443 research outputs found
Dichromatic state sum models for four-manifolds from pivotal functors
A family of invariants of smooth, oriented four-dimensional manifolds is defined via handle decompositions and the Kirby calculus of framed link diagrams. The invariants are parametrised by a pivotal functor from a spherical fusion category into a ribbon fusion category.
A state sum formula for the invariant is constructed via the chain-mail procedure, so a large class of topological state sum models can be expressed as link invariants. Most prominently, the Crane-Yetter state sum over an arbitrary ribbon fusion category is recovered, including the nonmodular case. It is shown that the Crane-Yetter invariant for nonmodular categories is stronger than signature and Euler invariant.
A special case is the four-dimensional untwisted Dijkgraaf-Witten model. Derivations of state space dimensions of TQFTs arising from the state sum model agree with recent calculations of ground state degeneracies in Walker-Wang models.
Relations to different approaches to quantum gravity such as Cartan geometry and teleparallel gravity are also discussed
On the perturbative expansion of a quantum field theory around a topological sector
The idea of treating general relativistic theories in a perturbative
expansion around a topological theory has been recently put forward in the
quantum gravity literature. Here we investigate the viability of this idea, by
applying it to conventional Yang--Mills theory on flat spacetime. We find that
the expansion around the topological theory coincides with the usual expansion
around the abelian theory, though the equivalence is non-trivial. In this
context, the technique appears therefore to be viable, but not to bring
particularly new insights. Some implications for gravity are discussed.Comment: 7 page
On the single mode approximation in spinor-1 atomic condensate
We investigate the validity conditions of the single mode approximation (SMA)
in spinor-1 atomic condensate when effects due to residual magnetic fields are
negligible. For atomic interactions of the ferromagnetic type, the SMA is shown
to be exact, with a mode function different from what is commonly used.
However, the quantitative deviation is small under current experimental
conditions (for Rb atoms). For anti-ferromagnetic interactions, we find
that the SMA becomes invalid in general. The differences among the mean field
mode functions for the three spin components are shown to depend strongly on
the system magnetization. Our results can be important for studies of beyond
mean field quantum correlations, such as fragmentation, spin squeezing, and
multi-partite entanglement.Comment: Revised, newly found analytic proof adde
The dynamics of quantum phases in a spinor condensate
We discuss the quantum phases and their diffusion dynamics in a spinor-1
atomic Bose-Einstein condensate. For ferromagnetic interactions, we obtain the
exact ground state distribution of the phases associated with the total atom
number (), the total magnetization (), and the alignment (or
hypercharge) () of the system. The mean field ground state is stable against
fluctuations of atom numbers in each of the spin components, and the phases
associated with the order parameter for each spin components diffuse while
dynamically recover the two broken continuous symmetries [U(1) and SO(2)] when
and are conserved as in current experiments. We discuss the
implications to the quantum dynamics due to an external (homogeneous) magnetic
field. We also comment on the case of a spinor-1 condensate with
anti-ferromagnetic interactions.Comment: 5 figures, an extended version of cond-mat/030117
Axisymmetric versus Non-axisymmetric Vortices in Spinor Bose-Einstein Condensates
The structure and stability of various vortices in F=1 spinor Bose-Einstein
condensates are investigated by solving the extended Gross-Pitaevskii equation
under rotation. We perform an extensive search for stable vortices, considering
both axisymmetric and non-axisymmetric vortices and covering a wide range of
ferromagnetic and antiferromagnetic interactions. The topological defect called
Mermin-Ho (Anderson-Toulouse) vortex is shown to be stable for ferromagnetic
case. The phase diagram is established in a plane of external rotation Omega vs
total magnetization M by comparing the free energies of possible vortices. It
is shown that there are qualitative differences between axisymmetric and
non-axisymmetric vortices which are manifested in the Omega- and M-dependences.Comment: 9 pages, 9 figure
Quantum Gravity
General lectures on quantum gravity.Comment: Lectures given at Karpacz. 40 pages, submitted to Lecture Notes in
Physics. Bigger figure
Search for the Proton Decay Mode proton to neutrino K+ in Soudan 2
We have searched for the proton decay mode proton to neutrino K+ using the
one-kiloton Soudan 2 high resolution calorimeter. Contained events obtained
from a 3.56 kiloton-year fiducial exposure through June 1997 are examined for
occurrence of a visible K+ track which decays at rest into mu+ nu or pi+ pi0.
