7,337 research outputs found
Self-forces from generalized Killing fields
A non-perturbative formalism is developed that simplifies the understanding
of self-forces and self-torques acting on extended scalar charges in curved
spacetimes. Laws of motion are locally derived using momenta generated by a set
of generalized Killing fields. Self-interactions that may be interpreted as
arising from the details of a body's internal structure are shown to have very
simple geometric and physical interpretations. Certain modifications to the
usual definition for a center-of-mass are identified that significantly
simplify the motions of charges with strong self-fields. A derivation is also
provided for a generalized form of the Detweiler-Whiting axiom that pointlike
charges should react only to the so-called regular component of their
self-field. Standard results are shown to be recovered for sufficiently small
charge distributions.Comment: 21 page
Numerical Bifurcation Analysis of Conformal Formulations of the Einstein Constraints
The Einstein constraint equations have been the subject of study for more
than fifty years. The introduction of the conformal method in the 1970's as a
parameterization of initial data for the Einstein equations led to increased
interest in the development of a complete solution theory for the constraints,
with the theory for constant mean curvature (CMC) spatial slices and closed
manifolds completely developed by 1995. The first general non-CMC existence
result was establish by Holst et al. in 2008, with extensions to rough data by
Holst et al. in 2009, and to vacuum spacetimes by Maxwell in 2009. The non-CMC
theory remains mostly open; moreover, recent work of Maxwell on specific
symmetry models sheds light on fundamental non-uniqueness problems with the
conformal method as a parameterization in non-CMC settings. In parallel with
these mathematical developments, computational physicists have uncovered
surprising behavior in numerical solutions to the extended conformal thin
sandwich formulation of the Einstein constraints. In particular, numerical
evidence suggests the existence of multiple solutions with a quadratic fold,
and a recent analysis of a simplified model supports this conclusion. In this
article, we examine this apparent bifurcation phenomena in a methodical way,
using modern techniques in bifurcation theory and in numerical homotopy
methods. We first review the evidence for the presence of bifurcation in the
Hamiltonian constraint in the time-symmetric case. We give a brief introduction
to the mathematical framework for analyzing bifurcation phenomena, and then
develop the main ideas behind the construction of numerical homotopy, or
path-following, methods in the analysis of bifurcation phenomena. We then apply
the continuation software package AUTO to this problem, and verify the presence
of the fold with homotopy-based numerical methods.Comment: 13 pages, 4 figures. Final revision for publication, added material
on physical implication
Observational evidence of spin-induced precession in active galactic nuclei
We show that it is possible to explain the physical origin of jet precession
in active galactic nuclei (AGNs) through the misalignment between the rotation
axes of the accretion disk and of the Kerr black hole. We apply this scenario
to quasars, Seyfert galaxies and also to the Galactic Center black hole Sgr A*,
for which signatures of either jet or disk precession have been found. The
formalism adopted is parameterized by the ratio of the precession period to the
black hole mass and can be used to put constraints to the physical properties
of the accretion disk as well as to the black hole spin in those systems.Comment: 10 pages, 1 figure, accepted for publication in ApJ Letter
The brightest OH maser in the sky: a flare of emission in W75 N
A flare of maser radio emission in the OH-line 1665 MHz has been discovered
in the star forming region W75 N in 2003, with the flux density of about 1000
Jy. At the time it was the strongest OH maser detected during the whole history
of observations since the discovery of cosmic masers in 1965. The flare
emission is linearly polarized with a degree of polarization near 100%. A
weaker flare with a flux of 145 Jy was observed in this source in 2000 - 2001,
which was probably a precursor of the powerful flare. Intensity of two other
spectral features has decreased after beginning of the flare. Such variation of
the intensity of maser condensation emission (increasing of one and decreasing
of the other) can be explained by passing of the magneto hydrodynamic shock
across regions of enhanced gas concentration.Comment: 9 pages with 2 figures, accepted for publication in Astronomy Letter
Conversion of an Atomic Fermi Gas to a Long-Lived Molecular Bose Gas
We have converted an ultracold Fermi gas of Li atoms into an ultracold
gas of Li molecules by adiabatic passage through a Feshbach resonance.
