Related papers: On the global minimum of the classical potential e…
The pair-specific ground state energy of Newtonian N-body systems grows monotonically in N. This furnishes a whole family of simple new tests for minimality of putative ground state energies obtained through computer experiments. Inspection…
We present our study of kaonic three-body $\overset{\_}{K}NN$, $\overset{\_}{K}\overset{\_}{K}N$ and $KK\overset{\_}{K}$ and four-body $\overset{\_}{K}% NNN $, $\ $and $\overset{\_}{K}\overset{\_}{K}NN$ clusters within the framework of a…
For the well-known model of a system of N particles with interaction (N-body problem), we consider the spatial problem of finding the minimum of the function of the kinetic energy of a system on its phase space under conditions on its size…
The N-dependence of the non-relativistic bosonic ground state energy is studied for quantum N-body systems with either Coulomb or Newton interactions. The Coulomb systems are "bosonic atoms," with their nucleus fixed, and the Newton systems…
We present three-body nonrelativistic calculations within the framework of a potential model for the kaonic cluster ${K^-}pp$ using two completely different methods: the method of hyperspherical harmonics in the momentum representation and…
This note advertises a simple necessary condition for optimality that any list $N\mapsto v^x(N)$ of computer-generated putative lowest average pair energies $v^x(N)$ of clusters that consist of $N$ monomers has to satisfy, whenever the…
The quantum $N$-body problem is studied in the context of nonrelativistic quantum mechanics with a one-dimensional deformed Heisenberg algebra of the form $[\hat x,\hat p]=i(1+\beta \hat p^2)$, leading to the existence of a minimal…
Bosonic two-dimensional self-bound clusters consisting of $N$ atoms interacting through additive van der Waals potentials become unbound at a critical mass m*(N); m*(N) has been predicted to be independent of the size of the system.…
The ground state energies of universal N-body clusters tied to Efimov trimers, for N even, are shown to be encapsulated in the statistical distribution of two particles interacting with a background auxiliary field at large Euclidean time…
We report on a study of a finite system of classical confined particles in two-dimensions in the presence of a uniform magnetic field and interacting via a two-body repulsive potential. We develop a simple analytical method of analysis to…
Magnetic systems with frustration often have large classical degeneracy. We show that their low-energy physics can be understood as dynamics within the space of classical ground states. We demonstrate this mapping in a family of quantum…
We analyze many-body entanglement in interacting fermionic systems by using the $M$-body reduced density matrix. We demonstrate that if a particle number conserving fermionic Hamiltonian contains only up to $M$-body interaction terms, then…
The existence of compactly supported global minimisers for continuum models of particles interacting through a potential is shown under almost optimal hypotheses. The main assumption on the potential is that it is catastrophic, or not…
We address the question of minimal requirements for the existence of quantum bound states. In particular, we demonstrate that a few-body system with zero-range momentum-independent two-body interactions is unstable against decay into…
We study the effect of many-body quantum interference on the dynamics of coupled periodically kicked systems whose classical dynamics is chaotic and shows an unbounded energy increase. We specifically focus on a $N$ coupled kicked rotors…
Good a-priori bounds on the smallest pairwise distance $r_{\rm{{min}}}(\mbox{LJ}_N^{\rm{gmin}})$ for a three-dimensional (3D) Lennard-Jones $N$-body cluster of globally minimal energy can significantly reduce the computational search space…
We consider a system of $N\gg 1$ interacting fermionic particles in three dimensions, confined in a periodic box of volume $1$, in the mean-field scaling. We assume that the interaction potential is bounded and small enough. We prove upper…
In any dimension $N \geq 1$, for given mass $m > 0$ and for the $C^1$ energy functional \begin{equation*} I(u):=\frac{1}{2}\int_{\mathbb{R}^N}|\nabla u|^2dx-\int_{\mathbb{R}^N}F(u)dx, \end{equation*} we revisit the classical problem of…
We derive coupled-cluster equations for three-body Hamiltonians. The equations for the one- and two-body cluster amplitudes are presented in a factorized form that leads to an efficient numerical implementation. We employ low-momentum two-…
We study an intrinsic model for collective behaviour on the hyperbolic space $\bbh^\dm$. We investigate the equilibria of the aggregation equation (or equivalently, the critical points of the associated interaction energy) for interaction…