Related papers: Constrained energy problems with external fields
Effective field theories (EFT) are strongly constrained by fundamental principles such as unitarity, locality, causality, and Lorentz invariance. In this paper, we consider the EFT of photons (or other $U(1)$ gauge field) and compare…
We study kernel quadrature rules with convex weights. Our approach combines the spectral properties of the kernel with recombination results about point measures. This results in effective algorithms that construct convex quadrature rules…
Although the black holes are an integral part of the standard model of astrophysics and cosmology, their existence poses some serious fundamental problems. In recent years, several horizonless compact object models were proposed to address…
Solar system observations have traditionally allowed for very stringent tests of Einstein's theory of general relativity. We here revisit the possibility of using these observations to constrain gravitational parity violation as…
The existence of compactly supported global minimisers for continuum models of particles interacting through a potential is shown under almost optimal hypotheses. The main assumption on the potential is that it is catastrophic, or not…
We make a study of unipotent elements in a connected reductive group over an algebraically closed field with emphasis on the case where the characteristic is a bad prime. We try to see how much of the theory of Dynkin-Kostant extends to…
The energy spectrum of an electron confined to an arbitrary surface of revolution in an external magnetic field, parallel to the symmetry axis, is studied analitycally and numerically. The problem is reduced via conformal mapping to one on…
Two- and three-dimensional electron gases with a uniform neutralizing background are studied at negative compressibility. Parametrized expressions for the dielectric function are used to access this strong-coupling regime, where the…
The response of the system, consisting of two kinds of opposite-charged fermions and their bound states (hydrogen-like atoms), to the perturbation by the external electromagnetic field in low particle kinetic energies region is studied.…
For a general dark-energy equation of state, we estimate the maximum possible radius of massive structures that are not destabilized by the acceleration of the cosmological expansion. A comparison with known stable structures constrains the…
We introduce a rigorous approach to the study of the symmetry breaking and pattern formation phenomenon for isotropic functionals with local/nonlocal interactions in competition. We consider a general class of nonlocal variational problems…
For any bounded convex domain \Omega in R^N, we assign a positive finite Borel measure associated with the solution to a su-blinear elliptic equation in \Omega. We prove that this measure is weakly continuous in the sense of measure with…
This paper is about two related decision theoretic problems, nonparametric two-sample testing and independence testing. There is a belief that two recently proposed solutions, based on kernels and distances between pairs of points, behave…
We study the existence of weak solutions of (E) $ (-\Delta)^\alpha u+g(u)=\nu $ in a bounded regular domain $\Omega$ in $\R^N (N\ge2)$ which vanish on $\R^N\setminus\Omega$, where $(-\Delta)^\alpha$ denotes the fractional Laplacian with…
A quantum particle moving under the influence of singular interactions on embedded surfaces furnish an interesting example from the spectral point of view. In these problems, the possible occurrence of a bound state is perhaps the most…
The low-energy structure of hadrons can be described systematically using effective field theory, and the parameters of the effective theory can be determined from lattice QCD computations. Recent work, however, points to inconsistencies…
For two continuous and isotropic positive definite kernels on the same compact two-point homogeneous space, we determine necessary and sufficient conditions in order that their product be strictly positive definite. We also provide a…
For a bounded weak Lipschitz domain we show the so called `Maxwell compactness property', that is, the space of square integrable vector fields having square integrable weak rotation and divergence and satisfying mixed tangential and normal…
Regularity results for minimal configurations of variational problems involving both bulk and surface energies and subject to a volume constraint are established. The bulk energies are convex functions with p-power growth, but are otherwise…
Recent progress in the quantization of nonrenormalizable scalar fields has found that a suitable non-classical modification of the ground state wave function leads to a result that eliminates term-by-term divergences that arise in a…