相关论文: From Quasars to Extraordinary N-body Problems

Consider n=2l>=4 point particles with equal masses in space, subject to the following symmetry constraint: at each instant they form an orbit of the dihedral group D_l, where D_l is the group of order 2l generated by two rotations of angle…

The dynamics of extended bodies is a fundamental problem in any gravitational theory. In the case of General Relativity, this problem is under study since the theory was published. Several methods have been developed and different…

The problem of three particles interacting through harmonic forces is discussed within the Newtonian formalism. By means of a didactic approach, an exact analytical solution is found, and ways to extend it to the N-body case are pointed…

We study the quantum mechanical many-body problem of $N \geq 1$ non-relativistic electrons with spin interacting with their self-generated classical electromagnetic field and $K \geq 0$ static nuclei. We model the dynamics of the electrons…

Causality is one of the most fundamental -- and yet elusive -- concepts in physics. From its intuitive role in everyday experience to its formal and often implicit role in scientific theories, causality has challenged philosophers and…

Two recent findings necessitate a closer look at the existing standard models of Particle Physics and Cosmology. These are the discovery of Neutrino oscillation, and hence a non zero mass on the one hand and, on the other, observations of…

Towards the end of nineteenth century, Celestial Mechanics provided the most powerful tools to test Newtonian gravity in the solar system, and led also to the discovery of chaos in modern science. Nowadays, in light of general relativity,…

Theoretical research into many-body quantum systems has mostly focused on regular structures which have a small, simple unit cell and where a vanishingly small number of pairs of the constituents directly interact. Motivated by advances in…

Closed quantum many-body systems out of equilibrium pose several long-standing problems in physics. Recent years have seen a tremendous progress in approaching these questions, not least due to experiments with cold atoms and trapped ions…

We consider the two-body problem in post-Newtonian approximations of general relativity. We report the recent results concerning the equations of motion, and the associated Lagrangian formulation, of compact binary systems, at the third…

Since the discovery of the figure-8 orbit for the three-body problem [Moore 1993] a large number of periodic orbits of the n-body problem with equal masses and beautiful symmetries have been discovered. However, most of those that have…

Vlasov equations can be formally derived from N-body dynamics in the mean-field limit. In some suitable singular limits, they may themselves converge to fluid dynamics equations. Motivated by this heuristic, we introduce natural scalings…

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…

The $N$-body problem is of historical significance because it was the first implementation of the Newtonian dynamical laws for the description of our Solar System. Motivated by this, the project's goal is to revisit this problem for small…

The only widely accepted explanation for the various arrows of time that everywhere and at all epochs point in the same direction is the `past hypothesis': the Universe had a very special low-entropy initial state. We present the first…

We present several examples of quasi-exactly solvable $N$-body problems in one, two and higher dimensions. We study various aspects of these problems in some detail. In particular, we show that in some of these examples the corresponding…

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,…

The famous three-body problem is investigated by means of a numerical approach with negligible numerical noises in a long enough time interval, namely the Clean Numerical Simulation (CNS). From physical viewpoints, position of any bodies…

Several completely integrable, indeed solvable, Hamiltonian many-body problems are exhibited, characterized by Newtonian equations of motion ("acceleration equal force"), with linear and cubic forces, in N-dimensional space (N being an…

I present the exact energy eigenstates and eigenvalues of a quantum many-body system of bosons on non-commutative space and in a harmonic oszillator confining potential at the selfdual point. I also argue that this exactly solvable system…