Related papers: No Infinite Spin for Planar Total Collision
We consider an ensemble of $n$ nonintersecting Brownian particles on the unit circle with diffusion parameter $n^{-1/2}$, which are conditioned to begin at the same point and to return to that point after time $T$, but otherwise not to…
The restricted (equilateral) four-body problem consists of three bodies of masses m1, m2 and m3 (called primaries) lying in a Lagrangian config- uration of the three-body problem, i,e,. they remain fixed at the apices of an equilateral…
In a general setting of a Hamiltonian system with two degrees of freedom and assuming some properties for the undergoing potential, we study the dynamics close and tending to a singularity of the system which in models of $N$-body problems…
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.…
We examine classical and quantum aspects of the planar non-compact spin system coupled with Chern-Simons gauge field in the presence of background charge. We first define our classical spin system as non- relativistic non-linear sigma model…
In this paper we consider the planar circular restricted three body problem (PCRTBP), which models the motion of a massless body under the attraction of other two bodies, the primaries, which describe circular orbits around their common…
The existence of an unbounded sequence of solutions to a conformally invariant elliptic equation having nonlocal critical-power nonlinearity is established. The primary obstacle to establishing existence of solutions is the failure of…
The problem of a disc and a ball rolling on a horizontal plane without slipping is considered. Differential constrained equations are shown to be integrated when the trajectory of the point of contact is taken in a form of the natural…
We discuss the problem of spin-orbit interaction in a 2D chaotic or diffusive quantum dot in the presence of exchange correlations. Spin-orbit scattering breaks spin rotation invariance, and in the crossover regime between different…
For the Newtonian 4-body problem in space we prove that any zero angular momentum bounded solution suffers infinitely many coplanar instants, that is, times at which all 4 bodies lie in the same plane. This result generalizes a known result…
We consider the unrestricted problem of two mutually attracting rigid bodies, an uniform sphere (or a point mass) and an axially symmetric body. We present a global, geometric approach for finding all relative equilibria (stationary…
An intriguing open problem in general relativity is whether a stationary equilibrium configuration of multiple, physically relevant black holes can exist. In such a hypothetical setup, the gravitational attraction would need to be balanced…
For the Newtonian (gravitational) $n$-body problem in the Euclidean $d$-dimensional space, the simplest possible solutions are provided by those rigid motions (homographic solutions) in which each body moves along a Keplerian orbit and the…
We determine the complete set of generalized spin squeezing inequalities. These are entanglement criteria that can be used for the experimental detection of entanglement in a system of spin-1/2 particles in which the spins cannot be…
We present a new particle model that generalize for constant curvature space an infinite spin particle in flat space. The model is described by commuting Weyl spinor additional coordinates. It proved that such a model is consistent only in…
We show the existence of some infinite families of periodic solutions of the planar Newtonian n-body problem --with positive masses-- which are symmetric with respect to suitable actions of finite groups (under a strong--force assumption,…
We consider the reflection of a Dirac plane wave on a perfectly reflecting plane described by chiral MIT boundary conditions and determine the rotation of the spin in the reflected component of the wave. We solve the analogous problem for a…
This paper is concerned with the existence, shape and dynamical stability of infinite-energy equilibria for a general class of spatially homogeneous kinetic equations in space dimensions $d \geq 3$. Our results cover in particular…
We study the second order elliptic equations of non-divergence form in a planar domain with complicated geometry. In this case the domain winds around a fixed circle infinitely many times and converges to it when the rotating angle goes to…
The relative equilibria of planar Newtonian $N$-body problem become coorbital around a central mass in the limit when all but one of the masses becomes zero. We prove a variety of results about the coorbital relative equilibria, with an…