2,017 research outputs found
The Coulomb impurity problem in graphene
We address the problem of an unscreened Coulomb charge in graphene, and
calculate the local density of states and displaced charge as a function of
energy and distance from the impurity. This is done non-perturbatively in two
different ways: (1) solving the problem exactly by studying numerically the
tight-binding model on the lattice; (2) using the continuum description in
terms of the 2D Dirac equation. We show that the Dirac equation, when properly
regularized, provides a qualitative and quantitative low energy description of
the problem. The lattice solution shows extra features that cannot be described
by the Dirac equation, namely bound state formation and strong renormalization
of the van Hove singularities.Comment: 3 Figures; minor typo corrections and minor update in Fig. 3
Quantum Gravity Vacuum and Invariants of Embedded Spin Networks
We show that the path integral for the three-dimensional SU(2) BF theory with
a Wilson loop or a spin network function inserted can be understood as the
Rovelli-Smolin loop transform of a wavefunction in the Ashtekar connection
representation, where the wavefunction satisfies the constraints of quantum
general relativity with zero cosmological constant. This wavefunction is given
as a product of the delta functions of the SU(2) field strength and therefore
it can be naturally associated to a flat connection spacetime. The loop
transform can be defined rigorously via the quantum SU(2) group, as a spin foam
state sum model, so that one obtains invariants of spin networks embedded in a
three-manifold. These invariants define a flat connection vacuum state in the
q-deformed spin network basis. We then propose a modification of this
construction in order to obtain a vacuum state corresponding to the flat metric
spacetime.Comment: 15 pages, revised version to appear in Class. Quant. Gra
Indicators of Sustainability for Production and Biodiversity Conservation in Australian Rangelands
Disclinations, dislocations and continuous defects: a reappraisal
Disclinations, first observed in mesomorphic phases, are relevant to a number
of ill-ordered condensed matter media, with continuous symmetries or frustrated
order. They also appear in polycrystals at the edges of grain boundaries. They
are of limited interest in solid single crystals, where, owing to their large
elastic stresses, they mostly appear in close pairs of opposite signs. The
relaxation mechanisms associated with a disclination in its creation, motion,
change of shape, involve an interplay with continuous or quantized dislocations
and/or continuous disclinations. These are attached to the disclinations or are
akin to Nye's dislocation densities, well suited here. The notion of 'extended
Volterra process' takes these relaxation processes into account and covers
different situations where this interplay takes place. These concepts are
illustrated by applications in amorphous solids, mesomorphic phases and
frustrated media in their curved habit space. The powerful topological theory
of line defects only considers defects stable against relaxation processes
compatible with the structure considered. It can be seen as a simplified case
of the approach considered here, well suited for media of high plasticity
or/and complex structures. Topological stability cannot guarantee energetic
stability and sometimes cannot distinguish finer details of structure of
defects.Comment: 72 pages, 36 figure
Tunnel magnetoresistance and interfacial electronic state
We study the relation between tunnel magnetoresistance (TMR) and interfacial
electronic states modified by magnetic impurities introduced at the interface
of the ferromagnetic tunnel junctions, by making use of the periodic Anderson
model and the linear response theory. It is indicated that the TMR ratio is
strongly reduced depending on the position of the -levels of impurities,
based on reduction in the spin-dependent -electron tunneling in the majority
spin state. The results are compared with experimental results for Cr-dusted
ferromagnetic tunnel junctions, and also with results for metallic multilayers
for which similar reduction in giant magnetoresistance has been reported.Comment: 5 pages, 4 figures, 2 column revtex4 format, ICMFS 2002 (Kyoto
Untwisting of a Strained Cholesteric Elastomer by Disclination Loop Nucleation
The application of a sufficiently strong strain perpendicular to the pitch
axis of a monodomain cholesteric elastomer unwinds the cholesteric helix.
Previous theoretical analyses of this transition ignored the effects of Frank
elasticity which we include here. We find that the strain needed to unwind the
helix is reduced because of the Frank penalty and the cholesteric state becomes
metastable above the transition. We consider in detail a previously proposed
mechanism by which the topologically stable helical texture is removed in the
metastable state, namely by the nucleation of twist disclination loops in the
plane perpendicular to the pitch axis. We present an approximate calculation of
the barrier energy for this nucleation process which neglects possible spatial
variation of the strain fields in the elastomer, as well as a more accurate
calculation based on a finite element modeling of the elastomer.Comment: 12 pages, 9 figure
Casimir interaction between normal or superfluid grains in the Fermi sea
We report on a new force that acts on cavities (literally empty regions of
space) when they are immersed in a background of non-interacting fermionic
matter fields. The interaction follows from the obstructions to the (quantum
mechanical) motions of the fermions caused by the presence of bubbles or other
(heavy) particles in the Fermi sea, as, for example, nuclei in the neutron sea
in the inner crust of a neutron star or superfluid grains in a normal Fermi
liquid. The effect resembles the traditional Casimir interaction between
metallic mirrors in the vacuum. However, the fluctuating electromagnetic fields
are replaced by fermionic matter fields. We show that the fermionic Casimir
problem for a system of spherical cavities can be solved exactly, since the
calculation can be mapped onto a quantum mechanical billiard problem of a
point-particle scattered off a finite number of non-overlapping spheres or
disks. Finally we generalize the map method to other Casimir systems,
especially to the case of a fluctuating scalar field between two spheres or a
sphere and a plate under Dirichlet boundary conditions.Comment: 8 pages, 2 figures, submitted to the Proceedings of QFEXT'05,
Barcelona, Sept. 5-9, 200
Shear Modulus of an Elastic Solid under External Pressure as a function of Temperature: The case of Helium
The energy of a dislocation loop in a continuum elastic solid under pressure
is considered within the framework of classical mechanics. For a circular loop,
this is a function with a maximum at pressures that are well within reach of
experimental conditions for solid helium suggesting, in this case, that
dislocation loops can be generated by a pressure-assisted thermally activated
process. It is also pointed out that pinned dislocations segments can alter the
shear response of solid helium, by an amount consistent with current
measurements, without any unpinning.Comment: 5 pages, 3 figure
Fourier transform spectroscopy of d-wave quasiparticles in the presence of atomic scale pairing disorder
The local density of states power spectrum of optimally doped
BiSrCaCuO (BSCCO) has been interpreted in terms of
quasiparticle interference peaks corresponding to an "octet'' of scattering
wave vectors connecting k-points where the density of states is maximal. Until
now, theoretical treatments have not been able to reproduce the experimentally
observed weights and widths of these "octet'' peaks; in particular, the
predominance of the dispersing "q'' peak parallel to the Cu-O bond
directions has remained a mystery. In addition, such theories predict
"background'' features which are not observed experimentally. Here, we show
that most of the discrepancies can be resolved when a realistic model for the
out-of-plane disorder in BSCCO is used. Weak extended potential scatterers,
which are assumed to represent cation disorder, suppress large-momentum
features and broaden the low-energy "q''-peaks, whereas scattering at order
parameter variations, possibly caused by a dopant-modulated pair interaction
around interstitial oxygens, strongly enhances the dispersing "q''-peaks.Comment: 7 pages, 3 figure
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