451 research outputs found
A Tale of Two Fractals: The Hofstadter Butterfly and The Integral Apollonian Gaskets
This paper unveils a mapping between a quantum fractal that describes a
physical phenomena, and an abstract geometrical fractal. The quantum fractal is
the Hofstadter butterfly discovered in 1976 in an iconic condensed matter
problem of electrons moving in a two-dimensional lattice in a transverse
magnetic field. The geometric fractal is the integer Apollonian gasket
characterized in terms of a 300 BC problem of mutually tangent circles. Both of
these fractals are made up of integers. In the Hofstadter butterfly, these
integers encode the topological quantum numbers of quantum Hall conductivity.
In the Apollonian gaskets an infinite number of mutually tangent circles are
nested inside each other, where each circle has integer curvature. The mapping
between these two fractals reveals a hidden threefold symmetry embedded in the
kaleidoscopic images that describe the asymptotic scaling properties of the
butterfly. This paper also serves as a mini review of these fractals,
emphasizing their hierarchical aspects in terms of Farey fractions
KiloHertz Quasi-Periodic oscillations in Island State of 4U 1608-52 as observed with RXTE/PCA
KiloHertz Quasi-Periodic oscillations in Island State of 4U 1608-52 as observed with RXTE/PCA
Effects of Anomalous Magnetic Moment in the Quantum Motion of Neutral Particle in Magnetic and Electric Fields Produced by a Linear Source in a Conical Spacetime
In this paper we analyse the effect of the anomalous magnetic moment on the
non-relativistic quantum motion of a neutral particle in magnetic and electric
fields produced by linear sources of constant current and charge density,
respectively.Comment: 17 pages, no figur
Effect of Chaotic Noise on Multistable Systems
In a recent letter [Phys.Rev.Lett. {\bf 30}, 3269 (1995), chao-dyn/9510011],
we reported that a macroscopic chaotic determinism emerges in a multistable
system: the unidirectional motion of a dissipative particle subject to an
apparently symmetric chaotic noise occurs even if the particle is in a
spatially symmetric potential. In this paper, we study the global dynamics of a
dissipative particle by investigating the barrier crossing probability of the
particle between two basins of the multistable potential. We derive
analytically an expression of the barrier crossing probability of the particle
subject to a chaotic noise generated by a general piecewise linear map. We also
show that the obtained analytical barrier crossing probability is applicable to
a chaotic noise generated not only by a piecewise linear map with a uniform
invariant density but also by a non-piecewise linear map with non-uniform
invariant density. We claim, from the viewpoint of the noise induced motion in
a multistable system, that chaotic noise is a first realization of the effect
of {\em dynamical asymmetry} of general noise which induces the symmetry
breaking dynamics.Comment: 14 pages, 9 figures, to appear in Phys.Rev.
Conformal linear gravity in de Sitter space II
From the group theoretical point of view, it is proved that the theory of
linear conformal gravity should be written in terms of a tensor field of rank-3
and mixed symmetry [Binegar, et al, Phys. Rev. D 27, (1983) 2249]. We obtained
such a field equation in de Sitter space [Takook, et al, J. Math. Phys. 51,
(2010) 032503]. In this paper, a proper solution to this equation is obtained
as a product of a generalized polarization tensor and a massless scalar field
and then the conformally invariant two-point function is calculated. This
two-point function is de Sitter invariant and free of any pathological
large-distance behavior.Comment: 16 pages, no figure, published versio
Naked Singularity Formation In f(R) Gravity
We study the gravitational collapse of a star with barotropic equation of
state in the context of theories of gravity.
Utilizing the metric formalism, we rewrite the field equations as those of
Brans-Dicke theory with vanishing coupling parameter. By choosing the
functionality of Ricci scalar as , we
show that for an appropriate initial value of the energy density, if
and satisfy certain conditions, the resulting singularity would be naked,
violating the cosmic censorship conjecture. These conditions are the ratio of
the mass function to the area radius of the collapsing ball, negativity of the
effective pressure, and the time behavior of the Kretschmann scalar. Also, as
long as parameter obeys certain conditions, the satisfaction of the
weak energy condition is guaranteed by the collapsing configuration.Comment: 15 pages, 4 figures, to appear in GR
Production and Decay of D_1(2420)^0 and D_2^*(2460)^0
We have investigated and final states and
observed the two established charmed mesons, the with mass
MeV/c and width MeV/c and
the with mass MeV/c and width
MeV/c. Properties of these final states, including
their decay angular distributions and spin-parity assignments, have been
studied. We identify these two mesons as the doublet predicted
by HQET. We also obtain constraints on {\footnotesize } as a function of the cosine of the relative phase of the two
amplitudes in the decay.Comment: 15 pages in REVTEX format. hardcopies with figures can be obtained by
sending mail to: [email protected]
Measurement of the branching fraction for
We have studied the leptonic decay of the resonance into tau
pairs using the CLEO II detector. A clean sample of tau pair events is
identified via events containing two charged particles where exactly one of the
particles is an identified electron. We find . The result is consistent with
expectations from lepton universality.Comment: 9 pages, RevTeX, two Postscript figures available upon request, CLNS
94/1297, CLEO 94-20 (submitted to Physics Letters B
The Kuiper Belt and Other Debris Disks
We discuss the current knowledge of the Solar system, focusing on bodies in
the outer regions, on the information they provide concerning Solar system
formation, and on the possible relationships that may exist between our system
and the debris disks of other stars. Beyond the domains of the Terrestrial and
giant planets, the comets in the Kuiper belt and the Oort cloud preserve some
of our most pristine materials. The Kuiper belt, in particular, is a
collisional dust source and a scientific bridge to the dusty "debris disks"
observed around many nearby main-sequence stars. Study of the Solar system
provides a level of detail that we cannot discern in the distant disks while
observations of the disks may help to set the Solar system in proper context.Comment: 50 pages, 25 Figures. To appear in conference proceedings book
"Astrophysics in the Next Decade
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