Related papers: Relative equilibria in quasi-homogeneous three bod…
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 discuss the stability of three- and four-particle system interacting by pure Coulomb interactions, as a function of the masses and charges of the particles. We present a certain number of general properties which allow to answer a…
A new coordinate system on the tangent space to planar configurations is introduced to simplify some calculations on central configurations and relative equilibria in the $N$-body problem with a homogeneous potential, which includes the…
In this paper it is proved that relative hyperbolicity is an invariant of quasi-isometry. As a byproduct of the arguments, simplified definitions of relative hyperbolicity are obtained. In particular we obtain a new definition very similar…
The physics of a many-particle system is determined by the correlations in its quantum state. Therefore, analyzing these correlations is the foremost task of many-body physics. Any 'a priori' constraint for the properties of the global vs.…
The equations of the Newtonian $n$-body problem have a matrix form, where an $n\times n$ matrix depending on the masses and on the mutual distances appears as a factor. The $n$ eigenvalues of this matrix are real and nonnegative. In a…
We consider periodic and quasi-periodic solutions of the three-body problem with homogeneous potential from the point of view of the equivariant calculus of variations. First, we show that symmetry groups of the Lagrangian action functional…
An approach is developed to find approximate solutions to the classical Newtonian problem of N bodies. Sets of N gravitating bodies having spherically symmetric mass distributions, small angular velocities (< 1 rad/s) and bounded position…
In this paper we discuss the use of wavelet bases to solve the relativistic three-body problem. Wavelet bases can be used to transform momentum-space scattering integral equations into an approximate system of linear equations with a sparse…
Saari's homographic conjecture claims that, in the N-body problem under the homogeneous potential, $U=\alpha^{-1}\sum m_i m_j/r_{ij}^\alpha$ for $\alpha\ne 0$, a motion having constant configurational measure $\mu=I^{\alpha/2}U$ is…
We generalize the Newtonian n-body problem to spaces of curvature k=constant, and study the motion in the 2-dimensional case. For k>0, the equations of motion encounter non-collision singularities, which occur when two bodies are antipodal.…
The relativistic two-body system in (1+1)-dimensional quantum electrodynamics is studied. It is proved that the eigenvalue problem for the two-body Hamiltonian without the self-interaction terms reduces to the problem of solving an…
In a preprint by Montgomery \cite{Mo99}, the author attempted to prove the existence of a shape space Figure-$8$ solution of the Newtonian three body problem with two equal masses (it looks like a figure $8$ in the shape space, which is…
In this paper, we consider the elliptic relative equilibria of the restricted $4$-body problems, where the three primaries form an Euler collinear configuration and the four bodies span $\mathbf{R}^2$. We obtain the symplectic reduction to…
In quasi-exactly solvable problems partial analytic solution (energy spectrum and associated wavefunctions) are obtained if some potential parameters are assigned specific values. We introduce a new class in which exact solutions are…
The cosmological many-body problem is effectively an infinite system of gravitationally interacting masses in an expanding universe. Despite the interactions' long-range nature, an analytical theory of statistical mechanics describes the…
Low-lying bound states for the problem of two Coulomb charges of finite masses on a plane subject to a constant magnetic field $B$ perpendicular to the plane are considered. Major emphasis is given to two systems: two charges with the equal…
We consider two identical impurities immersed in a Fermi sea for a broad range of masses and for both interacting and non-interacting impurities. The interaction between the particles is described through attractive zero-range potentials…
Based on a three-potential formalism we propose mathematically well-behaved Faddeev-type integral equations for the atomic three-body problem and descibe their solutions in Coulomb-Sturmian space representation. Although the system contains…
We show the existence of Borromean bound states in a one-dimensional quantum three-body system composed of two identical bosons and a distinguishable particle. It is assumed that there is no interaction between the two bosons, while the…