Related papers: The size of two-body weakly bound objects : short …
The invariant mass of free particles is used to derive a bound-state equation for the hydrogen atom at rest. This equation has the well-known solutions for the single-particle states. Existence of two-particle bound states, for which the…
The Kratzer's potential $V(r)=g_{1}/r^{2}-g_{2}/r$ is studied in quantum mechanics with a generalized uncertainty principle, which includes a minimal length $\left( \Delta X\right) _{\min}=\hbar\sqrt{5\beta}$. In momentum representation,…
In the framework of non-relativistic quantum mechanics and with the help of the Greens functions formalism we study the behavior of weakly bound states as they approach the continuum threshold. Through estimating the Green's function for…
We study a multivariate Hawkes process with long-range interactions, where the interaction strength decays as a power-law in the distance of the particles with exponent $1+\alpha.$ Our main focus is on the long-time asymptotic behavior of…
Isotropic soft-core potentials with two characteristic length scales have been used since 40 years to describe systems with polymorphism. In the recent years intense research is showing that these potentials also display polyamorphism and…
Non-equilibrium diffusive systems are known to exhibit long-range correlations, which decay like the inverse 1/L of the system size L in one dimension. Here, taking the example of the ABC model, we show that this size dependence becomes…
The linear response of two-dimensional amorphous elastic bodies to an external delta force is determined in analogy with recent experiments on granular aggregates. For the generated forces, stress and displacement fields, we find strong…
Quantum physics rules the dynamics of small objects as they interact over microscopic length scales. Nevertheless, quantum correlations involving macroscopic distances can be observed between entangled photons as well as in atomic gases and…
We obtain large deviation bounds for the measure of deviation sets associated to asymptotically additive and sub-additive potentials under some weak specification properties. In particular a large deviation principle is obtained in the case…
The two-body problem in general relativity is reduced to the problem of an effective particle (with an energy-dependent relativistic reduced mass) in an external field. The effective potential is evaluated from the Born diagram of the…
Observed self-gravitating systems reveal often fragmented non-equilibrium structures that feature characteristic long-range correlations. However, models accounting for non-linear structure growth are not always consistent with observations…
We provide a statistical and correlational analysis of the spatial and energetic properties of equilibrium configurations of a few-body system of two to eight equally charged classical particles that are confined on a one-dimensional…
We investigate the momentum-resolved spin and charge susceptibilities, as well as the chemical potential and double occupancy in the two-dimensional Hubbard model as functions of doping, temperature and interaction strength. Through these…
We briefly review some equilibrium and nonequilibrium properties of systems with long-range interactions. Such systems, which are characterized by a potential that weakly decays at large distances, have striking properties at equilibrium,…
We prove a limiting absorption principle at zero energy for two-body Schr\"odinger operators with long-range potentials having a positive virial at infinity. More precisely, we establish a complete asymptotic expansion of the resolvent in…
We study analytically the radial Schr\"odinger equation with long-range attractive potentials whose asymptotic behaviors are dominated by inverse power-law tails of the form $V(r)=-\beta_n r^{-n}$ with $n>2$. In particular, assuming that…
We consider three-body systems in two dimensions with zero-range interactions for general masses and interaction strengths. The momentum-space Schr\"odinger equation is solved numerically and in the Born-Oppenheimer (BO) approximation. The…
We study the scaling behaviour of dispersion potentials and forces under very general conditions. We prove that a rescaling of an arbitrary geometric arrangement by a factor a changes the atom-atom and atom-body potentials in the…
Quantal systems are predicted to show a change-over from exponential decay to power law decay at very long times. Although most theoretical studies predict integer power-law exponents, recent measurements by Rothe et al. of decay…
We apply the renormalisation-group to two-body scattering by a combination of known long-range and unknown short-range forces. A crucial feature is that the low-energy effective theory is regulated by applying a cut-off in the basis of…