Related papers: The 4-Body Problem in a (1+1)-Dimensional Self-Gra…
The restricted (equilateral) four-body problem consists of three bodies of masses m1, m2 and m3 (called primaries) lying in a Lagrangian configuration of the three-body problem i.e., they remain fixed at the apices of an equilateral…
We revisit the equilibrium one-dimensional $\phi^4$ model from the dynamical systems point of view. We find an infinite number of periodic orbits which are computationally stable. At the same time some of the orbits are found to exhibit…
We investigate the geometric phases and the Bargmann invariants associated with a multi-level quantum systems. In particular, we show that a full set of `gauge-invariant' objects for an $n$-level system consists of $n$ geometric phases and…
We consider a one-dimensional system of four inelastic hard spheres, colliding with a fixed restitution coefficient $r$, and we study the inelastic collapse phenomenon for such a particle system. We study a periodic, asymmetric collision…
This work is devoted to the thermodynamics of gravitational clustering, a collective phenomenon with a great relevance in the $N$-body cosmological problem. We study a classical self-gravitating gas of identical non-relativistic particles…
Fractal basin boundaries provide an important means of characterizing chaotic systems. We apply these ideas to general relativity, where other properties such as Lyapunov exponents are difficult to define in an observer independent manner.…
A new class of solvable $N$-body problems is identified. They describe $N$ unit-mass point particles whose time-evolution, generally taking place in the complex plane, is characterized by Newtonian equations of motion "of goldfish type"…
Analytical methods are used to prove the existence of a periodic, symmetric solution with singularities in the planar 4-body problem. A numerical calculation and simulation are used to generate the orbit. The analytical method easily…
The motion of a particle that suffers the influence of simple inner (outer) periodic perturbations when it evolves around a center of attraction modeled by an inverse square law plus a quadrupole-like term is studied. The equations of…
We obtain the Maxwell-J\"uttner distribution function at first order in the post-Newtonian approximation within the framework of general relativity. Taking into account the aforesaid distribution function, we compute the particle four-flow…
In this work, we revisit the planar restricted four-body problem to study the dynamics of an infinitesimal mass under the gravitational force produced by three heavy bodies with unequal masses, forming an equilateral triangle configuration.…
For the $\mathfrak{so}(4)$ free rigid body the stability problem for the isolated equilibria has been completely solved using Lie-theoretical and topological arguments. For each case of nonlinear stability previously found we construct a…
The discovery of Pluto's small moons in the last decade brought attention to the dynamics of the dwarf planet's satellites. With such systems in mind, we study a planar $N$-body system in which all the bodies are point masses, except for a…
Three dimensional self-gravitating systems do not evolve to thermodynamic equilibrium, but become trapped in nonequilibrium quasistationary states. In this Letter we present a theory which allows us to a priori predict the particle…
Some recent results concerning a particle confined in a one-dimensional box with moving walls are briefly reviewed. By exploiting the same techniques used for the 1D problem, we investigate the behavior of a quantum particle confined in a…
It is believed that the theory of quantum gravity describing our universe is unitary. Nonetheless, if we only have access to a subsystem, its dynamics is described by nonequilibrium physics. Motivated by this, we investigate the planar…
In this thesis, I go through the well-known solutions to the one and two-particle systems trapped in a quantum harmonic oscillator and then continue to the three, four and many-body quantum systems. This is done by developing new analytical…
We study turbulence in self-gravitating superfluids by performing direct numerical simulations of the 3D Gross-Pitaevskii-Poisson (GPP) equation, which is also a model for dark matter haloes around galaxies. In the absence of self-gravity,…
We investigate a relativistic self-interacting gas in the field of an external {\it pp} gravitational wave. Based on symmetry considerations we ask for those forces which are able to compensate the imprint of the gravitational wave on the…
Self-gravitating systems have acquired growing interest in statistical mechanics, due to the peculiarities of the 1/r potential. Indeed, the usual approach of statistical mechanics cannot be applied to a system of many point particles…