7,756 research outputs found
Quantum Hall conductance of two-terminal graphene devices
Measurement and theory of the two-terminal conductance of monolayer and
bilayer graphene in the quantum Hall regime are compared. We examine features
of conductance as a function of gate voltage that allow monolayer, bilayer, and
gapped samples to be distinguished, including N-shaped distortions of quantum
Hall plateaus and conductance peaks and dips at the charge neutrality point.
Generally good agreement is found between measurement and theory. Possible
origins of discrepancies are discussed
The geometry of the Barbour-Bertotti theories II. The three body problem
We present a geometric approach to the three-body problem in the
non-relativistic context of the Barbour-Bertotti theories. The Riemannian
metric characterizing the dynamics is analyzed in detail in terms of the
relative separations. Consequences of a conformal symmetry are exploited and
the sectional curvatures of geometrically preferred surfaces are computed. The
geodesic motions are integrated. Line configurations, which lead to curvature
singularities for , are investigated. None of the independent scalars
formed from the metric and curvature tensor diverges there.Comment: 16 pages, 2 eps figures, to appear in Classical and Quantum Gravit
Trans-Planckian Dark Energy?
It has recently been proposed by Mersini et al. 01, Bastero-Gil and Mersini
02 that the dark energy could be attributed to the cosmological properties of a
scalar field with a non-standard dispersion relation that decreases
exponentially at wave-numbers larger than Planck scale (k_phys > M_Planck). In
this scenario, the energy density stored in the modes of trans-Planckian
wave-numbers but sub-Hubble frequencies produced by amplification of the vacuum
quantum fluctuations would account naturally for the dark energy. The present
article examines this model in detail and shows step by step that it does not
work. In particular, we show that this model cannot make definite predictions
since there is no well-defined vacuum state in the region of wave-numbers
considered, hence the initial data cannot be specified unambiguously. We also
show that for most choices of initial data this scenario implies the production
of a large amount of energy density (of order M_Planck^4) for modes with
momenta of order M_Planck, far in excess of the background energy density. We
evaluate the amount of fine-tuning in the initial data necessary to avoid this
back-reaction problem and find it is of order H/M_Planck. We also argue that
the equation of state of the trans-Planckian modes is not vacuum-like.
Therefore this model does not provide a suitable explanation for the dark
energy.Comment: RevTeX - 15 pages, 7 figures: final version to appear in PRD, minor
changes, 1 figure adde
Probing renormalization group flows using entanglement entropy
In this paper we continue the study of renormalized entanglement entropy
introduced in [1]. In particular, we investigate its behavior near an IR fixed
point using holographic duality. We develop techniques which, for any static
holographic geometry, enable us to extract the large radius expansion of the
entanglement entropy for a spherical region. We show that for both a sphere and
a strip, the approach of the renormalized entanglement entropy to the IR fixed
point value contains a contribution that depends on the whole RG trajectory.
Such a contribution is dominant, when the leading irrelevant operator is
sufficiently irrelevant. For a spherical region such terms can be anticipated
from a geometric expansion, while for a strip whether these terms have
geometric origins remains to be seen.Comment: 58 pages, 6 figure
Beyond developable: computational design and fabrication with auxetic materials
We present a computational method for interactive 3D design and rationalization of surfaces via auxetic materials, i.e., flat flexible material that can stretch uniformly up to a certain extent. A key motivation for studying such material is that one can approximate doubly-curved surfaces (such as the sphere) using only flat pieces, making it attractive for fabrication. We physically realize surfaces by introducing cuts into approximately inextensible material such as sheet metal, plastic, or leather. The cutting pattern is modeled as a regular triangular linkage that yields hexagonal openings of spatially-varying radius when stretched. In the same way that isometry is fundamental to modeling developable surfaces, we leverage conformal geometry to understand auxetic design. In particular, we compute a global conformal map with bounded scale factor to initialize an otherwise intractable non-linear optimization. We demonstrate that this global approach can handle non-trivial topology and non-local dependencies inherent in auxetic material. Design studies and physical prototypes are used to illustrate a wide range of possible applications
Statistical Physics of Fracture Surfaces Morphology
Experiments on fracture surface morphologies offer increasing amounts of data
that can be analyzed using methods of statistical physics. One finds scaling
exponents associated with correlation and structure functions, indicating a
rich phenomenology of anomalous scaling. We argue that traditional models of
fracture fail to reproduce this rich phenomenology and new ideas and concepts
are called for. We present some recent models that introduce the effects of
deviations from homogeneous linear elasticity theory on the morphology of
fracture surfaces, succeeding to reproduce the multiscaling phenomenology at
least in 1+1 dimensions. For surfaces in 2+1 dimensions we introduce novel
methods of analysis based on projecting the data on the irreducible
representations of the SO(2) symmetry group. It appears that this approach
organizes effectively the rich scaling properties. We end up with the
proposition of new experiments in which the rotational symmetry is not broken,
such that the scaling properties should be particularly simple.Comment: A review paper submitted to J. Stat. Phy
Generation of scale invariant magnetic fields in bouncing universes
We consider the generation of primordial magnetic fields in a class of
bouncing models when the electromagnetic action is coupled non-minimally to a
scalar field that, say, drives the background evolution. For scale factors that
have the power law form at very early times and non-minimal couplings which are
simple powers of the scale factor, one can easily show that scale invariant
spectra for the magnetic field can arise before the bounce for certain values
of the indices involved. It will be interesting to examine if these power
spectra retain their shape after the bounce. However, analytical solutions for
the Fourier modes of the electromagnetic vector potential across the bounce are
difficult to obtain. In this work, with the help of a new time variable that we
introduce, which we refer to as the --fold, we investigate
these scenarios numerically. Imposing the initial conditions on the modes in
the contracting phase, we numerically evolve the modes across the bounce and
evaluate the spectra of the electric and magnetic fields at a suitable time
after the bounce. As one could have intuitively expected, though the complete
spectra depend on the details of the bounce, we find that, under the original
conditions, scale invariant spectra of the magnetic fields do arise for
wavenumbers much smaller than the scale associated with the bounce. We also
show that magnetic fields which correspond to observed strengths today can be
generated for specific values of the parameters. But, we find that, at the
bounce, the backreaction due to the electromagnetic modes that have been
generated can be significantly large calling into question the viability of the
model. We briefly discuss the implications of our results.Comment: v1: 19 pages, 5 figures; v2: 20 pages, 5 figures, minor revisions, to
appear in JCA
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