51,993 research outputs found
Symmetries of the Einstein Equations
Generalized symmetries of the Einstein equations are infinitesimal
transformations of the spacetime metric that formally map solutions of the
Einstein equations to other solutions. The infinitesimal generators of these
symmetries are assumed to be local, \ie at a given spacetime point they are
functions of the metric and an arbitrary but finite number of derivatives of
the metric at the point. We classify all generalized symmetries of the vacuum
Einstein equations in four spacetime dimensions and find that the only
generalized symmetry transformations consist of: (i) constant scalings of the
metric (ii) the infinitesimal action of generalized spacetime diffeomorphisms.
Our results rule out a large class of possible ``observables'' for the
gravitational field, and suggest that the vacuum Einstein equations are not
integrable.Comment: 15 pages, FTG-114-USU, Plain Te
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
Fano effect and Kondo effect in quantum dots formed in strongly coupled quantum wells
We present lateral transport measurements on strongly, vertically coupled
quantum dots formed in separate quantum wells in a GaAs/AlGaAs heterostructure.
Coulomb oscillations are observed forming a honeycomb lattice consistent with
two strongly coupled dots. When the tunnel barriers in the upper well are
reduced we observe the Fano effect due to the interfering paths through a
resonant state in the lower well and a continuum state in the upper well. In
both regimes an in plane magnetic field reduces the coupling between the wells
when the magnetic length is comparable to the center to center separation of
the wells. We also observe the Kondo effect which allows the spin states of the
double dot system to be probed.Comment: 4 pages, 5 figure
Sensitivity of the magnetic state of a spin lattice on itinerant electron orbital phase
Spatially extended localized spins can interact via indirect exchange
interaction through Friedel oscillations in the Fermi sea. In arrays of
localized spins such interaction can lead to a magnetically ordered phase.
Without external magnetic field such a phase is well understood via a
"two-impurity" Kondo model. Here we employ non-equilibrium transport
spectroscopy to investigate the role of the orbital phase of conduction
electrons on the magnetic state of a spin lattice. We show experimentally, that
even tiniest perpendicular magnetic field can influence the magnitude of the
inter-spin magnetic exchange.Comment: To be published in PhysicaE EP2DS proceedin
Gravitational Waves: Just Plane Symmetry
We present some remarkable properties of the symmetry group for gravitational
plane waves. Our main observation is that metrics with plane wave symmetry
satisfy every system of generally covariant vacuum field equations except the
Einstein equations. The proof uses the homothety admitted by metrics with plane
wave symmetry and the scaling behavior of generally covariant field equations.
We also discuss a mini-superspace description of spacetimes with plane wave
symmetry.Comment: 10 pages, TeX, uses IOP style file
Conserved currents of massless fields of spin s>0
A complete and explicit classification of all locally constructed conserved
currents and underlying conserved tensors is obtained for massless linear
symmetric spinor fields of any spin s>0 in four dimensional flat spacetime.
These results generalize the recent classification in the spin s=1 case of all
conserved currents locally constructed from the electromagnetic spinor field.
The present classification yields spin s>0 analogs of the well-known
electromagnetic stress-energy tensor and Lipkin's zilch tensor, as well as a
spin s>0 analog of a novel chiral tensor found in the spin s=1 case. The chiral
tensor possesses odd parity under a duality symmetry (i.e., a phase rotation)
on the spin s field, in contrast to the even parity of the stress-energy and
zilch tensors. As a main result, it is shown that every locally constructed
conserved current for each s>0 is equivalent to a sum of elementary linear
conserved currents, quadratic conserved currents associated to the
stress-energy, zilch, and chiral tensors, and higher derivative extensions of
these currents in which the spin s field is replaced by its repeated
conformally-weighted Lie derivatives with respect to conformal Killing vectors
of flat spacetime. Moreover, all of the currents have a direct, unified
characterization in terms of Killing spinors. The cases s=2, s=1/2 and s=3/2
provide a complete set of conserved quantities for propagation of gravitons
(i.e., linearized gravity waves), neutrinos and gravitinos, respectively, on
flat spacetime. The physical meaning of the zilch and chiral quantities is
discussed.Comment: 26 pages; final version with minor changes, accepted in Proc. Roy.
Soc. A (London
A Variational Formulation of Symplectic Noncommutative Mechanics
The standard lore in noncommutative physics is the use of first order
variational description of a dynamical system to probe the space
noncommutativity and its consequences in the dynamics in phase space. As the
ultimate goal is to understand the inherent space noncommutativity we propose a
variational principle for noncommutative dynamical systems in configuration
space, based on results of our previous work [14]. We hope that this
variational formulation in configuration space can be of help to elucidate the
definition of some global and dynamical properties of classical and quantum
noncommutative space.Comment: 17 pages, Latex. Accepted for publication in IJGMM
Stability of Inhomogeneous Superstructures from Renormalized Mean-field Theory of the t--J Model
Using the t--J model (which can also include Coulomb repulsion) and the
``plain vanilla'' renormalized mean-field theory of Zhang et al. (1988),
stability of inhomogeneous 4a x 4a superstructures as those observed in
cuprates superconductors around hole doping 1/8 is investigated. We find a
non-uniform 4a x 4a bond order wave involving simultaneously small (~ 10^-2 t)
inhomogeneous staggered plaquette currents as well as a small charge density
modulation similar to pair density wave order. On the other hand, no supersolid
phase involving a decoupling in the superconducting particle-particle channel
is found.Comment: 4 page
Foundations of Relational Particle Dynamics
Relational particle dynamics include the dynamics of pure shape and cases in
which absolute scale or absolute rotation are additionally meaningful. These
are interesting as regards the absolute versus relative motion debate as well
as discussion of conceptual issues connected with the problem of time in
quantum gravity. In spatial dimension 1 and 2 the relative configuration spaces
of shapes are n-spheres and complex projective spaces, from which knowledge I
construct natural mechanics on these spaces. I also show that these coincide
with Barbour's indirectly-constructed relational dynamics by performing a full
reduction on the latter. Then the identification of the configuration spaces as
n-spheres and complex projective spaces, for which spaces much mathematics is
available, significantly advances the understanding of Barbour's relational
theory in spatial dimensions 1 and 2. I also provide the parallel study of a
new theory for which positon and scale are purely relative but orientation is
absolute. The configuration space for this is an n-sphere regardless of the
spatial dimension, which renders this theory a more tractable arena for
investigation of implications of scale invariance than Barbour's theory itself.Comment: Minor typos corrected; references update
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