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We study the relationship between the masses and the geometric properties of central configurations. We prove that in the planar four-body problem, a convex central configuration is symmetric with respect to one diagonal if and only if the masses of the two particles on the other diagonal are equal. If these two masses are unequal, then the less massive one is closer to the former diagonal. Finally, we extend these results to the case of non-planar central configurations of five particles.
We study the many body quantum evolution of bosonic systems in the mean field limit. The dynamics is known to be well approximated by the Hartree equation. So far, the available results have the form of a law of large numbers. In this paper we go one
Zitterbewegung is the exotic phenomenon associated either with the relativistic electron-positron rapid oscillation or to the electron-hole transitions in the narrow gap semiconductors. In the present work, we enlarge concept of Zitterbewegung and sh
Families of three-body Hamiltonian systems in one dimension have been recently proved to be maximally superintegrable by interpreting them as one-body systems in the three-dimensional Euclidean space, examples are the Calogero, Wolfes and Tramblay Tu
Due to its great importance for applications, we generalize and extend the approach of our previous papers to study aspects of the quantum and classical dynamics of a $4$-body system with equal masses in {it $d$}-dimensional space with interaction de
As a generalization and extension of our previous paper {it J. Phys. A: Math. Theor. 53 055302} cite{AME2020}, in this work we study a quantum 4-body system in $mathbb{R}^d$ ($dgeq 3$) with quadratic and sextic pairwise potentials in the {it relative