131,019 research outputs found
Free vacuum for loop quantum gravity
We linearize extended ADM-gravity around the flat torus, and use the
associated Fock vacuum to construct a state that could play the role of a free
vacuum in loop quantum gravity. The state we obtain is an element of the
gauge-invariant kinematic Hilbert space and restricted to a cutoff graph, as a
natural consequence of the momentum cutoff of the original Fock state. It has
the form of a Gaussian superposition of spin networks. We show that the peak of
the Gaussian lies at weave-like states and derive a relation between the
coloring of the weaves and the cutoff scale. Our analysis indicates that the
peak weaves become independent of the cutoff length when the latter is much
smaller than the Planck length. By the same method, we also construct
multiple-graviton states. We discuss the possible use of these states for
deriving a perturbation series in loop quantum gravity.Comment: 30 pages, 3 diagrams, treatment of phase factor adde
On the phonon-induced superconductivity of disordered alloys
A model of alloy is considered which includes both quenched disorder in the
electron subsystem (``alloy'' subsystem) and electron-phonon interaction. For
given approximate solution for the alloy part of the problem, which is assumed
to be conserving in Baym's sense, we construct the generating functional and
derive the Eliashberg-type equations which are valid to the lowest order in the
adiabatic parameter.The renormalization of bare electron-phonon interaction
vertices by disorder is taken into account consistently with the approximation
for the alloy self-energy. For the case of exact configurational averaging the
same set of equations is established within the usual T-matrix approach. We
demonstrate that for any conserving approximation for the alloy part of the
self-energy the Anderson's theorem holds in the case of isotropic singlet
pairing provided disorder renormalizations of the electron-phonon interaction
vertices are neglected. Taking account of the disorder renormalization of the
electron-phonon interaction we analyze general equations qualitatively and
present the expressions for for the case of weak and intermediate
electron-phonon coupling. Disorder renormalizations of the logarithmic
corrections to the effective coupling, which arise when the effective
interaction kernel for the Cooper channel has the second energy scale, as well
as the renormalization of the dilute paramagnetic impurity suppression are
discussed.Comment: 59 pages, 10 Eps figures, LaTe
Renormalization group flows into phases with broken symmetry
We describe a way to continue the fermionic renormalization group flow into
phases with broken global symmetry. The method does not require a
Hubbard-Stratonovich decoupling of the interaction. Instead an infinitesimally
small symmetry-breaking component is inserted in the initial action, as an
initial condition for the flow of the selfenergy. Its flow is driven by the
interaction and at low scales it saturates at a nonzero value if there is a
tendency for spontaneous symmetry breaking in the corresponding channel. For
the reduced BCS model we show how a small initial gap amplitude flows to the
value given by the exact solution of the model. We also discuss the emergence
of the Goldstone boson in this approach.Comment: 30 pages, LaTeX, 8 figure
Markov models for fMRI correlation structure: is brain functional connectivity small world, or decomposable into networks?
Correlations in the signal observed via functional Magnetic Resonance Imaging
(fMRI), are expected to reveal the interactions in the underlying neural
populations through hemodynamic response. In particular, they highlight
distributed set of mutually correlated regions that correspond to brain
networks related to different cognitive functions. Yet graph-theoretical
studies of neural connections give a different picture: that of a highly
integrated system with small-world properties: local clustering but with short
pathways across the complete structure. We examine the conditional independence
properties of the fMRI signal, i.e. its Markov structure, to find realistic
assumptions on the connectivity structure that are required to explain the
observed functional connectivity. In particular we seek a decomposition of the
Markov structure into segregated functional networks using decomposable graphs:
a set of strongly-connected and partially overlapping cliques. We introduce a
new method to efficiently extract such cliques on a large, strongly-connected
graph. We compare methods learning different graph structures from functional
connectivity by testing the goodness of fit of the model they learn on new
data. We find that summarizing the structure as strongly-connected networks can
give a good description only for very large and overlapping networks. These
results highlight that Markov models are good tools to identify the structure
of brain connectivity from fMRI signals, but for this purpose they must reflect
the small-world properties of the underlying neural systems
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