Related papers: Critical strength of attractive central potentials

After reviewing the general properties of zero-energy quantum states, we give the explicit solutions of the \seq with $E=0$ for the class of potentials $V=-|\gamma|/r^{\nu}$, where $-\infty < \nu < \infty$. For $\nu > 2$, these solutions…

Strong-type inhomogeneous Strichartz estimates are shown to be false for the wave equation outside the so-called acceptable region. On a critical line where the acceptability condition marginally fails, we prove substitute estimates with a…

The qualitative study of solutions to the coupled parabolic-elliptic chemotaxis system with nonlinear diffusion for two species will be considered in the whole Euclidean space $\mathbb{R}^d$ ($d\geq 3$). It was proven in \cite{CK2021-ANA}…

We study the time evolution of the wave function of a particle bound by an attractive $\delta$-function potential when it is subjected to time dependent variations of the binding strength (parametric excitation). The simplicity of this…

Our aim in this paper is to study the Cahn-Hilliard equation with singular potentials and dynamic boundary conditions. In particular, we prove, owing to proper approximations of the singular potential and a suitable notion of variational…

Using the recent reformulation for the Eliashberg theory of superconductivity in terms of a classical interacting Bloch spin chain model, rigorous upper and lower bounds on the critical temperature $T_c$ are obtained for the $\gamma$ model…

The question of stability of the Higgs potential in the Standard Model is revisited employing advanced theoretical precision and recent experimental results. We show that the top mass and strong coupling constants are key observables in…

Let $\Omega \subset {\mathbb R}^N$ ($N \geq 3$) be a $C^2$ bounded domain and $\delta$ be the distance to $\partial \Omega$. We study positive solutions of equation (E) $-L_\mu u+ g(|\nabla u|) = 0$ in $\Omega$ where $L_\mu=\Delta +…

We prove the existence of an infinite family of smooth positive bound states for (N +1)-coupled long-wave--short-wave interaction equations. The system describes the interaction between N short waves and a long wave and is of interest in…

The binding energy of a negatively charged hydrogenic impurity with on- and off-center position in a spherical Gaussian quantum dot was calculated with the configuration interaction method. Our calculations show that $E_b$ is always…

A lower bound on the amount of noise that must be added to a GHZ-like entangled state to make it separable (also called the random robustness) is found using the transposition condition. The bound is applicable to arbitrary numbers of…

We analyse recent contradictory results and conclusions about the spectrum of the screened Coulomb potential $V(r)=-r^{-1}e^{-C/r}$. The well known Hellmann-Feynman theorem shows that all the bound states of the Coulomb potential ($C=0$)…

We study the CP domain walls and the consequent gravitational waves induced by the spontaneous breaking of the CP symmetry in the complex singlet extension to the Standard Model. We impose the constraints from the unitarity, stability and…

In this paper, we present different proofs of very recent results on the necessary as well as sufficient conditions on the decrease of the potential at infinity for the validity of effective range formulas in 3-D in low energy potential…

We study a class of exactly solvable models for strongly correlated electrons, defined on a set of N cells, and with infinite on-site repulsion on part of the sites of each cell. For 2N or more electrons the exact ground state is known. We…

In this paper we consider the higher order Lioville-type equation $(-\Delta)^{m} u=\rho^{2m} V(x) e^{u}$ in $\Omega\subseteq\mathbb{R}^{2m}$ with $V\neq0$ a given smooth potential, $\rho\in\mathbb{R}^{+}$ a small parameter which tends to…

Holes in cubic semiconductors have effective spin 3/2 and very strong spin orbit interaction. Due to these factors properties of hole bound states are highly unusual. We consider a single hole bound by a spherically symmetric potential,…

The focusing critical wave equation in three dimensions exhibits a special class of static solutions which are linearly unstable. These solutions decay like an inverse first power. We construct small codimension one stable manifolds in the…

Local(multiplicative) effective potential energy theories of electronic structure comprise the transformation of the Schr{\"o}dinger equation for interacting fermi systems to model noninteracting fermi or bose systems whereby the equivalent…

In dimensions one to three, the fundamental solution to the free wave equation is positive. Therefore, there exists a simple positivity criterion for solutions. We use this to obtain large global solutions to two well-studied…