Related papers: Zero range interactions in d=3 and d=2 revisited
Contact has been well established as an important quantity to govern dilute quantum systems, in which the pairwise correlation at short distance traces a broad range of thermodynamic properties. So far, studies have been focusing on contact…
We develop an approach on how to define single-point interactions under the application of external fields. The essential feature relies on an asymptotic method based on the one-point approximation of multi-layered heterostructures that are…
A complete set of parity- and time-reversal conserving relativistic nucleon-nucleon contact operators is identified up to the order $O(p^4)$ of the expansion in soft momenta $p$. A basis is also provided for the corresponding…
Long-range effective methods are ubiquitous in physics and in quantum theory, in particular. Furthermore, the reliability of such methods is higher when the nature of short-ranged interactions need not be modeled explicitly. This may be…
We reconsider the norm resolvent limit of $-\Delta + V_\ell$ with $V_\ell$ tending to a point interaction in three dimensions. We are mainly interested in potentials $V_\ell$ modelling short range interactions of cold atomic gases. In order…
Contact interactions can be used to describe a system of particles at unitarity, contribute to the leading part of nuclear interactions and are numerically non-trivial because they require a proper regularization and renormalization scheme.…
We consider a few number of identical bosons trapped in a 2D isotropic harmonic potential and also the $N$-boson system when it is feasible. The atom-atom interaction is modelled by means of a finite-range Gaussian interaction. The spectral…
We qualify the main features of the spectrum of the Hamiltonian of point interaction for a three-dimensional quantum system consisting of three point-like particles, two identical fermions, plus a third particle of different species, with…
Regularization and renormalization is discussed in the context of low-energy effective field theory treatments of two or more heavy particles (such as nucleons). It is desirable to regulate the contact interactions from the outset by…
We consider the spectrum of two ultracold harmonically trapped atoms interacting via short-range interactions. The Green's function approach is used to unify the two and three dimensional cases. We derive criteria for the universality of…
Contact reduction is very closely related to symplectic reduction, but it allows symmetries that are not manifest in Hamiltonian mechanics and moreover, solution of the reduced problems yields solution of the original problem without…
We establish a duality between the free massless relativistic particle in d dimensions, the non-relativistic hydrogen atom (1/r potential) in (d-1) space dimensions, and the harmonic oscillator in (d-2) space dimensions with its mass given…
We study the two dimensional three-body problem in the general case of three distinguishable particles interacting through zero-range potentials. The Faddeev decomposition is used to write the momentum-space wave function. We show that the…
We qualify a relevant range of fractional powers of the so-called Hamiltonian of point interaction in three dimensions, namely the singular perturbation of the negative Laplacian with a contact interaction supported at the origin. In…
Resonant P-wave interactions can be described by a minimal zero-range model defined by a truncated effective range expansion, so that the only 2-body interaction parameters are the inverse scattering volume 1/a_P and the P-wave effective…
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 show that for ultra-cold neutral bosonic atoms held in a three-dimensional periodic potential or optical lattice, a Hubbard model with dominant, attractive three-body interactions can be generated. In fact, we derive that the effect of…
Nonlinear contact dynamics are widely regarded as intrinsically nonlinear systems whose behaviour depends strongly on geometry and impact conditions. Here we show that any one-dimensional conservative contact system satisfying monotone…
In this work, considering the background dynamics of flat Friedmann-Lemaitre-Robertson-Walker(FLRW) model of the universe, we investigate a scalar field model as dark energy candidate which interacting with the pressure-less dust as dark…
Several families of one-point interactions are derived from the system consisting of two and three $\delta$-potentials which are regularized by piecewise constant functions. In physical terms such an approximating system represents two or…