Boson star with particle size effects

A simple model to study boson stars is to consider these stellar objects as quantum systems of $N$ identical self-gravitating particles within a non-relativistic framework. Some results obtained with point-like particles are recalled as well as the validity limits of this model. Approximate analytical calculations are performed using envelope theory for a truncated Coulomb-like potential simulating a particle size. If the boson mass is sufficiently small, the description of small mass boson stars is possible within non-relativistic formalism. The mass and radius of these stellar objects are strongly dependent on the value of the truncation parameter.Comment: Proceedings of the Workshop in honour of the 65th birthday of Professor Philippe Spindel (UMONS, 2015

An upper bound for asymmetrical spinless Salpeter equations

Using the auxiliary field method, a generic upper bound is obtained for the spinless Salpeter equation with two different masses. Analytical results are presented for the cases of the Coulomb and linear potentials when a mass is vanishing.Comment: Improved presentation and new reference

Quantum support to BoHua Sun's conjecture

A generalization of the Kepler's third law has been proposed by BoHua Sun for $N$-body periodic orbits in a Newtonian gravitation field. In this paper, it is shown that this formula can apply for a quantum system of $N$ self-gravitating identical particles, for a good choice of the period for the quantum motion.Comment: Two references and a justification are adde

Improvement of the envelope theory with the dominantly orbital state method

The envelope theory, also known as the auxiliary field method, is a simple technique to compute approximate solutions of Hamiltonians for $N$ identical particles in $D$ dimensions. The quality of the approximate eigenvalues can be improved by adding a free parameter in the characteristic global quantum number of the solutions. A method is proposed to determine the value of this parameter by comparing the eigenvalues computed with the envelope theory to the corresponding ones computed with a $N$-body generalization of the dominantly orbital state method. The accuracy of the procedure is tested with several systems.Comment: arXiv admin note: text overlap with arXiv:1501.0138

Penrose-Carter diagram for an uniformly accelerated observer

An uniformly accelerated observer can build his proper system of coordinates in a delimited sector of the flat Minkowski spacetime. The properties of the position and time coordinate lines for such an observer are studied and compared with the coordinate lines for an inertial observer in a Penrose-Carter diagram for this spacetime.Comment: 5 figure

Equation of motion of an interstellar Bussard ramjet with radiation and mass losses

An interstellar Bussard ramjet is a spaceship using the protons of the interstellar medium in a fusion engine to produce thrust. In recent papers, it was shown that the relativistic equation of motion of an ideal ramjet and of a ramjet with radiation loss are analytical. When a mass loss appears, the limit speed of the ramjet is more strongly reduced. But, the parametric equations, in terms of the ramjet's speed, for the position of the ramjet in the inertial frame of the interstellar medium, the time in this frame, and the proper time indicated by the clocks on board the spaceship, can still be obtained in an analytical form. The non-relativistic motion and the motion near the limit speed are studied.Comment: 4 figure

Bound cyclic systems with the envelope theory

Approximate but reliable solutions of a quantum system with $N$ identical particles can be easily computed with the envelope theory, also known as the auxiliary field method. This technique has been developed for Hamiltonians with arbitrary kinematics and one- or two-body potentials. It is adapted here for cyclic systems with $N$ identical particles, that is to say systems in which a particle $i$ has only an interaction with particles $i-1$ and $i+1$ (with $N+1\equiv 1$)

Auxiliary fields and the flux tube model

It is possible to eliminate exactly all the auxiliary fields (einbein fields) appearing in the rotating string Hamiltonian to obtain the classical equations of motion of the relativistic flux tube model. A clear interpretation can then be done for the characteristic variables of the rotating string model.Comment: No table, No figur

Numerical tests of the envelope theory for few-boson systems

The envelope theory, also known as the auxiliary field method, is a simple technique to compute approximate solutions of Hamiltonians for $N$ identical particles in $D$-dimension. The accuracy of this method is tested by computing the ground state of $N$ identical bosons for various systems. A method is proposed to improve the quality of the approximations by modifying the characteristic global quantum number of the method.Comment: A reference is updated. To appear in Few-Body System