The equations of motion of compact binary systems and their associated Lagrangian formulation have been derived in previous works at the third post-Newtonian (3PN) approximation of general relativity in harmonic coordinates. In the present work we investigate the binary’s relative dynamics in the center-of-frame frame (center of mass located at the origin of the coordinates). We obtain the 3PN-...

We study the periodic dynamics of Henon-Heiles Hamiltonian system with additional singular gravitational term . The modelizes how stars move around a galactic center. addition this allows to modelize motion in pseudo or post-Newtonian dynamics. Thus model predict phenomena which cannot be detected by classical Newtonian mechanics. Using averaging theory first order we analytically existence two...

A method is presented to define unique continuum states for the two-center Dirac Hamiltonian. In the spherical limit these states become the familiar angular-momentum eigenstates of the radial Coulomb potential. The different states for a fixed total energy I E I > m may be distinguished by considering the asymptotic spin-angular distribution of states with unique scattering phases. The first n...

The center-of-mass system for many bodies in R admits a natural action of the rotation group SO(3). According to the orbit types for the SO(3) action, the center-of-mass system M is stratified into strata. A quantum Hamiltonian system and a classical Lagrangian system are defined on L(M) and on T (M), respectively. These systems are also stratified according to the stratification of M , and the...

in this paper we provide explicit formulas for the number of elements/subgroups/cyclic subgroups of a given order and for the total number of subgroups/cyclic subgroups in a finite hamiltonian group. the coverings with three proper subgroups and the principal series of such a group are also counted. finally, we give a complete description of the lattice of characteristic subgroups of a finite h...

A well-studied scenario in quantum parameter estimation theory arises when the parameter to be estimated is imprinted on the initial state by a Hamiltonian of the form θG. For such “phase shift Hamiltonians” it has been shown that one cannot improve the channel quantum Fisher information by adding ancillas and letting the system interact with them. Here we investigate the general case, where th...

We study local optima of the Hamiltonian of the Sherrington-Kirkpatrick model. We compute the exponent of the expected number of local optima and determine the “typical” value of the Hamiltonian. *Supported by NSERC Discovery Grant 341845. †Supported by the Natural Sciences and Engineering Research Council (NSERC) of Canada. ‡Supported by the SpanishMinistry of Economy and Competitiveness, Gran...