Related papers: Critical strength of attractive central potentials
Singular potentials (the inverse-square potential, for example) arise in many situations and their quantum treatment leads to well-known ambiguities in choosing boundary conditions for the wave-function at the position of the potential's…
We study few-body bound states of charged particles subject to attractive zero-range/short-range plus repulsive Coulomb interparticle forces. The characteristic length scales of the system at zero energy are set by the Coulomb length scale…
We study the excited states of the pairing Hamiltonian providing an expansion for their energy in the strong coupling limit. To assess the role of the pairing interaction we apply the formalism to the case of a heavy atomic nucleus. We show…
We define a potential-weighted connective constant that measures the effective strength of a repulsive pair potential of a Gibbs point process modulated by the geometry of the underlying space. We then show that this definition leads to…
Motivated by a recent analysis which presents explicitly the general solution, we consider the eigenvalue problem of the spinless Salpeter equation with a ("hard-core amended") Coulomb potential in one dimension. We prove the existence of a…
In order to shed some light on the current discussion about f(R)-gravity theories we derive and discuss the bounds imposed by the energy conditions on a general f(R) functional form. The null and strong energy conditions in this framework…
Imaginary potentials such as $V(x)=-iv 1_\Omega(x)$ (with $v>0$ a constant, $\Omega$ a subset of 3-space, and $1_\Omega$ its characteristic function) have been used in quantum mechanics as models of a detector. They represent the effect of…
Relationships between the coupling constant and the binding energy of threshold bound states are obtained in a simple manner from an iterative algorithm for solving the eigenvalue problem. The absence of threshold bound states in higher…
We consider a constrained minimal energy problem with an external field over noncompact classes of infinite dimensional vector measures on a locally compact space. The components are positive measures (charges) that are constrained from…
We estimate the ratio $R=g_{3}/g_{2}$ of the critical coupling constants $g_{2}$ and $g_{3}$ which are required to achieve binding of 2 or 3 bosons, respectively, with a short-range interaction, and examine how this ratio depends on the…
Data from a number of different experimental measurements have been used to construct caloric curves for five different regions of nuclear mass. These curves are qualitatively similar and exhibit plateaus at the higher excitation energies.…
We demonstrate the existence of confined states in one- and two-dimensional (1D and 2D) systems of two linearly-coupled components, with the confining harmonic-oscillator (HO) potential acting upon one component, and an expulsive anti-HO…
We consider the existence of bound and ground states for a family of nonlinear elliptic systems in $\mathbb{R}^N$, which involves equations with critical power nonlinearities and Hardy-type singular potentials. The equations are coupled by…
In the mean-field approximation, the well-known effect of the critical quantum collapse in a 3D gas of particles pulled to the center by potential U(r) = -U_0/r^2 is suppressed by repulsive interparticle interactions, which create the…
We obtain, using the Birman-Schwinger method, upper limits on the total number of bound states and on the number of $\ell$-wave bound states of the semirelativistic spinless Salpeter equation. We also obtain a simple condition, in the…
We establish the well-posedness of a strongly damped semilinear wave equation equipped with nonlinear hyperbolic dynamic boundary conditions. Results are carried out with the presence of a parameter distinguishing whether the underlying…
We present a sufficient criterion for the emergence of cluster phases in an ensemble of interacting classical particles with repulsive two-body interactions. Through a zero-temperature analysis in the low density region we determine the…
For a general inelastic Kac-like equation recently proposed, this paper studies the long-time behaviour of its probability-valued solution. In particular, the paper provides necessary and sufficient conditions for the initial datum in order…
By taking advantage of a stability criterion established recently, the critical temperature $T_c$ is reckoned with help of the microscopic parameters, characterising the normal and superconducting electrons, namely the independent-electron…
The study deals with a minimal energy problem in the presence of an external field over noncompact classes of vector measures of infinite dimension in a locally compact space. The components are positive measures (charges) satisfying…