Related papers: Zero range interactions in d=3 and d=2 revisited
We introduce \emph{contact (zero range) interactions } , a special class of self-adjoint extensions of the N-body Schr\"odinger free hamiltonian $ H_0$ restricted to functions with support away from the \emph{contact manifold} $ \Gamma…
We describe \emph{zero range} (contact) interactions, weak and strong. Strong contact leads to the Efimov effect in Low Energy Nuclear Physics, weak contact leads to Bose-Einstein condensation and to the presence of Cooper pairs in…
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…
We introduce \emph{contact interactions hamiltonians} (self-adjointoperators defined by boundary conditions) between $N$ massive particles in $R^3$, $N \geq 3$. We prove that they are limits (in strong resolvent sense) when $ \epsilon \to…
We discuss a number of constraints on the effects of zero-range potentials in quantum mechanics. We show that for such a potential $p \cot(\delta)$, where $p$ is the momentum of the nucleon in the center of mass frame and $\delta$ is the…
We consider the three-boson problem with $\delta$-function interactions in one spatial dimension. Three different approaches are used to calculate the phase shifts, which we interpret in the context of the effective range expansion, for the…
Strongly interacting systems appear in several areas of physics and are characterized by attractive interactions that can almost, or just barely, loosely bind two particles. Although this definition is made at the two-body level, this gives…
We construct a four-parameter point-interaction for a non-relativistic particle moving on a line as the limit of a short range interaction with range tending toward zero. For particular choices of the parameters, we can obtain a…
We consider mathematical models of the weak decay of the vector bosons $W^{\pm}$ into leptons. The free quantum field hamiltonian is perturbed by an interaction term from the standard model of particle physics. After the introduction of…
We show that it is possible to define shape-independent three-dimensional short-range quantum interactions in two parameter form for non-spherical angular momentum channels through double rescaling of potential strength. Unlike the special…
We consider a negative Laplacian in multi-dimensional Euclidean space (or a multi-dimensional layer) with a weak disorder random perturbation. The perturbation consists of a sum of lattice translates of a delta interaction supported on a…
Contact interaction is a fundamental concept that appears in various areas of physics. It simplifies physical models by replacing the detailed short-range interaction with a zero-range contact potential which reproduces the same low-energy…
The dissipative Hofstadter model describes the quantum mechanics of a charged particle in two dimensions subject to a periodic potential, uniform magnetic field, and dissipative force. Its phase diagram exhibits an SL(2,Z) duality symmetry…
We study a non-relativistic particle subject to a three-dimensional spherical potential consisting of a finite well and a radial $\delta$-$\delta'$ contact interaction at the well edge. This contact potential is defined by appropriate…
The contact formalism, a useful tool for analyzing short-range correlations, is generalized here for systems with coupled channels, such as in nuclear physics. The relevant asymptotic form is presented and contact matrices are defined.…
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…
We consider a Hamiltonian describing three quantum particles in dimension one interacting through two-body short-range potentials. We prove that, as a suitable scale parameter in the potential terms goes to zero, such Hamiltonian converges…
The spectral and scattering theory for 1-dimensional Dirac operators with mass $m$ and with zero-range interactions are fully investigated. Explicit expressions for the wave operators and for the scattering operator are provided. These new…
We study the effects of the effective range of interaction on the eigenvalues and eigenstates of two particles confined in a three-dimensional (3D) isotropic as well as one- or quasi-one dimensional harmonic (1D) traps. For this we employ…
Starting from a complete set of relativistic nucleon-nucleon contact operators up to order $O(p^4)$ of the expansion in the soft (relative or nucleon) momentum $p$, we show that non-relativistic expansions of relativistic operators involve…