17,614 research outputs found
The U(1) symmetry of the non-tribimaximal pattern in the degenerate mass spectrum case of the neutrino mass matrix
On account of the new neutrino oscillation data signalling a non-zero value
for the smallest mixing angle (), we present an explicit realization
of the underlying U(1) symmetry characterizing the maximal atmospheric mixing
angle () pattern with two degenerate masses but now with
generic values of . We study the effects of the form invariance with
respect to U(1), and/or , subgroups, on the Yukawa couplings and the
mass terms. Later on, we specify to its experimental best fit value
(), and impose the symmetry in an entire model which includes
charged leptons, and many Higgs doublets or standard model singlet heavy
scalars, to show that it can make room for the charged lepton mass hierarchies.
In addition, we show for the non-tribimaximal value of within
type-I seesaw mechanism enhanced with flavor symmetry that neutrino mass
hierarchies can be generated. Furthermore, lepton/baryogenesis can be
interpreted via type-II seesaw mechanism within a setup meeting the flavor
U(1)-symmetry.Comment: latex, 1 table, 20 pages. Typos are corrected, shortened version to
appear in Phys. Rev.
Chaos in an Exact Relativistic 3-body Self-Gravitating System
We consider the problem of three body motion for a relativistic
one-dimensional self-gravitating system. After describing the canonical
decomposition of the action, we find an exact expression for the 3-body
Hamiltonian, implicitly determined in terms of the four coordinate and momentum
degrees of freedom in the system. Non-relativistically these degrees of freedom
can be rewritten in terms of a single particle moving in a two-dimensional
hexagonal well. We find the exact relativistic generalization of this
potential, along with its post-Newtonian approximation. We then specialize to
the equal mass case and numerically solve the equations of motion that follow
from the Hamiltonian. Working in hexagonal-well coordinates, we obtaining
orbits in both the hexagonal and 3-body representations of the system, and plot
the Poincare sections as a function of the relativistic energy parameter . We find two broad categories of periodic and quasi-periodic motions that we
refer to as the annulus and pretzel patterns, as well as a set of chaotic
motions that appear in the region of phase-space between these two types.
Despite the high degree of non-linearity in the relativistic system, we find
that the the global structure of its phase space remains qualitatively the same
as its non-relativisitic counterpart for all values of that we could
study. However the relativistic system has a weaker symmetry and so its
Poincare section develops an asymmetric distortion that increases with
increasing . For the post-Newtonian system we find that it experiences a
KAM breakdown for : above which the near integrable regions
degenerate into chaos.Comment: latex, 65 pages, 36 figures, high-resolution figures available upon
reques
Numerical modeling of dynamic powder compaction using the Kawakita equation of state
Dynamic powder compaction is analyzed using the assumption that the powder behaves, while it is being compacted, like a hydrodynamic fluid in which deviatoric stress and heat conduction effects can be ignored throughout the process. This enables techniques of computational fluid dynamics such the equilibrium flux method to be used as a modeling tool. The equation of state of the powder under compression is assumed to be a modified version of the Kawakita loading curve. Computer simulations using this model are performed for conditions matching as closely as possible with those from experiments by Page and Killen [Powder Metall. 30, 233 (1987)]. The numerical and experimental results are compared and a surprising degree of qualitative agreement is observed
Quasiclassical Coarse Graining and Thermodynamic Entropy
Our everyday descriptions of the universe are highly coarse-grained,
following only a tiny fraction of the variables necessary for a perfectly
fine-grained description. Coarse graining in classical physics is made natural
by our limited powers of observation and computation. But in the modern quantum
mechanics of closed systems, some measure of coarse graining is inescapable
because there are no non-trivial, probabilistic, fine-grained descriptions.
This essay explores the consequences of that fact. Quantum theory allows for
various coarse-grained descriptions some of which are mutually incompatible.
