14,061 research outputs found
Spin Foam Models of Matter Coupled to Gravity
We construct a class of spin foam models describing matter coupled to
gravity, such that the gravitational sector is described by the unitary
irreducible representations of the appropriate symmetry group, while the matter
sector is described by the finite-dimensional irreducible representations of
that group. The corresponding spin foam amplitudes in the four-dimensional
gravity case are expressed in terms of the spin network amplitudes for
pentagrams with additional external and internal matter edges. We also give a
quantum field theory formulation of the model, where the matter degrees of
freedom are described by spin network fields carrying the indices from the
appropriate group representation. In the non-topological Lorentzian gravity
case, we argue that the matter representations should be appropriate SO(3) or
SO(2) representations contained in a given Lorentz matter representation,
depending on whether one wants to describe a massive or a massless matter
field. The corresponding spin network amplitudes are given as multiple
integrals of propagators which are matrix spherical functions.Comment: 30 pages, 9 figures, further remarks and references added. Version to
appear in Class. Quant. Gra
Finiteness and Dual Variables for Lorentzian Spin Foam Models
We describe here some new results concerning the Lorentzian Barrett-Crane
model, a well-known spin foam formulation of quantum gravity. Generalizing an
existing finiteness result, we provide a concise proof of finiteness of the
partition function associated to all non-degenerate triangulations of
4-manifolds and for a class of degenerate triangulations not previously shown.
This is accomplished by a suitable re-factoring and re-ordering of integration,
through which a large set of variables can be eliminated. The resulting
formulation can be interpreted as a ``dual variables'' model that uses
hyperboloid variables associated to spin foam edges in place of representation
variables associated to faces. We outline how this method may also be useful
for numerical computations, which have so far proven to be very challenging for
Lorentzian spin foam models.Comment: 15 pages, 1 figur
Spin Foam Models of Yang-Mills Theory Coupled to Gravity
We construct a spin foam model of Yang-Mills theory coupled to gravity by
using a discretized path integral of the BF theory with polynomial interactions
and the Barret-Crane ansatz. In the Euclidian gravity case we obtain a vertex
amplitude which is determined by a vertex operator acting on a simple spin
network function. The Euclidian gravity results can be straightforwardly
extended to the Lorentzian case, so that we propose a Lorentzian spin foam
model of Yang-Mills theory coupled to gravity.Comment: 10 page
Selective spin coupling through a single exciton
We present a novel scheme for performing a conditional phase gate between two
spin qubits in adjacent semiconductor quantum dots through delocalized single
exciton states, formed through the inter-dot Foerster interaction. We consider
two resonant quantum dots, each containing a single excess conduction band
electron whose spin embodies the qubit. We demonstrate that both the two-qubit
gate, and arbitrary single-qubit rotations, may be realized to a high fidelity
with current semiconductor and laser technology.Comment: 5 pages, 3 figures; published version, equation formatting improved,
references adde
Asymptotics of 10j symbols
The Riemannian 10j symbols are spin networks that assign an amplitude to each
4-simplex in the Barrett-Crane model of Riemannian quantum gravity. This
amplitude is a function of the areas of the 10 faces of the 4-simplex, and
Barrett and Williams have shown that one contribution to its asymptotics comes
from the Regge action for all non-degenerate 4-simplices with the specified
face areas. However, we show numerically that the dominant contribution comes
from degenerate 4-simplices. As a consequence, one can compute the asymptotics
of the Riemannian 10j symbols by evaluating a `degenerate spin network', where
the rotation group SO(4) is replaced by the Euclidean group of isometries of
R^3. We conjecture formulas for the asymptotics of a large class of Riemannian
and Lorentzian spin networks in terms of these degenerate spin networks, and
check these formulas in some special cases. Among other things, this conjecture
implies that the Lorentzian 10j symbols are asymptotic to 1/16 times the
Riemannian ones.Comment: 25 pages LaTeX with 8 encapsulated Postscript figures. v2 has various
clarifications and better page breaks. v3 is the final version, to appear in
Classical and Quantum Gravity, and has a few minor corrections and additional
reference
On the causal Barrett--Crane model: measure, coupling constant, Wick rotation, symmetries and observables
We discuss various features and details of two versions of the Barrett-Crane
spin foam model of quantum gravity, first of the Spin(4)-symmetric Riemannian
model and second of the SL(2,C)-symmetric Lorentzian version in which all
tetrahedra are space-like. Recently, Livine and Oriti proposed to introduce a
causal structure into the Lorentzian Barrett--Crane model from which one can
construct a path integral that corresponds to the causal (Feynman) propagator.
