6,623 research outputs found
Equivariant -theory of GKM bundles
Given a fiber bundle of GKM spaces, , we analyze the
structure of the equivariant -ring of as a module over the equivariant
-ring of by translating the fiber bundle, , into a fiber bundle of
GKM graphs and constructing, by combinatorial techniques, a basis of this
module consisting of -classes which are invariant under the natural holonomy
action on the -ring of of the fundamental group of the GKM graph of .
We also discuss the implications of this result for fiber bundles where and are generalized partial flag varieties and show how
our GKM description of the equivariant -ring of a homogeneous GKM space is
related to the Kostant-Kumar description of this ring.Comment: 15 page
Non-commutative integrable systems on -symplectic manifolds
In this paper we study non-commutative integrable systems on -Poisson
manifolds. One important source of examples (and motivation) of such systems
comes from considering non-commutative systems on manifolds with boundary
having the right asymptotics on the boundary. In this paper we describe this
and other examples and we prove an action-angle theorem for non-commutative
integrable systems on a -symplectic manifold in a neighbourhood of a
Liouville torus inside the critical set of the Poisson structure associated to
the -symplectic structure
Quantum geometry from phase space reduction
In this work we give an explicit isomorphism between the usual spin network
basis and the direct quantization of the reduced phase space of tetrahedra. The
main outcome is a formula that describes the space of SU(2) invariant states by
an integral over coherent states satisfying the closure constraint exactly, or
equivalently, as an integral over the space of classical tetrahedra. This
provides an explicit realization of theorems by Guillemin--Sternberg and Hall
that describe the commutation of quantization and reduction. In the final part
of the paper, we use our result to express the FK spin foam model as an
integral over classical tetrahedra and the asymptotics of the vertex amplitude
is determined.Comment: 33 pages, 1 figur
Geometric Prequantization of the Moduli Space of the Vortex equations on a Riemann surface
The moduli space of solutions to the vortex equations on a Riemann surface
are well known to have a symplectic (in fact K\"{a}hler) structure. We show
this symplectic structure explictly and proceed to show a family of symplectic
(in fact, K\"{a}hler) structures on the moduli space,
parametrised by , a section of a line bundle on the Riemann surface.
Next we show that corresponding to these there is a family of prequantum line
bundles on the moduli space whose curvature is
proportional to the symplectic forms .Comment: 8 page
From twistors to twisted geometries
In a previous paper we showed that the phase space of loop quantum gravity on
a fixed graph can be parametrized in terms of twisted geometries, quantities
describing the intrinsic and extrinsic discrete geometry of a cellular
decomposition dual to the graph. Here we unravel the origin of the phase space
from a geometric interpretation of twistors.Comment: 9 page
Minimal Universal Two-qubit Quantum Circuits
We give quantum circuits that simulate an arbitrary two-qubit unitary
operator up to global phase. For several quantum gate libraries we prove that
gate counts are optimal in worst and average cases. Our lower and upper bounds
compare favorably to previously published results. Temporary storage is not
used because it tends to be expensive in physical implementations.
For each gate library, best gate counts can be achieved by a single universal
circuit. To compute gate parameters in universal circuits, we only use
closed-form algebraic expressions, and in particular do not rely on matrix
exponentials. Our algorithm has been coded in C++.Comment: 8 pages, 2 tables and 4 figures. v3 adds a discussion of asymetry
between Rx, Ry and Rz gates and describes a subtle circuit design problem
arising when Ry gates are not available. v2 sharpens one of the loose bounds
in v1. Proof techniques in v2 are noticeably revamped: they now rely less on
circuit identities and more on directly-computed invariants of two-qubit
operators. This makes proofs more constructive and easier to interpret as
algorithm
Manifolds associated with -colored regular graphs
In this article we describe a canonical way to expand a certain kind of
-colored regular graphs into closed -manifolds by
adding cells determined by the edge-colorings inductively. We show that every
closed combinatorial -manifold can be obtained in this way. When ,
we give simple equivalent conditions for a colored graph to admit an expansion.
In addition, we show that if a -colored regular graph
admits an -skeletal expansion, then it is realizable as the moment graph of
an -dimensional closed -manifold.Comment: 20 pages with 9 figures, in AMS-LaTex, v4 added a new section on
reconstructing a space with a -action for which its moment graph is
a given colored grap
Cohomology of GKM Fiber Bundles
The equivariant cohomology ring of a GKM manifold is isomorphic to the
cohomology ring of its GKM graph. In this paper we explore the implications of
this fact for equivariant fiber bundles for which the total space and the base
space are both GKM and derive a graph theoretical version of the Leray-Hirsch
theorem. Then we apply this result to the equivariant cohomology theory of flag
varieties.Comment: The paper has been accepted by the Journal of Algebraic
Combinatorics. The final publication is available at springerlink.co
Noncommutative geometry and lower dimensional volumes in Riemannian geometry
In this paper we explain how to define "lower dimensional'' volumes of any
compact Riemannian manifold as the integrals of local Riemannian invariants.
For instance we give sense to the area and the length of such a manifold in any
dimension. Our reasoning is motivated by an idea of Connes and involves in an
essential way noncommutative geometry and the analysis of Dirac operators on
spin manifolds. However, the ultimate definitions of the lower dimensional
volumes don't involve noncommutative geometry or spin structures at all.Comment: 12 page
Mg II Absorption Systems in SDSS QSO Spectra
We present the results of a MgII absorption-line survey using QSO spectra
from the SDSS EDR. Over 1,300 doublets with rest equivalent widths greater than
0.3\AA and redshifts were identified and measured. We
find that the rest equivalent width ()
distribution is described very well by an exponential function , with
and \AA. Previously reported power law
fits drastically over-predict the number of strong lines. Extrapolating our
exponential fit under-predicts the number of \AA systems,
indicating a transition in near \AA. A combination of
two exponentials reproduces the observed distribution well, suggesting that
MgII absorbers are the superposition of at least two physically distinct
populations of absorbing clouds. We also derive a new redshift parameterization
for the number density of \AA lines:
and \AA. We find that the distribution steepens with decreasing redshift,
with decreasing from \AA at to \AA at
. The incidence of moderately strong MgII lines does not
show evidence for evolution with redshift. However, lines stronger than
\AA show a decrease relative to the no-evolution prediction with
decreasing redshift for . The evolution is stronger for
increasingly stronger lines. Since in saturated absorption lines is an
indicator of the velocity spread of the absorbing clouds, we interpret this as
an evolution in the kinematic properties of galaxies from moderate to low z.Comment: 50 pages, 26 figures, accepted for publication in Ap
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