For most purposes, however, we are interested in the small subset of
``quasiclassical descriptions'' defined by ranges of values of averages over
small volumes of densities of conserved quantities such as energy and momentum
and approximately conserved quantities such as baryon number. The
near-conservation of these quasiclassical quantities results in approximate
decoherence, predictability, and local equilibrium, leading to closed sets of
equations of motion. In any description, information is sacrificed through the
coarse graining that yields decoherence and gives rise to probabilities for
histories. In quasiclassical descriptions, further information is sacrificed in
exhibiting the emergent regularities summarized by classical equations of
motion. An appropriate entropy measures the loss of information. For a
``quasiclassical realm'' this is connected with the usual thermodynamic entropy
as obtained from statistical mechanics. It was low for the initial state of our
universe and has been increasing since.Comment: 17 pages, 0 figures, revtex4, Dedicated to Rafael Sorkin on his 60th
birthday, minor correction
Chaos in a Relativistic 3-body Self-Gravitating System
We consider the 3-body problem in relativistic lineal gravity and obtain an
exact expression for its Hamiltonian and equations of motion. While
general-relativistic effects yield more tightly-bound orbits of higher
frequency compared to their non-relativistic counterparts, as energy increases
we find in the equal-mass case no evidence for either global chaos or a
breakdown from regular to chaotic motion, despite the high degree of
non-linearity in the system. We find numerical evidence for a countably
infinite class of non-chaotic orbits, yielding a fractal structure in the outer
regions of the Poincare plot.Comment: 9 pages, LaTex, 3 figures, final version to appear in Phys. Rev. Let
Neutrino mixing matrix in the 3-3-1 model with heavy leptons and symmetry
We study the lepton sector in the model based on the local gauge group
which do not contain particles with
exotic electric charges. The seesaw mechanism and discrete symmetry are
introduced into the model to understand why neutrinos are especially light and
the observed pattern of neutrino mixing. The model provides a method for
obtaining the tri-bimaximal mixing matrix in the leading order. A non-zero
mixing angle presents in the modified mixing matrix.Comment: 10 page
Dirac neutrino mass from the beta decay end-point modified by the dynamics of a Lorentz-violating equation of motion
Using a generalized procedure for obtaining the equation of motion of a
propagating fermionic particle, we examine previous claims for a lightlike
preferred axis embedded in the framework of Lorentz-invariance violation with
preserved algebra. In a high energy scale, the corresponding equation of motion
is reduced to a conserving lepton number chiral (VSR) equation, and in a low
energy scale, the Dirac equation for a free is recovered. The new dynamics
introduces some novel ingredients (modified cross section) to the phenomenology
of the tritium beta decay end-point.Comment: 11 pages, 4 figure
Nonextensive aspects of self-organized scale-free gas-like networks
We explore the possibility to interpret as a 'gas' the dynamical
self-organized scale-free network recently introduced by Kim et al (2005). The
role of 'momentum' of individual nodes is played by the degree of the node, the
'configuration space' (metric defining distance between nodes) being determined
by the dynamically evolving adjacency matrix. In a constant-size network
process, 'inelastic' interactions occur between pairs of nodes, which are
realized by the merger of a pair of two nodes into one. The resulting node
possesses the union of all links of the previously separate nodes. We consider
chemostat conditions, i.e., for each merger there will be a newly created node
which is then linked to the existing network randomly. We also introduce an
interaction 'potential' (node-merging probability) which decays with distance
d_ij as 1/d_ij^alpha; alpha >= 0). We numerically exhibit that this system
exhibits nonextensive statistics in the degree distribution, and calculate how
the entropic index q depends on alpha. The particular cases alpha=0 and alpha
to infinity recover the two models introduced by Kim et al.Comment: 7 pages, 5 figure
Entwined Paths, Difference Equations and the Dirac Equation
Entwined space-time paths are bound pairs of trajectories which are traversed
in opposite directions with respect to macroscopic time. In this paper we show
that ensembles of entwined paths on a discrete space-time lattice are simply
described by coupled difference equations which are discrete versions of the
Dirac equation. There is no analytic continuation, explicit or forced, involved
in this description. The entwined paths are `self-quantizing'. We also show
that simple classical stochastic processes that generate the difference
equations as ensemble averages are stable numerically and converge at a rate
governed by the details of the stochastic process. This result establishes the
Dirac equation in one dimension as a phenomenological equation describing an
underlying classical stochastic process in the same sense that the Diffusion
and Telegraph equations are phenomenological descriptions of stochastic
processes.Comment: 15 pages, 5 figures Replacement 11/02 contains minor editorial
change
Electroweak Symmetry Breaking and Proton Decay in SO(10) SUSY-GUT with TeV W_R
In a recent paper, we proposed a new class of supersymmetric SO(10) models
for neutrino masses where the TeV scale electroweak symmetry is SU(2)_L\times
SU(2)_R\times U(1)_{B-L} making the associated gauge bosons W_R and Z'
accessible at the Large Hadron Collider. We showed that there exists a domain
of Yukawa coupling parameters and symmetry breaking patterns which give an
excellent fit to all fermion masses including neutrinos. In this sequel, we
discuss an alternative Yukawa pattern which also gives good fermion mass fit
and then study the predictions of both models for proton lifetime. Consistency
with current experimental lower limits on proton life time require the squark
masses of first two generations to be larger than ~ 1.2 TeV. We also discuss
how one can have simultaneous breaking of both SU(2)_R\times U(1)_{B-L} and
standard electroweak symmetries via radiative corrections.Comment: 31 pages, 5 figures, 4 tables
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