Related papers: Critical strength of attractive central potentials
We consider a class of particle systems which appear in various applications such as approximation theory, plasticity, potential theory and space-filling designs. The positions of the particles on the real line are described as a global…
Positivity constraints on the pion-nucleon scattering amplitude are derived in this article with the help of general S-matrix arguments, such as analyticity, crossing symmetry and unitarity, in the upper part of Mandelstam triangle, R.…
We refine previous results concerning the Renewal Contact Processes. We significantly widen the family of distributions for the interarrival times for which the critical value can be shown to be strictly positive. The result now holds for…
Compact algebraic equations are derived, which connect the binding energy and the asymptotic normalization constant (ANC) of a subthreshold bound state with the effective-range expansion of the corresponding partial wave. These relations…
Recently obtained results on linear energy bounds are generalized to arbitrary spin quantum numbers and coupling schemes. Thereby the class of so-called independent magnon states, for which the relative ground-state property can be…
We investigate bound states of light $\Omega_{3x}$-clusters ($x = s, c$), motivated by the $\Omega_{3s}N$ potential recently developed by the HAL QCD collaboration. To regularize this potential, we remove the deeply attractive core at $r <…
Bound states of the generalized spiked harmonic oscillator potential are calculated accurately by using the generalized pseudospectral method. Energy eigenvalues, various expectation values, radial densities are obtained through a…
In this paper, we study the initial boundary value problem for the two dimensional strong damped wave equation with exponentially growing source and damping terms. We first show the well-posedness of this problem and then prove the…
Limit theorems of strong law of large numbers and central limit theorem types are obtained for the compositions of independent identically distributed random unitary channels.
Electron-electron interactions generally reduce the low temperature resistivity due to the screening of the impurity potential by the electron gas. In the weak-coupling limit, the magnitude of this screening effect is determined by the…
We present the first exact calculation of the energy of the bound state of a one dimensional Dirac massive particle in weak short-range arbitrary potentials, using perturbation theory to fourth order (the analogous result for two…
For strongly positively recurrent countable state Markov shifts, we bound the distance between an invariant measure and the measure of maximal entropy in terms of the difference of their entropies. This extends an earlier result for…
The existence of a positive solution to a class of Choquard equations with potential going at a positive limit at infinity possibly from above or oscillating is proved. Our results include the physical case and do not require any symmetry…
We present bound state spectra of the 3D rational potential, $V(r)=r^2 + \lambda r^2/(1+gr^2)$, $g>0$, by means of the generalized pseudospectral method. All the thirty states corresponding to $n$=0--9 are considered for the first time for…
We discuss some general features of the effective range expansion, the content of its parameters with respect to the nature of the pertinent near-threshold states and the necessary modifications in the presence of coupled channels, isospin…
The energy spectrum of gravitational waves (GWs), which depicts the energy of GWs per unit volume of space per logarithmic frequency interval normalized to the critical density of the Universe, is a widely used way for quantifying the…
Critical exponents have been obtained for a 3D spin particle system. Clusters are formed and system reaches a critical behavior when fragment size distribution follows a power law, as predicted by Fisher Liquid Droplet Model. Also,…
We establish existence and uniqueness of global, bounded weak solutions to quasilinear PDEs with bounded, uniformly continuous initial data and investigate their properties. Moreover, we establish existence of bounded weak solutions when…
New physics at the TeV scale or lower may destabilise the electroweak vacuum. How low could the vacuum instability scale be? This fundamental question may be tied to a deeper understanding of the Higgs potential and its associated hierarchy…
We consider the two-dimensional Pauli operator perturbed by a weakly coupled, attractive potential. We show that besides the eigenvalues arising from the Aharonov-Casher zero modes there are two or one (depending on whether the flux of the…