Related papers: On contact interactions as limits of short-range p…
We consider weakly interacting bosonic gases with local and non-local multi-body interactions. By using the Bogoliubov approximation, we first investigate contact interactions, studying the case in which the interparticle potential can be…
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…
We show that the support of any local minimizer of the interaction energy consists of isolated points whenever the interaction potential is of class $C^2$ and mildly repulsive at the origin; moreover, if the minimizer is global, then its…
In this paper, we discuss a possibility to improve constraints on spin-dependent short-range interactions in the range of 1 - 200 micrometer significantly. For such interactions, our constraints are without competition at the moment. They…
A general method to find an effective potential of interaction between far separated 2D and 3D solitons is elaborated, including the case of 2D vortex solitons. The method is based on explicit calculation of the overlapping term in the full…
In this work, we study the probability distribution for the force and potential energy of a test particle interacting with $N$ point random sources in the limit $N\rightarrow\infty$. The interaction is given by a central potential…
We consider, for $h, E > 0$, resolvent estimates for the semiclassical Schr\"odinger operator $-h^2 \Delta + V - E$. Near infinity, the potential takes the form $V = V_L+ V_S$, where $V_L$ is a long range potential which is Lipschitz with…
The repulsive short distance core is one of the main paradigms of nuclear physics which even seems confirmed by QCD lattice calculations. On the other hand nuclear potentials at short distances are motivated by high energy behavior where…
The treatment of the electron-nucleus interaction based on the Mott differential cross section was extended to account for effects due to screened Coulomb potentials, finite sizes and finite rest masses of nuclei for electrons above 200 keV…
The term "long-range interactions" refers to electrostatic and magnetostatic potential energies between atoms and molecules with mutual distances ranging from a few tens to a few hundreds Bohr radii. The involved energies are much smaller…
We obtain several sequences of necessary and sufficient conditions for the existence of bound states applicable to attractive (purely negative) central potentials. These conditions yields several sequences of upper and lower limits on the…
The proof of the existence of the thermodynamic limit for electrons and nuclei interacting via the Coulomb potential, in the framework of non-relativistic quantum mechanics, was accomplished decades ago. This result did not take account of…
We discuss the scaling of the interaction energy with particle numbers for a harmonically trapped two-species mixture at thermal equilibrium experiencing interactions of arbitrary strength and range. In the limit of long-range interactions…
Recently the leading order of the correlation energy of a Fermi gas in a coupled mean-field and semiclassical scaling regime has been derived, under the assumption of an interaction potential with a small norm and with compact support in…
Particles interacting through long-range attraction and short-range repulsion given by power-laws have been widely used to model physical and biological systems, and to predict or explain many of the patterns they display. Apart from rare…
We consider interacting one-dimensional bosons in the universal low-energy regime. The interactions consist of a combination of attractive and repulsive parts that can stabilize quantum gases, droplets and liquids. In particular, we study…
We show that the planar circular restricted three body problem is of restricted contact type for all energies below the first critical value (action of the first Lagrange point) and for energies slightly above it. This opens up the…
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…
Generalized uncertainty relations are known to provide a minimal length $\hbar\sqrt{\beta}$. The effect of such minimal length in the Casimir-Polder interactions between neutral atoms (molecules) is studied. The first order correction term…
For the interactions between two atoms or between an ion and an electron the connections between the Casimir-Polder-type potentials and the relativistic potentials arising from the Breit-Pauli Hamiltonian are surveyed.