107,627 research outputs found
Recursive Integral Method with Cayley Transformation
Recently, a non-classical eigenvalue solver, called RIM, was proposed to
compute (all) eigenvalues in a region on the complex plane. Without solving any
eigenvalue problem, it tests if a region contains eigenvalues using an
approximate spectral projection. Regions that contain eigenvalues are
subdivided and tested recursively until eigenvalues are isolated with a
specified precision. This makes RIM an eigensolver distinct from all existing
methods. Furthermore, it requires no a priori spectral information. In this
paper, we propose an improved version of {\bf RIM} for non-Hermitian eigenvalue
problems. Using Cayley transformation and Arnoldi's method, the computation
cost is reduced significantly. Effectiveness and efficiency of the new method
are demonstrated by numerical examples and compared with 'eigs' in Matlab
Localization of Relative-Position of Two Atoms Induced by Spontaneous Emission
We revisit the back-action of emitted photons on the motion of the relative
position of two cold atoms. We show that photon recoil resulting from the
spontaneous emission can induce the localization of the relative position of
the two atoms through the entanglement between the spatial motion of individual
atoms and their emitted photons. The result provides a more realistic model for
the analysis of the environment-induced localization of a macroscopic object.Comment: 8 pages and 4 figure
Phantom Energy Accretion onto Black Holes in Cyclic Universe
Black holes pose a serious problem in the cyclic or oscillating cosmology. It
is speculated that, in the cyclic universe with phantom turnarounds, black
holes will be torn apart by the phantom energy before turnaround before they
can create any problems. In this paper, using the mechanism of the phantom
accretion onto black holes, we find that black holes do not disappear before
the phantom turnaround. But the remanent black holes will not cause any
problems due to the Hawking evaporation.Comment: 8 pages, no figure; typographical errors are correcte
Binomial coefficients, Catalan numbers and Lucas quotients
Let be an odd prime and let be integers with and . In this paper we determine
mod for ; for example,
where is the Jacobi symbol, and is the Lucas
sequence given by , and for
. As an application, we determine modulo for any integer , where denotes the
Catalan number . We also pose some related conjectures.Comment: 24 pages. Correct few typo
Phantom Accretion by Five Dimensional Charged Black Hole
This paper deals with the dynamical behavior of phantom field near five
dimensional charged black hole. We formulate equations of motion for
steady-state spherically symmetric flow of phantom fluids. It is found that
phantom energy accretes onto black holes for . Further, the location of
critical point of accretion are evaluated that leads to mass to charge ratio
for 5D charged black hole. This ratio implies that accretion cannot transform a
black hole into a naked singularity. We would like to mention here that this
work is an irreducible extension of 4D charged black hole.Comment: 8 pages, accepted for publication in Mod. Phys. Lett.
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