2,078 research outputs found
Effects of interaction on an adiabatic quantum electron pump
We study the effects of inter-electron interactions on the charge pumped
through an adiabatic quantum electron pump. The pumping is through a system of
barriers, whose heights are deformed adiabatically. (Weak) interaction effects
are introduced through a renormalisation group flow of the scattering matrices
and the pumped charge is shown to {\it always} approach a quantised value at
low temperatures or long length scales. The maximum value of the pumped charge
is set by the number of barriers and is given by . The
correlation between the transmission and the charge pumped is studied by seeing
how much of the transmission is enclosed by the pumping contour. The (integer)
value of the pumped charge at low temperatures is determined by the number of
transmission maxima enclosed by the pumping contour. The dissipation at finite
temperatures leading to the non-quantised values of the pumped charge scales as
a power law with the temperature (), or with
the system size (), where is a
measure of the interactions and vanishes at . For a double
barrier system, our result agrees with the quantisation of pumped charge seen
in Luttinger liquids.Comment: 9 pages, 9 figures, better quality figures available on request from
author
Embedding initial data for black hole collisions
We discuss isometric embedding diagrams for the visualization of initial data
for the problem of the head-on collision of two black holes. The problem of
constructing the embedding diagrams is explicitly presented for the best
studied initial data, the Misner geometry. We present a partial solution of the
embedding diagrams and discuss issues related to completing the solution.Comment: (27pp text, 11 figures
Constraints on Gauss-Bonnet Gravity in Dark Energy Cosmologies
Models with a scalar field coupled to the Gauss-Bonnet Lagrangian appear
naturally from Kaluza-Klein compactifications of pure higher-dimensional
gravity. We study linear, cosmological perturbations in the limits of weak
coupling and slow-roll, and derive simple expressions for the main observable
sub-horizon quantities: the anisotropic stress factor, the time-dependent
gravitational constant, and the matter perturbation growth factor. Using
present observational data, and assuming slow-roll for the dark energy field,
we find that the fraction of energy density associated with the coupled
Gauss-Bonnet term cannot exceed 15%. The bound should be treated with caution,
as there are significant uncertainies in the data used to obtain it. Even so,
it indicates that the future prospects for constraining the coupled
Gauss-Bonnet term with cosmological observations are encouraging.Comment: 15 pages. v3: extended analysis, conclusions change
Defects and boundary layers in non-Euclidean plates
We investigate the behavior of non-Euclidean plates with constant negative
Gaussian curvature using the F\"oppl-von K\'arm\'an reduced theory of
elasticity. Motivated by recent experimental results, we focus on annuli with a
periodic profile. We prove rigorous upper and lower bounds for the elastic
energy that scales like the thickness squared. In particular we show that are
only two types of global minimizers -- deformations that remain flat and saddle
shaped deformations with isolated regions of stretching near the edge of the
annulus. We also show that there exist local minimizers with a periodic profile
that have additional boundary layers near their lines of inflection. These
additional boundary layers are a new phenomenon in thin elastic sheets and are
necessary to regularize jump discontinuities in the azimuthal curvature across
lines of inflection. We rigorously derive scaling laws for the width of these
boundary layers as a function of the thickness of the sheet
Dynamics of ripple formation on silicon surfaces by ultrashort laser pulses in sub-ablation conditions
An investigation of ultrashort pulsed laser induced surface modification due
to conditions that result in a superheated melted liquid layer and material
evaporation are considered. To describe the surface modification occurring
after cooling and resolidification of the melted layer and understand the
underlying physical fundamental mechanisms, a unified model is presented to
account for crater and subwavelength ripple formation based on a synergy of
electron excitation and capillary waves solidification. The proposed
theoretical framework aims to address the laser-material interaction in
sub-ablation conditions and thus minimal mass removal in combination with a
hydrodynamics-based scenario of the crater creation and ripple formation
following surface irradiation with single and multiple pulses, respectively.
