17,298 research outputs found
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
Statistical Mechanics of Relativistic One-Dimensional Self-Gravitating Systems
We consider the statistical mechanics of a general relativistic
one-dimensional self-gravitating system. The system consists of -particles
coupled to lineal gravity and can be considered as a model of
relativistically interacting sheets of uniform mass. The partition function and
one-particle distitrubion functions are computed to leading order in
where is the speed of light; as results for the
non-relativistic one-dimensional self-gravitating system are recovered. We find
that relativistic effects generally cause both position and momentum
distribution functions to become more sharply peaked, and that the temperature
of a relativistic gas is smaller than its non-relativistic counterpart at the
same fixed energy. We consider the large-N limit of our results and compare
this to the non-relativistic case.Comment: latex, 60 pages, 22 figure
Dynamical N-body Equlibrium in Circular Dilaton Gravity
We obtain a new exact equilibrium solution to the N-body problem in a
one-dimensional relativistic self-gravitating system. It corresponds to an
expanding/contracting spacetime of a circle with N bodies at equal proper
separations from one another around the circle. Our methods are
straightforwardly generalizable to other dilatonic theories of gravity, and
provide a new class of solutions to further the study of (relativistic)
one-dimensional self-gravitating systems.Comment: 4 pages, latex, reference added, minor changes in wordin
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.
Critical Collapse in Einstein-Gauss-Bonnet Gravity in Five and Six Dimensions
Einstein-Gauss-Bonnet gravity (EGB) provides a natural higher dimensional and
higher order curvature generalization of Einstein gravity. It contains a new,
presumably microscopic, length scale that should affect short distance
properties of the dynamics, such as Choptuik scaling. We present the results of
a numerical analysis in generalized flat slice co-ordinates of self-gravitating
massless scalar spherical collapse in five and six dimensional EGB gravity near
the threshold of black hole formation. Remarkably, the behaviour is universal
(i.e. independent of initial data) but qualitatively different in five and six
dimensions. In five dimensions there is a minimum horizon radius, suggestive of
a first order transition between black hole and dispersive initial data. In six
dimensions no radius gap is evident. Instead, below the GB scale there is a
change in the critical exponent and echoing period.Comment: 21 pages, 39 figures, a couple of references and two new figures
adde
Light Scalar Mesons as Manifestation of Spontaneously Broken Chiral Symmetry
Attention is paid to the production mechanisms of light scalars that reveal
their nature. We reveal the chiral shielding of the \sigma(600) meson. We show
that the kaon loop mechanism of the \phi radiative decays, ratified by
experiment, points to the four-quark nature of light scalars. We show also that
the light scalars are produced in the two photon collisions via four-quark
transitions in contrast to the classic P wave tensor q\bar q mesons that are
produced via two-quark transitions . The history of
spontaneous breaking of symmetry in quantum physics is discussed in Appendix.Comment: Talk at The International Bogolyubov Conference "Problems of
Theoretical and Mathematical Physics" devoted to the 100th anniversary of
N.N.Bogolyubov's birth that was held from August 21 to August 22,2009 in
Moscow at the Russian Academy of Sciences (RAS) and from August 23 to August
27, 2009 in Dubna at the Joint Institute for Nuclear Research (JINR
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
Flavour-Dependent Type II Leptogenesis
We reanalyse leptogenesis via the out-of-equilibrium decay of the lightest
right-handed neutrino in type II seesaw scenarios, taking into account
flavour-dependent effects. In the type II seesaw mechanism, in addition to the
type I seesaw contribution, an additional direct mass term for the light
neutrinos is present. We consider type II seesaw scenarios where this
additional contribution arises from the vacuum expectation value of a Higgs
triplet, and furthermore an effective model-independent approach. We
investigate bounds on the flavour-specific decay asymmetries, on the mass of
the lightest right-handed neutrino and on the reheat temperature of the early
universe, and compare them to the corresponding bounds in the type I seesaw
framework. We show that while flavour-dependent thermal type II leptogenesis
becomes more efficient for larger mass scale of the light neutrinos, and the
bounds become relaxed, the type I seesaw scenario for leptogenesis becomes more
constrained. We also argue that in general, flavour-dependent effects cannot be
ignored when dealing with leptogenesis in type II seesaw models.Comment: 19 pages, 8 figures; v3: minor additions, typos corrected, results
and conclusions unchange
Gauged Discrete Symmetries and Proton Stability
We discuss the results of a search for anomaly free Abelian Z_N discrete
symmetries that lead to automatic R-parity conservation and prevents dangerous
higher-dimensional proton decay operators in simple extensions of the minimal
supersymmetric extension of the standard model (MSSM) based on the left-right
symmetric group, the Pati-Salam group and SO(10). We require that the
superpotential for the models have enough structures to be able to give correct
symmetry breaking to MSSM and potentially realistic fermion masses. We find
viable models in each of the extensions and for all the cases, anomaly freedom
of the discrete symmetry restricts the number of generations.Comment: 8 pages, 2 figures; v2 : typos fixed, references adde
Seesaw Right Handed Neutrino as the Sterile Neutrino for LSND
We show that a double seesaw framework for neutrino masses with
exchange symmetry can lead to one of the righthanded seesaw partners of the
light neutrinos being massless. This can play the role of a light sterile
neutrino, giving a model that explains the LSND results. We get a very
economical scheme, which makes it possible to predict the full
neutrino mass matrix if CP is conserved. Once CP violation is included, effect
of the LSND mass range sterile neutrino is to eliminate the lower bound on
neutrinoless double beta decay rate which exists for the three neutrino case
with inverted mass hierarchy. The same strategy can also be used to generate a
natural model for LSND, which is also equally predictive for the CP
conserving case in the limit of exact symmetry.Comment: 13 pages and one figure; model extended to 3+2 cas
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