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 $Q_{\rm max} = n_b -1$. 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 ($Q-Q_{\rm int} \propto T^{2\alpha}$), or with the system size ($Q-Q_{\rm int} \propto L_s^{-2\alpha}$), where $\alpha$ is a measure of the interactions and vanishes at $T=0 ~(L_s=\infty)$. 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 $\mathscr{T}$ 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 $\mathscr{Z}$ of the trapped region as that part of $\mathscr{T}$ 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