We found one candidate event consistent with background, yielding a limit,
tau/B > 4.3 10^{31} years at 90% CL with no background subtraction.Comment: 13 pages, Latex, 3 tables and 3 figures, Accepted by Physics Letters
Correlations of structural, magnetic, and dielectric properties of undoped and doped CaCu3Ti4O12
The present work reports synthesis, as well as a detailed and careful
characterization of structural, magnetic, and dielectric properties of
differently tempered undoped and doped CaCu3Ti4O12 (CCTO) ceramics. For this
purpose, neutron and x-ray powder diffraction, SQUID measurements, and
dielectric spectroscopy have been performed. Mn-, Fe-, and Ni-doped CCTO
ceramics were investigated in great detail to document the influence of
low-level doping with 3d metals on the antiferromagnetic structure and
dielectric properties. In the light of possible magnetoelectric coupling in
these doped ceramics, the dielectric measurements were also carried out in
external magnetic fields up to 7 T, showing a minor but significant dependence
of the dielectric constant on the applied magnetic field. Undoped CCTO is
well-known for its colossal dielectric constant in a broad frequency and
temperature range. With the present extended characterization of doped as well
as undoped CCTO, we want to address the question why doping with only 1% Mn or
0.5% Fe decreases the room-temperature dielectric constant of CCTO by a factor
of ~100 with a concomitant reduction of the conductivity, whereas 0.5% Ni
doping changes the dielectric properties only slightly. In addition,
diffraction experiments and magnetic investigations were undertaken to check
for possible correlations of the magnitude of the colossal dielectric constants
with structural details or with magnetic properties like the magnetic ordering,
the Curie-Weiss temperatures, or the paramagnetic moment. It is revealed, that
while the magnetic ordering temperature and the effective moment of all
investigated CCTO ceramics are rather similar, there is a dramatic influence of
doping and tempering time on the Curie-Weiss constant.Comment: 10 pages, 11 figure
Loop Quantum Gravity: An Inside View
This is a (relatively) non -- technical summary of the status of the quantum
dynamics in Loop Quantum Gravity (LQG). We explain in detail the historical
evolution of the subject and why the results obtained so far are non --
trivial. The present text can be viewed in part as a response to an article by
Nicolai, Peeters and Zamaklar [hep-th/0501114]. We also explain why certain no
go conclusions drawn from a mathematically correct calculation in a recent
paper by Helling et al [hep-th/0409182] are physically incorrect.Comment: 58 pages, no figure
An Integrated TCGA Pan-Cancer Clinical Data Resource to Drive High-Quality Survival Outcome Analytics
For a decade, The Cancer Genome Atlas (TCGA) program collected clinicopathologic annotation data along with multi-platform molecular profiles of more than 11,000 human tumors across 33 different cancer types. TCGA clinical data contain key features representing the democratized nature of the data collection process. To ensure proper use of this large clinical dataset associated with genomic features, we developed a standardized dataset named the TCGA Pan-Cancer Clinical Data Resource (TCGA-CDR), which includes four major clinical outcome endpoints. In addition to detailing major challenges and statistical limitations encountered during the effort of integrating the acquired clinical data, we present a summary that includes endpoint usage recommendations for each cancer type. These TCGA-CDR findings appear to be consistent with cancer genomics studies independent of the TCGA effort and provide opportunities for investigating cancer biology using clinical correlates at an unprecedented scale. Analysis of clinicopathologic annotations for over 11,000 cancer patients in the TCGA program leads to the generation of TCGA Clinical Data Resource, which provides recommendations of clinical outcome endpoint usage for 33 cancer types
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