1,606 research outputs found
The Extended Loop Representation of Quantum Gravity
A new representation of Quantum Gravity is developed. This formulation is
based on an extension of the group of loops. The enlarged group, that we call
the Extended Loop Group, behaves locally as an infinite dimensional Lie group.
Quantum Gravity can be realized on the state space of extended loop dependent
wavefunctions. The extended representation generalizes the loop representation
and contains this representation as a particular case. The resulting
diffeomorphism and hamiltonian constraints take a very simple form and allow to
apply functional methods and simplify the loop calculus. In particular we show
that the constraints are linear in the momenta. The nondegenerate solutions
known in the loop representation are also solutions of the constraints in the
new representation. The practical calculation advantages allows to find a new
solution to the Wheeler-DeWitt equation. Moreover, the extended representation
puts in a precise framework some of the regularization problems of the loop
representation. We show that the solutions are generalized knot invariants,
smooth in the extended variables, and any framing is unnecessary.Comment: 27 pages, report IFFC/94-1
Extended Loops: A New Arena for Nonperturbative Quantum Gravity
We propose a new representation for gauge theories and quantum gravity. It
can be viewed as a generalization of the loop representation. We make use of a
recently introduced extension of the group of loops into a Lie Group. This
extension allows the use of functional methods to solve the constraint
equations. It puts in a precise framework the regularization problems of the
loop representation. It has practical advantages in the search for quantum
states. We present new solutions to the Wheeler-DeWitt equation that reinforce
the conjecture that the Jones Polynomial is a state of nonperturbative quantum
gravity.Comment: 12pp, Revtex, no figures, CGPG-93/12-
No many-scallop theorem: Collective locomotion of reciprocal swimmers
To achieve propulsion at low Reynolds number, a swimmer must deform in a way
that is not invariant under time-reversal symmetry; this result is known as the
scallop theorem. We show here that there is no many-scallop theorem. We
demonstrate that two active particles undergoing reciprocal deformations can
swim collectively; moreover, polar particles also experience effective
long-range interactions. These results are derived for a minimal dimers model,
and generalized to more complex geometries on the basis of symmetry and scaling
arguments. We explain how such cooperative locomotion can be realized
experimentally by shaking a collection of soft particles with a homogeneous
external field
Is the third coefficient of the Jones knot polynomial a quantum state of gravity?
Some time ago it was conjectured that the coefficients of an expansion of the
Jones polynomial in terms of the cosmological constant could provide an
infinite string of knot invariants that are solutions of the vacuum Hamiltonian
constraint of quantum gravity in the loop representation. Here we discuss the
status of this conjecture at third order in the cosmological constant. The
calculation is performed in the extended loop representation, a generalization
of the loop representation. It is shown that the the Hamiltonian does not
annihilate the third coefficient of the Jones polynomal () for general
extended loops. For ordinary loops the result acquires an interesting
geometrical meaning and new possibilities appear for to represent a
quantum state of gravity.Comment: 22 page
Effect of carrier recombination on ultrafast carrier dynamics in thin films of the topological insulator Bi2Se3
Transient reflectivity (TR) from thin films (6 - 40 nm thick) of the
topological insulator Bi2Se3 reveal ultrafast carrier dynamics, which suggest
the existence of both radiative and non-radiative recombination between
electrons residing in the upper cone of initially unoccupied high energy Dirac
surface states (SS) and holes residing in the lower cone of occupied low energy
Dirac SS. The modeling of measured TR traces allowed us to conclude that
recombination is induced by the depletion of bulk electrons in films below ~20
nm thick due to the charge captured on the surface defects. We predict that
such recombination processes can be observed using time-resolved
photoluminescence techniques
Detecting series periodicity with horizontal visibility graphs
The horizontal visibility algorithm has been recently introduced as a mapping
between time series and networks. The challenge lies in characterizing the
structure of time series (and the processes that generated those series) using
the powerful tools of graph theory. Recent works have shown that the visibility
graphs inherit several degrees of correlations from their associated series,
and therefore such graph theoretical characterization is in principle possible.
