KS) density functional theory (DFT). The equivalence between either a local or global minimizer of the KS total energy minimization problem and the solution to…
The calculation of the underground density field from measured gravity data has been done by a variety of methods of varied types. The use of the vector gravity components is here addressed in order to develop one accurate gravity inversion…
We propose a simple and efficient method to calculate the electronic self-energy in dynamical mean-field theory (DMFT), addressing a numerical instability often encountered when solving the Dyson equation. Our approach formulates the Dyson…
We obtain an approximate global stationary and axisymmetric solution of Einstein's equations which can be considered as a simple star model: a self-gravitating perfect fluid ball with constant mass density rotating in rigid motion. Using…
We prove some improved estimates for the Ginzburg-Landau energy (with or without magnetic field) in two dimensions, relating the asymptotic energy of an arbitrary configuration to its vortices and their degrees, with possibly unbounded…
We propose and study a regularization method for recovering an approximate electrical conductivity solely from the magnitude of one interior current density field. Without some minimal knowledge of the boundary voltage potential, the…
A scheme is developed which enables one to trace backwards in time the cosmic density and velocity fields, and to determine accurately the current-epoch velocity field from the current-epoch density field, or vice versa. The scheme…
The paper considers a set of equations describing the static isotropic gravity field of a macroscopic body within the framework of the theory of gravity with a constraint. A general approximate solution of these equations is obtained. The…
The discovery of cosmic acceleration has triggered a consistent body of theoretical work aimed at modeling its phenomenology and understanding its fundamental physical nature. In recent years, a powerful formalism that accomplishes both…
In arXiv:1601.02203 and arXiv:1702.07063, we have proposed a topological model with a simple Lagrangian density and have tried to solve one of the cosmological constant problems. The Lagrangian density is the BRS exact and therefore the…
We give a derivation of the Einstein equation for gravity which employs a definition of the local energy density of the gravitational field as a symmetric second rank tensor whose value for each observer gives the trace of the spatial part…