Related papers: L\"uscher equation with long-range forces
The exchange of a pair of low-mass neutrinos between electrons, protons and neutrons produces a "long-range" $1/r^5$ potential, which can be sought for in phenomena originating on the atomic and sub-atomic length scales. We calculate the…
In this paper we consider the inverse scattering problem at a fixed energy for the Schr\"odinger equation with a long-range potential in $\ere^d, d\geq 3$. We prove that the long-range part can be uniquely reconstructed from the leading…
Within general partial-wave mixing, a method for reducing the high dimension of the finite-volume Hamiltonian from Hamiltonian effective field theory is proposed. This method provides a new viewpoint on partial-wave mixing, and a set of…
The L\"uscher scattering formalism, the standard approach for relating the discrete finite-volume energy spectrum to two-to-two scattering amplitudes, fails when analytically continued so far below the infinite-volume two-particle threshold…
The work reviews on a general level various modified Poisson-Boltzmann equations and demonstrates their use on the specific system of charged particles at an interface. This system is special, first, because it exhibits the long-range…
We consider an inverse problem for the linear one-dimensional wave equation with variable coefficients consisting in determining an unknown source term from a boundary observation. A method to obtain approximations of this inverse problem…
We continue the study of scattering theory for the system consisting of a Schr"odinger equation and a wave equation with a Yukawa type coupling in space dimension 3. In a previous paper we proved the existence of modified wave operators for…
We study two particles colliding in a $d$-dimensional finite volume and generalize L\"uscher's formula to arbitrary $d$ spatial dimensions. We obtain the $s$- and $p$-wave approximations of the generalized L\"uscher's formula. For resonant…
Using non-relativistic effective field theory, we derive a three-particle analog of the Lellouch-L\"uscher formula at the leading order. This formula relates the three-particle decay amplitudes in a finite volume with their infinite-volume…
We consider the existence and uniqueness of a minimizer of the extremal problem for weighted combined energy between two concentric annuli and obtain that the extremal mapping is a certain radial mapping. Meanwhile, this in turn implies a…
In this paper, L\"uscher's formula is generalized to the case of two spin-$\frac{1}{2}$ particles in two-channel scattering based on Ref. \cite{Li:2012bi}. This is first done in a non-relativistic quantum mechanics model and then…
We analyze the low-energy e-N2 collisions within the framework of the Modified-Effective Range Theory (MERT) for the long-range potentials, developed by O'Malley, Spruch and Rosenberg [Journal of Math. Phys. 2, 491 (1961)]. In comparison to…
We show in this paper that the basic representations of position and momentum in a quantum mechanical system, that are guided by a generalized uncertainty principle and lead to a corresponding one-parameter eigenvalue problem, can be…
We discuss a novel effective-field-theory-based approach for extracting two-body scattering information from finite volume energies, serving as an alternative to L\"uscher's method. By explicitly incorporating one-pion exchange, we overcome…
We consider the numerical approximation of a system of partial differential equations involving a nonlinear Schr\"odinger equation coupled with a hyperbolic conservation law. This system arises in models for the interaction of short and…
Lattice quantum chromodynamics calculations of multi-baryon systems with physical quark masses would start a new age of ab initio predictions in nuclear physics. Performed on a finite grid, such calculations demand extrapolation of their…
We present a quantization condition for the spectrum of a system composed of three identical bosons in a finite volume with periodic boundary conditions. This condition gives a relation between the finite volume spectrum and infinite volume…
Euler's equation relates the change in angular momentum of a rigid body to the applied torque. This paper fills a gap in the literature by using Lagrangian dynamics to derive Euler's equation in terms of generalized coordinates. This is…
Collective coherent scattering of laser light by an ensemble of polarizable point particles creates long range interactions, whose properties can be tailored by choice of injected laser powers, frequencies and polarizations. We use a…
A formulation is developed for the calculation of the electromagnetic--fluctuation forces for dielectric objects of arbitrary geometry at small separations, as a perturbative expansion in the dielectric contrast. The resulting Lifshitz…