153,642 research outputs found
Emergent Geometry and Quantum Gravity
We explain how quantum gravity can be defined by quantizing spacetime itself.
A pinpoint is that the gravitational constant G = L_P^2 whose physical
dimension is of (length)^2 in natural unit introduces a symplectic structure of
spacetime which causes a noncommutative spacetime at the Planck scale L_P. The
symplectic structure of spacetime M leads to an isomorphism between symplectic
geometry (M, \omega) and Riemannian geometry (M, g) where the deformations of
symplectic structure \omega in terms of electromagnetic fields F=dA are
transformed into those of Riemannian metric g. This approach for quantum
gravity allows a background independent formulation where spacetime as well as
matter fields is equally emergent from a universal vacuum of quantum gravity
which is thus dubbed as the quantum equivalence principle.Comment: Invited Review for Mod. Phys. Lett. A, 17 page
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Endogenous Correlation
We model endogenous correlation in asset returns via the role of heterogeneous expectations in investor types, and the dynamic impact of imitative learning by investors. Learning is driven by relative performance. In addition, we allow a cautious slow learning pace to reflect institutional conditions. Imitative learning shapes the market ecology that influences price formation. Using the model of non-imitative agents as a benchmark, our results show that the dynamics of imitative learning endogenously induce a significant degree of asset dependency and patterns of non-constant correlation. The asymmetric learning effect on correlation, however, implies a self-reinforcing process, where a bearish condition amplifies the effect that further exacerbates asset dependency. We conclude that imitative learning, even when rational, can to a certain extent account for the phenomena of market crashes. Our results have implications for transparency in regulation issues
Edge Excitations and Non-Abelian Statistics in the Moore-Read State: A Numerical Study in the Presence of Coulomb Interaction and Edge Confinement
We study the ground state and low-energy excitations of fractional quantum
Hall systems on a disk at filling fraction , with Coulomb
interaction and background confining potential. We find the Moore-Read ground
state is stable within a finite but narrow window in parameter space. The
corresponding low-energy excitations contain a fermionic branch and a bosonic
branch, with widely different velocities. A short-range repulsive potential can
stabilize a charge quasihole at the center, leading to a different edge
excitation spectrum due to the change of boundary conditions for Majorana
fermions, clearly indicating the non-Abelian nature of the quasihole.Comment: 4 pages, 3 figures. New version shortened for PRL. Corrected typo
Quantum Loop Subalgebra and Eigenvectors of the Superintegrable Chiral Potts Transfer Matrices
It has been shown in earlier works that for Q=0 and L a multiple of N, the
ground state sector eigenspace of the superintegrable tau_2(t_q) model is
highly degenerate and is generated by a quantum loop algebra L(sl_2).
Furthermore, this loop algebra can be decomposed into r=(N-1)L/N simple sl_2
algebras. For Q not equal 0, we shall show here that the corresponding
eigenspace of tau_2(t_q) is still highly degenerate, but splits into two
spaces, each containing 2^{r-1} independent eigenvectors. The generators for
the sl_2 subalgebras, and also for the quantum loop subalgebra, are given
generalizing those in the Q=0 case. However, the Serre relations for the
generators of the loop subalgebra are only proven for some states, tested on
small systems and conjectured otherwise. Assuming their validity we construct
the eigenvectors of the Q not equal 0 ground state sectors for the transfer
matrix of the superintegrable chiral Potts model.Comment: LaTeX 2E document, using iopart.cls with iopams packages. 28 pages,
uses eufb10 and eurm10 fonts. Typeset twice! Version 2: Details added,
improvements and minor corrections made, erratum to paper 2 included. Version
3: Small paragraph added in introductio
Small eigenvalues of large Hankel matrices:The indeterminate case
In this paper we characterise the indeterminate case by the eigenvalues of
the Hankel matrices being bounded below by a strictly positive constant. An
explicit lower bound is given in terms of the orthonormal polynomials and we
find expresions for this lower bound in a number of indeterminate moment
problems.Comment: 14 pages, 1 figur
A nonlinear indentity for the scattering phase of integrable models
A nonlinear identity for the scattering phase of quantum integrable models is
proved.Comment: 5 pages, Latex, no figure
Correlation functions for the three state superintegrable chiral Potts spin chain of finite lengths
We compute the correlation functions of the three state superintegrable
chiral Potts spin chain for chains of length 3,4,5. From these results we
present conjectures for the form of the nearest neighbor correlation function.Comment: 10 pages; references update
The Fermi Bubbles: Gamma-ray, Microwave, and Polarization Signatures of Leptonic AGN Jets
The origin of the Fermi bubbles and the microwave haze is yet to be
determined. To disentangle different models requires detailed comparisons
between theoretical predictions and multi-wavelength observations. Our previous
simulations have demonstrated that the primary features of the Fermi bubbles
could be successfully reproduced by recent jet activity from the central active
galactic nucleus (AGN). In this work, we generate gamma-ray and microwave maps
and spectra based on the simulated properties of cosmic rays (CRs) and magnetic
fields in order to examine whether the observed bubble and haze emission could
be explained by leptons contained in the AGN jets. We also investigate the
model predictions of the polarization properties of the Fermi bubbles. We find
that: (1) The same population of leptons can simultaneously explain the bubble
and haze emission given that the magnetic fields within the bubbles are very
close to the exponentially distributed ambient field, which can be explained by
mixing in of the ambient field followed by turbulent field amplification; (2)
The centrally peaked microwave profile suggests CR replenishment, which is
consistent with the presence of a more recent second jet event; (3) The bubble
interior exhibits a high degree of polarization because of ordered radial
magnetic field lines stretched by elongated vortices behind the shocks;
highly-polarized signals could also be observed inside the draping layer; (4)
Enhancement of rotation measures could exist within the shock-compressed layer
because of increased gas density and more amplified and ordered magnetic
fields. We discuss the possibility that the deficient haze emission at b<-35
degrees is due to the suppression of magnetic fields, which is consistent with
the existence of lower-energy CRs causing the polarized emission at 2.3 GHz.
Possible AGN jet composition in the leptonic scenario is also discussed.Comment: 15 pages, 9 figures, matched with MNRAS published versio
The design of a mechanical referencing system for the rear drum of the Longwall Shearer Coal Miner
The design of two systems which reference the position of a longwall shearer coal miner to the mine roof of the present cut and of the last cut are presented. This system is part of an automation system that will guide the rear cutting drum in such a manner that the total depth of cut remains constant even though the front drum may be following an undulating roof profile. The rear drum referencing mechanism continually monitors the distance from the mine roof to the floor for the present cut. This system provides a signal to control a constant depth of cut. The last cut follower mechanism continually monitors the distance from the mine roof of the prior cut to the cutting drum. This latter system provides a signal to minimize the step height in the roof between cuts. The dynamic response of this hydraulic-pneumatic and mechanical system is analyzed to determine accumulator size and precharge pressure
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