However, both the mathematical grounding of this promising theory and its
applications are on its infancy. Following this line, here we address the
question of detecting hidden periodicity in series polluted with a certain
amount of noise. We first put forward some generic properties of horizontal
visibility graphs which allow us to define a (graph theoretical) noise
reduction filter. Accordingly, we evaluate its performance for the task of
calculating the period of noisy periodic signals, and compare our results with
standard time domain (autocorrelation) methods. Finally, potentials,
limitations and applications are discussed.Comment: To be published in International Journal of Bifurcation and Chao
Electromagnetic field fluctuations near a dielectric-vacuum boundary and surface divergences in the ideal conductor limit
We consider the electric and magnetic field fluctuations in the vacuum state
in the region external to a half-space filled with a homogeneous
non-dissipative dielectric. We discuss an appropriate limit to an ideal metal
and concentrate our interest on the renormalized field fluctuations, or
equivalently to renormalized electric and magnetic energy densities, in the
proximity of the dielectric-vacuum interface. We show that surface divergences
of field fluctuations arise at the interface in an appropriate ideal conductor
limit, and that our limiting procedure allows to discuss in detail their
structure. Field fluctuations close to the surface can be investigated through
the retarded Casimir-Polder interaction with an appropriate polarizable body.Comment: 6 pages, 2 figure
Primordial black holes as a tool for constraining non-Gaussianity
Primordial Black Holes (PBH's) can form in the early Universe from the
collapse of large density fluctuations. Tight observational limits on their
abundance constrain the amplitude of the primordial fluctuations on very small
scales which can not otherwise be constrained, with PBH's only forming from the
extremely rare large fluctuations. The number of PBH's formed is therefore
sensitive to small changes in the shape of the tail of the fluctuation
distribution, which itself depends on the amount of non-Gaussianity present. We
study, for the first time, how quadratic and cubic local non-Gaussianity of
arbitrary size (parameterised by f_nl and g_nl respectively) affects the PBH
abundance and the resulting constraints on the amplitude of the fluctuations on
very small scales. Intriguingly we find that even non-linearity parameters of
order unity have a significant impact on the PBH abundance. The sign of the
non-Gaussianity is particularly important, with the constraint on the allowed
fluctuation amplitude tightening by an order of magnitude as f_nl changes from
just -0.5 to 0.5. We find that if PBH's are observed in the future, then
regardless of the amplitude of the fluctuations, non-negligible negative f_nl
would be ruled out. Finally we show that g_nl can have an even larger effect on
the number of PBH's formed than f_nl.Comment: 9 pages, 5 figures, v2: version to appear in Phys. Rev. D with minor
changes, v3: typos corrected (including factor of 1/2 in erfc prefactor), no
changes to result
Geometric scaling of purely-elastic flow instabilities
We present a combined experimental, numerical and theoretical investigation
of the geometric scaling of the onset of a purely-elastic flow instability in a
serpentine channel. Good qualitative agreement is obtained between experiments,
using dilute solutions of flexible polymers in microfluidic devices, and
two-dimensional numerical simulations using the UCM model. The results are
confirmed by a simple theoretical analysis, based on the dimensionless
criterion proposed by Pakdel-McKinley for onset of a purely-elastic
instability
Traffic jams and intermittent flows in microfluidic networks
We investigate both experimentally and theoretically the traffic of particles
flowing in microfluidic obstacle networks. We show that the traffic dynamics is
a non-linear process: the particle current does not scale with the particle
density even in the dilute limit where no particle collision occurs. We
demonstrate that this non-linear behavior stems from long range hydrodynamic
interactions. Importantly, we also establish that there exists a maximal
current above which no stationary particle flow can be sustained. For higher
current values, intermittent traffic jams form thereby inducing the ejection of
the particles from the initial path and the subsequent invasion of the network.
Eventually, we put our findings in the broader context of the transport
proccesses of driven particles in low dimension
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