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 ($J_3$) for general extended loops. For ordinary loops the result acquires an interesting geometrical meaning and new possibilities appear for $J_3$ 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