Approximately molecules in the least-bound, ,
vibrational level of the X singlet state are produced with an
efficiency of 50%. The molecules remain confined in an optical trap for times
of up to 1 s before we dissociate them by a reverse adiabatic sweep.Comment: Accepted for publication in Phys. Rev. Letter
Self-energy of a scalar charge near higher-dimensional black holes
We study the problem of self-energy of charges in higher dimensional static
spacetimes. Application of regularization methods of quantum field theory to
calculation of the classical self-energy of charges leads to model-independent
results. The correction to the self-energy of a scalar charge due to the
gravitational field of black holes of the higher dimensional
Majumdar-Papapetrou spacetime is calculated exactly. It proves to be zero in
even dimensions, but it acquires non-zero value in odd dimensional spacetimes.
The origin of the self-energy correction in odd dimensions is similar to the
origin the conformal anomalies in quantum field theory in even dimensional
spacetimes.Comment: 9 page
Renyi Entropy of the XY Spin Chain
We consider the one-dimensional XY quantum spin chain in a transverse
magnetic field. We are interested in the Renyi entropy of a block of L
neighboring spins at zero temperature on an infinite lattice. The Renyi entropy
is essentially the trace of some power of the density matrix of the
block. We calculate the asymptotic for analytically in terms of
Klein's elliptic - function. We study the limiting entropy as a
function of its parameter . We show that up to the trivial addition
terms and multiplicative factors, and after a proper re-scaling, the Renyi
entropy is an automorphic function with respect to a certain subgroup of the
modular group; moreover, the subgroup depends on whether the magnetic field is
above or below its critical value. Using this fact, we derive the
transformation properties of the Renyi entropy under the map and show that the entropy becomes an elementary function of the
magnetic field and the anisotropy when is a integer power of 2, this
includes the purity . We also analyze the behavior of the entropy as
and and at the critical magnetic field and in the
isotropic limit [XX model].Comment: 28 Pages, 1 Figur
Integrable discretizations of some cases of the rigid body dynamics
A heavy top with a fixed point and a rigid body in an ideal fluid are
important examples of Hamiltonian systems on a dual to the semidirect product
Lie algebra . We give a Lagrangian derivation of
the corresponding equations of motion, and introduce discrete time analogs of
two integrable cases of these systems: the Lagrange top and the Clebsch case,
respectively. The construction of discretizations is based on the discrete time
Lagrangian mechanics on Lie groups, accompanied by the discrete time Lagrangian
reduction. The resulting explicit maps on are Poisson with respect to
the Lie--Poisson bracket, and are also completely integrable. Lax
representations of these maps are also found.Comment: arXiv version is already officia
Condensation and interaction range in harmonic boson traps: a variational approach
For a gas of N bosons interacting through a two-body Morse potential a
variational bound of the free energy of a confined system is obtained. The
calculation method is based on the Feynman-Kac functional projected on the
symmetric representation. Within the harmonic approximation a variational
estimate of the effect of the interaction range on the existence of
many-particle bound states, and on the N-T phase diagram is obtained.Comment: 14 pages+4 figures, submitted to phys.rev.
Elastic and inelastic collisions of 6Li in magnetic and optical traps
We use a full coupled channels method to calculate collisional properties of
magnetically or optically trapped ultracold 6Li. The magnetic field dependence
of the s-wave scattering lengths of several mixtures of hyperfine states are
determined, as are the decay rates due to exchange collisions. In one case, we
find Feshbach resonances at B=0.08 T and B=1.98 T. We show that the exact
coupled channels calculation is well approximated over the entire range of
magnetic fields by a simple analytical calculation.Comment: 4 pages revtex including 4 figures, submitted to PR
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