68,594 research outputs found
New Symbolic Tools for Differential Geometry, Gravitation, and Field Theory
DifferentialGeometry is a Maple software package which symbolically performs
fundamental operations of calculus on manifolds, differential geometry, tensor
calculus, Lie algebras, Lie groups, transformation groups, jet spaces, and the
variational calculus. These capabilities, combined with dramatic recent
improvements in symbolic approaches to solving algebraic and differential
equations, have allowed for development of powerful new tools for solving
research problems in gravitation and field theory. The purpose of this paper is
to describe some of these new tools and present some advanced applications
involving: Killing vector fields and isometry groups, Killing tensors and other
tensorial invariants, algebraic classification of curvature, and symmetry
reduction of field equations.Comment: 42 page
Presymplectic current and the inverse problem of the calculus of variations
The inverse problem of the calculus of variations asks whether a given system
of partial differential equations (PDEs) admits a variational formulation. We
show that the existence of a presymplectic form in the variational bicomplex,
when horizontally closed on solutions, allows us to construct a variational
formulation for a subsystem of the given PDE. No constraints on the
differential order or number of dependent or independent variables are assumed.
The proof follows a recent observation of Bridges, Hydon and Lawson and
generalizes an older result of Henneaux from ordinary differential equations
(ODEs) to PDEs. Uniqueness of the variational formulation is also discussed.Comment: v2: 17 pages, no figures, BibTeX; minor corrections, close to
published versio
Properties of the Scalar Universal Equations
The variational properties of the scalar so--called ``Universal'' equations
are reviewed and generalised. In particular, we note that contrary to earlier
claims, each member of the Euler hierarchy may have an explicit field
dependence. The Euler hierarchy itself is given a new interpretation in terms
of the formal complex of variational calculus, and is shown to be related to
the algebra of distinguished symmetries of the first source form.Comment: 15 pages, LaTeX articl
Effects of antiferromagnetic planes on the superconducting properties of multilayered high-Tc cuprates
We propose a mechanism for high critical temperature (T_c) in the coexistent
phase of superconducting- (SC) and antiferromagnetic (AF) CuO_2 planes in
multilayered cuprates. The Josephson coupling between the SC planes separated
by an AF insulator (Mott insulator) is calculated perturbatively up to the
fourth order in terms of the hopping integral between adjacent CuO_2 planes. It
is shown that the AF exchange splitting in the AF plane suppresses the
so-called pi-Josephson coupling, and the long-ranged 0-Josephson coupling leads
to coexistence with a rather high value of T_c.Comment: 4 pages including 4 figure
Electron energy spectrum of the spin-liquid state in a frustrated Hubbard model
Non-local correlation effects in the half-filled Hubbard model on an
isotropic triangular lattice are studied within a spin polarized extension of
the dual fermion approach. A competition between the antiferromagnetic
non-collinear and the spin liquid states is strongly enhanced by an
incorporation of a k-dependent self-energy beyond the local dynamical
mean-field theory. The dual fermion correc- tions drastically decrease the
energy of a spin liquid state while leaving the non-collinear magnetic states
almost non-affected. This makes the spin liquid to become a preferable state in
a certain interval of interaction strength of an order of the magnitude of a
bandwidth. The spectral function of the spin-liquid Mott insulator is
determined by a formation of local singlets which results in the energy gap of
about twice larger than that of the 120 degrees antiferromagnetic Neel state.Comment: 6 pages, 4 figure
New spectroscopic and polarimetric observations of the A0 supergiant HD92207
Our recent search for the presence of a magnetic field in the bright early
A-type supergiant HD92207 using FORS2 in spectropolarimetric mode revealed the
presence of a longitudinal magnetic field of the order of a few hundred Gauss.
However, the definite confirmation of the magnetic nature of this object
remained pending due to the detection of short-term spectral variability
probably affecting the position of line profiles in left- and right-hand
polarized spectra. We present new magnetic field measurements of HD92207
obtained on three different epochs in 2013 and 2014 using FORS2 in
spectropolarimetric mode. A 3sigma detection of the mean longitudinal magnetic
field using the entire spectrum, _all=104+-34G, was achieved in
observations obtained in 2014 January. At this epoch, the position of the
spectral lines appeared stable. Our analysis of spectral line shapes recorded
in opposite circularly polarized light, i.e. in light with opposite sense of
rotation, reveals that line profiles in the light polarized in a certain
direction appear slightly split. The mechanism causing such a behaviour in the
circularly polarized light is currently unknown. Trying to settle the issue of
short-term variability, we searched for changes in the spectral line profiles
on a time scale of 8-10min using HARPS polarimetric spectra and on a time scale
of 3-4min using time series obtained with the CORALIE spectrograph. No
significant variability was detected on these time scales during the epochs
studied.Comment: 10 pages, 11 figures, 2 tables, accepted for publication in
Astronomische Nachrichte
Oscillatory decay of a two-component Bose-Einstein condensate
We study the decay of a two-component Bose-Einstein condensate with negative
effective interaction energy. With a decreasing atom number due to losses, the
atom-atom interaction becomes less important and the system undergoes a
transition from a bistable Josephson regime to the monostable Rabi regime,
displaying oscillations in phase and number. We study the equations of motion
and derive an analytical expression for the oscillation amplitude. A quantum
trajectory simulation reveals that the classical description fails for low
emission rates, as expected from analytical considerations. Observation of the
proposed effect will provide evidence for negative effective interaction.Comment: 4 pages, 3 figue
Exotic order in simple models of bosonic systems
We show that simple Bose Hubbard models with unfrustrated hopping and short
range two-body repulsive interactions can support stable fractionalized phases
in two and higher dimensions, and in zero magnetic field. The simplicity of the
constructed models advances the possibility of a controlled experimental
realization and novel applications of such unconventional states.Comment: 4 pages, 4 figure
The Principle of Symmetric Criticality in General Relativity
We consider a version of Palais' Principle of Symmetric Criticality (PSC)
that is applicable to the Lie symmetry reduction of Lagrangian field theories.
PSC asserts that, given a group action, for any group-invariant Lagrangian the
equations obtained by restriction of Euler-Lagrange equations to
group-invariant fields are equivalent to the Euler-Lagrange equations of a
canonically defined, symmetry-reduced Lagrangian. We investigate the validity
of PSC for local gravitational theories built from a metric. It is shown that
there are two independent conditions which must be satisfied for PSC to be
valid. One of these conditions, obtained previously in the context of
transverse symmetry group actions, provides a generalization of the well-known
unimodularity condition that arises in spatially homogeneous cosmological
models. The other condition seems to be new. The conditions that determine the
validity of PSC are equivalent to pointwise conditions on the group action
alone. These results are illustrated with a variety of examples from general
relativity. It is straightforward to generalize all of our results to any
relativistic field theory.Comment: 46 pages, Plain TeX, references added in revised versio
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