The development of the periodic structures is attributed to the interference of
the incident wave with a surface plasmon wave. Details of the surface
morphology attained are elaborated as a function of the imposed conditions and
results are tested against experimental data
Covariant coarse-graining of inhomogeneous dust flow in General Relativity
A new definition of coarse-grained quantities describing the dust flow in
General Relativity is proposed. It assigns the coarse--grained expansion, shear
and vorticity to finite-size comoving domains of fluid in a covariant,
coordinate-independent manner. The coarse--grained quantities are all
quasi-local functionals, depending only on the geometry of the boundary of the
considered domain. They can be thought of as relativistic generalizations of
simple volume averages of local quantities in a flat space. The procedure is
based on the isometric embedding theorem for S^2 surfaces and thus requires the
boundary of the domain in question to have spherical topology and positive
scalar curvature. We prove that in the limit of infinitesimally small volume
the proposed quantities reproduce the local expansion, shear and vorticity. In
case of irrotational flow we derive the time evolution for the coarse-grained
quantities and show that its structure is very similar to the evolution
equation for their local counterparts. Additional terms appearing in it may
serve as a measure of the backreacton of small-scale inhomogeneities of the
flow on the large-scale motion of the fluid inside the domain and therefore the
result may be interesting in the context of the cosmological backreaction
problem. We also consider the application of the proposed coarse-graining
procedure to a number of known exact solutions of Einstein equations with dust
and show that it yields reasonable results.Comment: 17 pages, 5 figures. Version accepted in Classical and Quantum
Gravity
Nietzschean modes of gender construction in a post-feminist age
An arrogance of certainty besets discourses of gender in today’s culture, and denigrating as well as overly affirming accounts of masculinity leave theindividual man at risk of either self-loathing or self-aggrandizing. This article will look at various lay accounts of masculinity and the dynamics of itsconstruction in opposition to culturally dominant moral codes, and will interrogate the underlying philosophical positions at work through Nietzsche’s Genealogy of Morality. In doing so, we propose that it is helpful to see Nietzsche as an early philosopher of difference, and embrace a less fixed approach to ontologies of gender accordingly
Mean curvature flow and quasilocal mass for two-surfaces in Hamiltonian General Relativity
A family of quasilocal mass definitions that includes as special cases the
Hawking mass and the Brown-York ``rest mass'' energy is derived for spacelike
2-surfaces in spacetime. The definitions involve an integral of powers of the
norm of the spacetime mean curvature vector of the 2-surface, whose properties
are connected with apparent horizons. In particular, for any spacelike
2-surface, the direction of mean curvature is orthogonal (dual in the normal
space) to a unique normal direction in which the 2-surface has vanishing
expansion in spacetime. The quasilocal mass definitions are obtained by an
analysis of boundary terms arising in the gravitational ADM Hamiltonian on
hypersurfaces with a spacelike 2-surface boundary, using a geometric time-flow
chosen proportional to the dualized mean curvature vector field at the boundary
surface. A similar analysis is made choosing a geometric rotational flow given
in terms of the twist covector of the dual pair of mean curvature vector
fields, which leads to a family of quasilocal angular momentum definitions
involving the squared norm of the twist. The large sphere limit of these
definitions is shown to yield the ADM mass and angular momentum in
asymptotically flat spacetimes, while at apparent horizons a quasilocal version
of the Gibbons-Penrose inequality is derived. Finally, some results concerning
positivity are proved for the quasilocal masses, motivated by consideration of
spacelike mean curvature flow of 2-surfaces in spacetime.Comment: Revised version, includes an analysis of null flows with applications
to mass and angular momentum for apparent horizon
Fermi-Walker gauge in 2+1 dimensional gravity.
It is shown that the Fermi-Walker gauge allows the general solution of
determining the metric given the sources, in terms of simple quadratures. We
treat the general stationary problem providing explicit solving formulas for
the metric and explicit support conditions for the energy momentum tensor. The
same type of solution is obtained for the time dependent problem with circular
symmetry. In both cases the solutions are classified in terms of the invariants
of the Wilson loops outside the sources. The Fermi-Walker gauge, due to its
physical nature, allows to exploit the weak energy condition and in this
connection it is proved that, both for open and closed universes with
rotational invariance, the energy condition imply the total absence of closed
time like curves. The extension of this theorem to the general stationary
problem, in absence of rotational symmetry is considered. At present such
extension is subject to some assumptions on the behavior of the determinant of
the dreibein in this gauge. PACS number: 0420Comment: 28 pages, RevTex, no figure
The region with trapped surfaces in spherical symmetry, its core, and their boundaries
We consider the region in spacetime containing future-trapped
closed surfaces and its boundary \B, and derive some of their general
properties. We then concentrate on the case of spherical symmetry, but the
methods we use are general and applicable to other situations. We argue that
closed trapped surfaces have a non-local property, "clairvoyance", which is
inherited by \B. We prove that \B is not a marginally trapped tube in
general, and that it can have portions in regions whose whole past is flat. For
asymptotically flat black holes, we identify a general past barrier, well
inside the event horizon, to the location of \B under physically reasonable
conditions. We also define the core of the trapped region as that
part of which is indispensable to sustain closed trapped
surfaces. We prove that the unique spherically symmetric dynamical horizon is
the boundary of such a core, and we argue that this may serve to single it out.
To illustrate the results, some explicit examples are discussed, namely
Robertson-Walker geometries and the imploding Vaidya spacetime.Comment: 70 pages, 14 figures. Figure 6 has been replaced, and corrected.
Minor changes around Propositions 10.3 and 10.4, and some typos correcte
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