We show how to obtain convergent integrals for the 10j-symbols and how a
dimensionless constant can be introduced into the model. We propose a `Wick
rotation' which turns the rapidly oscillating complex amplitudes of the Feynman
path integral into positive real and bounded weights. This construction does
not yet have the status of a theorem, but it can be used as an alternative
definition of the propagator and makes the causal model accessible by standard
numerical simulation algorithms. In addition, we identify the local symmetries
of the models and show how their four-simplex amplitudes can be re-expressed in
terms of the ordinary relativistic 10j-symbols. Finally, motivated by possible
numerical simulations, we express the matrix elements that are defined by the
model, in terms of the continuous connection variables and determine the most
general observable in the connection picture. Everything is done on a fixed
two-complex.Comment: 22 pages, LaTeX 2e, 1 figur
The Construction of Sorkin Triangulations
Some time ago, Sorkin (1975) reported investigations of the time evolution
and initial value problems in Regge calculus, for one triangulation each of the
manifolds and . Here we display the simple, local characteristic
of those triangulations which underlies the structure found by Sorkin, and
emphasise its general applicability, and therefore the general validity of
Sorkin's conclusions. We also make some elementary observations on the
resulting structure of the time evolution and initial value problems in Regge
calculus, and add some comments and speculations.Comment: 5 pages (plus one figure not included, available from author on
request), Plain Tex, no local preprint number (Only change: omitted
"\magnification" command now replaced
Regge Calculus as a Fourth Order Method in Numerical Relativity
The convergence properties of numerical Regge calculus as an approximation to
continuum vacuum General Relativity is studied, both analytically and
numerically. The Regge equations are evaluated on continuum spacetimes by
assigning squared geodesic distances in the continuum manifold to the squared
edge lengths in the simplicial manifold. It is found analytically that,
individually, the Regge equations converge to zero as the second power of the
lattice spacing, but that an average over local Regge equations converges to
zero as (at the very least) the third power of the lattice spacing. Numerical
studies using analytic solutions to the Einstein equations show that these
averages actually converge to zero as the fourth power of the lattice spacing.Comment: 14 pages, LaTeX, 8 figures mailed in separate file or email author
directl
Observation of spinor dynamics in optically trapped 87Rb Bose-Einstein Condensates
We measure spin mixing of F=1 and F=2 spinor condensates of 87Rb atoms
confined in an optical trap. We determine the spin mixing time to be typically
less than 600 ms and observe spin population oscillations. The equilibrium spin
configuration in the F=1 manifold is measured for different magnetic fields and
found to show ferromagnetic behavior for low field gradients. An F=2 condensate
is created by microwave excitation from F=1 manifold, and this spin-2
condensate is observed to decay exponentially with time constant 250 ms.
Despite the short lifetime in the F=2 manifold, spin mixing of the condensate
is observed within 50 ms.Comment: 4 pages, 6 figure
A Storage Ring for Neutral Atoms
We have demonstrated a storage ring for ultra-cold neutral atoms. Atoms with
mean velocities of 1 m/s corresponding to kinetic energies of ~100 neV are
confined to a 2 cm diameter ring by magnetic forces produced by two
current-carrying wires. Up to 10^6 atoms are loaded at a time in the ring, and
7 revolutions are clearly observed. Additionally, we have demonstrated multiple
loading of the ring and deterministic manipulation of the longitudinal velocity
distribution of the atoms using applied laser pulses. Applications of this ring
include large area atom interferometers and cw monochromatic atomic beam
generation.Comment: 4 pages, 5 figure
- …