相关论文: Resonance Point Interactions
We present an inverse scattering construction of generalised point interactions (GPI) -- point-like objects with non-trivial scattering behaviour. The construction is developed for single centre $S$-wave GPI models with rational…
This text is a part of an unfinished project which deals with the generalized point interaction (GPI) in one dimension. We employ two natural parametrizations, which are known but have not attracted much attention, to express the resolvent…
The zero-range potential approach is extended for the description of situations where two-body scattering is resonant in arbitrary partial waves. The formalism generalizes the Fermi pseudopotential which can be used only for s-wave broad…
A physical system exposes to us in a real space, while its description often refers to its reciprocal momentum space. A connection between them can be established by exploring patterns of quasiparticles interference (QPI), which is…
A general prescription for the construction of $\pi \pi$ interaction potentials which preserve scattering length constraints from chiral symmetry when iterated in scattering equations is derived. The prescription involves only minor…
In view of recent experiments on ultra-cold polarized fermions, the zero-range potential approach is generalized to situations where two-body scattering is resonant in the p-wave channel. We introduce a modified scalar product which reveals…
We carry out an analysis of $\pi\pi$ scattering in the $IJ=00$, $11$ and $20$ channels in configuration space up to a maximal center-of-mass energy $\sqrt{s}=1.4$ GeV. We separate the interaction into two regions marked by an elementarity…
The general n-point information (n-pi) are introduced and equations for them are considered. The role of right and left invertible interaction operators occurring in these equations together with their interpretation is discussed. Some…
The Rigged Hilbert Space (RHS) theory of resonance scattering and decay is reviewed and contrasted with the standard Hilbert space (HS) theory of quantum mechanics. The main difference is in the choice of boundary conditions. Whereas the…
The spectrum of a quantum system has in general bound, scattering and resonant parts. The Hilbert space includes only the bound and scattering spectra, and discards the resonances. One must therefore enlarge the Hilbert space to a rigged…
Combining large $N_C$ techniques and partial wave dispersion theory to analyze the $\pi\pi$ scattering, without relying on any explicit resonance lagrangian, some interesting results are derived: (a) a general KSRF relation including the…
Perturbing resonant systems causes shifts in their associated scattering poles in the complex plane. In a previous study [arXiv: 2408.11360], we demonstrated that these shifts can be calculated numerically by analyzing the residue of a…
In constructing collinear operators, which describe the production of energetic jets or energetic hadrons, important constraints are provided by reparameterization invariance (RPI). RPI encodes Lorentz invariance in a power expansion about…
The main purpose of this paper is to construct convergent series for the approximate calculation of certain integrals over the Gaussian measure with a nuclear covariance operator, nonlocal propagator, in separable Hilbert space. Such series…
We present a coupled-channel Lagrangian approach (GiM) to describe the $\pi N \to \pi N$, $2\pi N$ scattering in the resonance energy region. The $2\pi N$ production has been significantly improved by using the isobar approximation with…
We derive the quantum effective action up to second order in gradients and up to two-loop order for an interacting scalar field theory. This expansion of the effective action is useful to study problems in cosmological settings where…
Recently, general point interactions in one dimension has been used to model a large number of different phenomena in quantum mechanics. Such potentials, however, requires some sort of regularization to lead to meaningful results. The usual…
Physics-compliant channel models of RIS-parametrized radio environments require the inversion of an "interaction matrix" to capture the mutual coupling between wireless entities (transmitters, receivers, RIS, environmental scattering…
The purpose of these lectures is to give an accessible and self contained introduction to quantum scattering theory in one dimension. Part A defines the theoretical playground, and develops basic concepts of scattering theory in the time…
Low-energy scattering is well described by the effective-range expansion. In quantum mechanics, a tower of contact interactions can generate terms in this expansion after renormalization. Scattering parameters are also encoded in the…