arXiv subjects

F. L. Dubeibe

Publications and source records attributed to F. L. Dubeibe.

22 records · Page 2Linked to original sources

arXiv2010

Solving the time-dependent Schrödinger equation with absorbing boundary conditions and source terms in Mathematica 6.0

In recent decades a lot of research has been done on the numerical solution of the time-dependent Schrödinger equation. On the one hand, some of the proposed numerical methods do not need any kind of matrix inversion, but source terms cannot be easily implemented into this schemes; on the other, some methods involving matrix inversion can implement source terms in a natural way, but are not easy to implement into some computational software programs widely used by non-experts in programming (e.g. Mathematica). We present a simple method to solve the time-dependent Schrödinger equation by using a standard Crank-Nicholson method together with a Cayley's form for the finite-difference representation of evolution operator. Here, such standard numerical scheme has been simplified by inverting analytically the matrix of the evolution operator in position representation. The analytical inversion of the N x N matrix let us easily and fully implement the numerical method, with or without source terms, into Mathematica or even into any numerical computing language or computational software used for scientific computing.

quant-ph↗

arXiv2010

Innermost stable circular orbits around magnetized rotating massive stars

In 1998, Shibata and Sasaki [Phys. Rev. D 58, 104011 (1998)] presented an approximate analytical formula for the radius of the innermost stable circular orbit (ISCO) of a neutral test particle around a massive, rotating and deformed source. In the present paper, we generalize their expression by including the magnetic dipole moment. We show that our approximate analytical formulas are accurate enough by comparing them with the six-parametric exact solution calculated by Pachón et. al. [Phys. Rev. D 73, 104038 (2006)] along with the numerical data presented by Berti and Stergioulas [MNRAS 350, 1416 (2004)] for realistic neutron stars. As a main result, we find that in general, the radius at ISCO exhibits a decreasing behavior with increasing magnetic field. However, for magnetic fields below 100GT the variation of the radius at ISCO is negligible and hence the non-magnetized approximate expression can be used. In addition, we derive approximate analytical formulas for angular velocity, energy and angular momentum of the test particle at ISCO.

gr-qc↗

arXiv2008

Pumping angular momentum by driven chaotic scattering

Chaotic scattering with an internal degree of freedom and the possibility to generate directed transport of angular momentum is studied in a specific model, a magnetic dipole moving in a periodically modulated magnetic field confined to a compact region in space. We show that this system is an irregular scatterer in large parts of its parameter space. If in addition all spatio-temporal symmetries are broken, directed transport of mass as well as angular momentum occurs. The sensitive parameter dependence of the corresponding currents includes frequent sign reversals. Zeros of either quantity entail the exclusive occurrence of the other and thus give rise in particular to angular-momentum separation without mass transport as a classical analogue of spin-polarized currents.

nlin.CD↗

arXiv2007

Chaotic dynamics around astrophysical objects with nonisotropic stresses

The existence of chaotic behavior for the geodesics of the test particles orbiting compact objects is a subject of much current research. Some years ago, Guéron and Letelier [Phys. Rev. E \textbf{66}, 046611 (2002)] reported the existence of chaotic behavior for the geodesics of the test particles orbiting compact objects like black holes induced by specific values of the quadrupolar deformation of the source using as models the Erez--Rosen solution and the Kerr black hole deformed by an internal multipole term. In this work, we are interesting in the study of the dynamic behavior of geodesics around astrophysical objects with intrinsic quadrupolar deformation or nonisotropic stresses, which induces nonvanishing quadrupolar deformation for the nonrotating limit. For our purpose, we use the Tomimatsu-Sato spacetime [Phys. Rev. Lett. \textbf{29} 1344 (1972)] and its arbitrary deformed generalization obtained as the particular vacuum case of the five parametric solution of Manko et al [Phys. Rev. D 62, 044048 (2000)], characterizing the geodesic dynamics throughout the Poincaré sections method. In contrast to the results by Guéron and Letelier we find chaotic motion for oblate deformations instead of prolate deformations. It opens the possibility that the particles forming the accretion disk around a large variety of different astrophysical bodies (nonprolate, e.g., neutron stars) could exhibit chaotic dynamics. We also conjecture that the existence of an arbitrary deformation parameter is necessary for the existence of chaotic dynamics.

gr-qc↗