28,978 research outputs found
Principle of Relativity, 24 possible kinematical algebras and new geometries with Poincar\'e symmetry
From the principle of relativity with two universal invariant parameters
and , 24 possible kinematical (including geometrical and static) algebras
can be obtained. Each algebra is of 10 dimensional, generating the symmetry of
a 4 dimensional homogeneous space-time or a pure space. In addition to the
ordinary Poincar\'e algebra, there is another Poincar\'e algebra among the 24
algebras. New 4d geometries with the new Poincar\'e symmetry are presented. The
motion of free particles on one of the new space-times is discussed.Comment: 11 pages, talk on the 9th Asia-Pacific International Conference on
Gravitation and Astrophysics, Jun. 29-Jul. 2, Wuhan, Chin
Effects of Dimension-5 Operators in Grand Unified Theories
The effective dimension-5 operators can be induced by quantum gravity or
inspired by string and M theories. They have important impacts on grand unified
theories. We investigate the group theoretic nature of them for the well known
E(6) model. Considering the breaking chains and , we derive and give all of the Clebsch-Gordan coefficients
associated with breaking to the standard model. Some
applications of the results are discussed shortly.Comment: 8 pages, latex, minor changes, accepted for the publication in MPL
Slow-light Airy wave packets and their active control via electromagnetically induced transparency
We propose a scheme to generate (3+1)-dimensional slow-light Airy wave
packets in a resonant -type three-level atomic gas via
electromagnetically induced transparency. We show that in the absence of
dispersion the Airy wave packets formed by a probe field consist of two Airy
wave packets accelerated in transverse directions and a longitudinal Gaussian
pulse with a constant propagating velocity lowered to ( is the
light speed in vacuum). We also show that in the presence of dispersion it is
possible to generate another type of slow-light Airy wave packets consisting of
two Airy beams in transverse directions and an Airy wave packet in the
longitudinal direction. In this case, the longitudinal velocity of the Airy
wave packet can be further reduced during propagation. Additionally, we further
show that the transverse accelerations (or bending) of the both types of
slow-light Airy wave packets can be completely eliminated and the motional
trajectories of them can be actively manipulated and controlled by using a
Stern-Gerlach gradient magnetic field.Comment: 19 pages, 5 figure
Stern-Gerlach Effect of Weak-Light Ultraslow Vector Solitons
We propose a scheme to exhibit Stern-Gerlach (SG) deflection of
high-dimensional vector optical soliton (VOS) at weak-light level in a cold
atomic gas via electromagnetically induced transparency. We show that the
propagating velocity and generation power of such VOS can be reduced to
( is light speed in vacuum) and lowered to magnitude of
nanowatt, respectively. The stabilization of the VOS may be realized by using
an optical lattice formed by a far-detuned laser field, and its trajectory can
be deflected significantly by using a SG magnetic field. Deflection angle of
the VOS can be of magnitude of rad when propagating several
millimeters. Different from atomic SG deflection, deflection angle of the VOS
can be distinct for different polarization components and can be manipulated in
a controllable way. The results obtained can be described in terms of a SG
effect for the VOS with quasispin and effective magnetic moment.Comment: 5 pages, 3 figure
Propagation effect of gravitational wave on detector response
The response of a detector to gravitational wave is a function of frequency.
When the time a photon moving around in the Fabry-Perot cavities is the same
order of the period of a gravitational wave, the phase-difference due to the
gravitational wave should be an integral along the path. We present a formula
description for detector response to gravitational wave with varied
frequencies. The LIGO data for GW150914 and GW 151226 are reexamined in this
framework. For GW150924, the traveling time of a photon in the LIGO detector is
just a bit larger than a half period of the highest frequency of gravitational
wave and the similar result is obtained with LIGO and Virgo collaborations.
However, we are not always so luck. In the case of GW151226, the time of a
photon traveling in the detector is larger than the period of the highest
frequency of gravitational wave and the announced signal cannot match well the
template with the initial black hole masses 14.2M and 7.5M
Guiding ultraslow weak-light bullets with Airy beams in a coherent atomic system
We investigate the possibility of guiding stable ultraslow weak-light bullets
by using Airy beams in a cold, lifetime-broadened four-level atomic system via
electromagnetically induced transparency (EIT). We show that under EIT
condition the light bullet with ultraslow propagating velocity and extremely
low generation power formed by the balance between diffraction and nonlinearity
in the probe field can be not only stabilized but also steered by the assisted
field. In particular, when the assisted field is taken to be an Airy beam, the
light bullet can be trapped into the main lobe of the Airy beam, propagate
ultraslowly in longitudinal direction, accelerate in transverse directions, and
move along a parabolic trajectory. We further show that the light bullet can
bypass an obstacle when guided by two sequential Airy beams. A technique for
generating ultraslow helical weak-light bullets is also proposed.Comment: 23 pages, 6 figure
Global classical solution to the Cauchy problem of 2D baratropic compressible Navier-Stokes system with large initial data
For periodic initial data with initial density, we establish the global
existence and uniqueness of strong and classical solutions for the
two-dimensional compressible Navier-Stokes equations with no restrictions on
the size of initial data provided the shear viscosity is a positive constant
and the bulk one is \lam=\rho^{\b} with \b>1.Comment: 12 pages. arXiv admin note: text overlap with arXiv:1205.5342,
arXiv:1207.3746 by other author
Ultraslow Helical Optical Bullets and Their Acceleration in Magneto-Optically Controlled Coherent Atomic Media
We propose a scheme to produce ultraslow (3+1)-dimensional helical optical
solitons, alias helical optical bullets, in a resonant three-level
-type atomic system via quantum coherence. We show that, due to the
effect of electromagnetically induced transparency, the helical optical bullets
can propagate with an ultraslow velocity up to ( is the light
speed in vacuum) in longitudinal direction and a slow rotational motion (with
velocity ) in transverse directions. The generation power of such
optical bullets can be lowered to microwatt, and their stability can be
achieved by using a Bessel optical lattice potential formed by a far-detuned
laser field. We also show that the transverse rotational motion of the optical
bullets can be accelerated by applying a time-dependent Stern-Gerlach magnetic
field. Because of the untraslow velocity in the longitudinal direction, a
significant acceleration of the rotational motion of optical bullets may be
observed for a very short medium length.Comment: 21 pages, 5 figure
Reformulation of Boundary BF Theory Approach to Statistical Explanation of the Entropy of Isolated Horizons
It is shown in this paper that the symplectic form for the system consisting
of -dimensional bulk Palatini gravity and SO BF theory on an isolated
horizon as a boundary just contains the bulk term. An alternative quantization
procedure for the boundary BF theory is presented. The area entropy is
determined by the degree of freedom of the bulk spin network states which
satisfy a suitable boundary condition. The gauge-fixing condition in the
approach and the advantages of the approach are also discussed.Comment: 17 pages, no figure
Graph Fourier Transform Based on Norm Variation Minimization
The definition of the graph Fourier transform is a fundamental issue in graph
signal processing. Conventional graph Fourier transform is defined through the
eigenvectors of the graph Laplacian matrix, which minimize the norm
signal variation. However, the computation of Laplacian eigenvectors is
expensive when the graph is large. In this paper, we propose an alternative
definition of graph Fourier transform based on the norm variation
minimization. We obtain a necessary condition satisfied by the Fourier
basis, and provide a fast greedy algorithm to approximate the Fourier
basis. Numerical experiments show the effectiveness of the greedy algorithm.
Moreover, the Fourier transform under the greedy basis demonstrates a similar
rate of decay to that of Laplacian basis for simulated or real signals
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