Low frequency elastic measurements on solid 4^{4}He in Vycor using a torsional oscillator

Torsional oscillator experiments involving solid $^{4}$He confined in the nanoscale pores of Vycor glass showed anomalous frequency changes at temperatures below 200 mK. These were initially attributed to decoupling of some of the helium's mass from the oscillator, the expected signature of a supersolid. However, these and similar anomalous effects seen with bulk $^{4}$He now appear to be artifacts arising from large shear modulus changes when mobile dislocations are pinned by $^{3}$He impurities. We have used a torsional oscillator (TO) technique to directly measure the shear modulus of the solid $^{4}$He/Vycor system at a frequency (1.2 kHz) comparable to that used in previous TO experiments. The shear modulus increases gradually as the TO is cooled from 1 K to 20 mK. We attribute the gradual modulus change to the freezing out of thermally activated relaxation processes in the solid helium. The absence of rapid changes below 200 mK is expected since mobile dislocations could not exist in pores as small as those of Vycor. Our results support the interpretation of a recent torsional oscillator experiment that showed no anomaly when elastic effects in bulk helium were eliminated by ensuring that there were no gaps around the Vycor sample.Comment: Accepted by Journal of Low Temperature Physic

Dislocation networks in helium-4 crystals

The mechanical behavior of crystals is dominated by dislocation networks, their structure and their interactions with impurities or thermal phonons. However, in classical crystals, networks are usually random with impurities often forming non-equilibrium clusters when their motion freezes at low temperature. Helium provides unique advantages for the study of dislocations: crystals are free of all but isotopic impurities, the concentration of these can be reduced to the ppb level, and the impurities are mobile at all temperatures and therefore remain in equilibrium with the dislocations. We have achieved a comprehensive study of the mechanical response of 4He crystals to a driving strain as a function of temperature, frequency and strain amplitude. The quality of our fits to the complete set of data strongly supports our assumption of string-like vibrating dislocations. It leads to a precise determination of the distribution of dislocation network lengths and to detailed information about the interaction between dislocations and both thermal phonons and 3He impurities. The width of the dissipation peak associated with impurity binding is larger than predicted by a simple Debye model, and much of this broadening is due to the distribution of network lengths.Comment: accepted by Phys. Rev.

The symplectic origin of conformal and Minkowski superspaces

Supermanifolds provide a very natural ground to understand and handle supersymmetry from a geometric point of view; supersymmetry in $d=3,4,6$ and $10$ dimensions is also deeply related to the normed division algebras. In this paper we want to show the link between the conformal group and certain types of symplectic transformations over division algebras. Inspired by this observation we then propose a new\,realization of the real form of the 4 dimensional conformal and Minkowski superspaces we obtain, respectively, as a Lagrangian supermanifold over the twistor superspace $\mathbb{C}^{4|1}$ and a big cell inside it. The beauty of this approach is that it naturally generalizes to the 6 dimensional case (and possibly also to the 10 dimensional one) thus providing an elegant and uniform characterization of the conformal superspaces.Comment: 15 pages, references added, minor change

The volume of causal diamonds, asymptotically de Sitter space-times and irreversibility

In this note we prove that the volume of a causal diamond associated with an inertial observer in asymptotically de Sitter 4-dimensional space-time is monotonically increasing function of cosmological time. The asymptotic value of the volume is that of in maximally symmetric de Sitter space-time. The monotonic property of the volume is checked in two cases: in vacuum and in the presence of a massless scalar field. In vacuum, the volume flow (with respect to cosmological time) asymptotically vanishes if and only if future space-like infinity is 3-manifold of constant curvature. The volume flow thus represents irreversibility of asymptotic evolution in spacetimes with positive cosmological constant.Comment: 15 pages, no figures; v.2: conjecture 1 on p. 11 made more precise; version published in jhe

Coercivity and stability results for an extended Navier-Stokes system

In this article we study a system of equations that is known to {\em extend} Navier-Stokes dynamics in a well-posed manner to velocity fields that are not necessarily divergence-free. Our aim is to contribute to an understanding of the role of divergence and pressure in developing energy estimates capable of controlling the nonlinear terms. We address questions of global existence and stability in bounded domains with no-slip boundary conditions. Even in two space dimensions, global existence is open in general, and remains so, primarily due to the lack of a self-contained $L^2$ energy estimate. However, through use of new $H^1$ coercivity estimates for the linear equations, we establish a number of global existence and stability results, including results for small divergence and a time-discrete scheme. We also prove global existence in 2D for any initial data, provided sufficient divergence damping is included.Comment: 29 pages, no figure

Simulation of Asymptotically AdS5 Spacetimes with a Generalized Harmonic Evolution Scheme

Motivated by the gauge/gravity duality, we introduce a numerical scheme based on generalized harmonic evolution to solve the Einstein field equations on asymptotically anti-de Sitter (AdS) spacetimes. We work in global AdS5, which can be described by the (t,r,\chi,\theta,\phi) spherical coordinates adapted to the R{\times}S3 boundary. We focus on solutions that preserve an SO(3) symmetry that acts to rotate the 2-spheres parametrized by \theta,\phi. In the boundary conformal field theory (CFT), the way in which this symmetry manifests itself hinges on the way we choose to embed Minkowski space in R{\times}S3. We present results from an ongoing study of prompt black hole formation via scalar field collapse, and explore the subsequent quasi-normal ringdown. Beginning with initial data characterized by highly distorted apparent horizon geometries, the metrics quickly evolve, via quasi-normal ringdown, to equilibrium static black hole solutions at late times. The lowest angular number quasi-normal modes are consistent with the linear modes previously found in perturbative studies, whereas the higher angular modes are a combination of linear modes and of harmonics arising from non-linear mode-coupling. We extract the stress energy tensor of the dual CFT on the boundary, and find that despite being highly inhomogeneous initially, it nevertheless evolves from the outset in a manner that is consistent with a thermalized N=4 SYM fluid. As a first step towards closer contact with relativistic heavy ion collision physics, we map this solution to a Minkowski piece of the R{\times}S3 boundary, and obtain a corresponding fluid flow in Minkowski space

A classification of local Weyl invariants in D=8

Following a purely algebraic procedure, we provide an exhaustive classification of local Weyl-invariant scalar densities in dimension D=8.Comment: LaTeX, 19 pages, typos corrected, one reference adde

Holographic formula for the determinant of the scattering operator in thermal AdS

A 'holographic formula' expressing the functional determinant of the scattering operator in an asymptotically locally anti-de Sitter(ALAdS) space has been proposed in terms of a relative functional determinant of the scalar Laplacian in the bulk. It stems from considerations in AdS/CFT correspondence of a quantum correction to the partition function in the bulk and the corresponding subleading correction at large N on the boundary. In this paper we probe this prediction for a class of quotients of hyperbolic space by a discrete subgroup of isometries. We restrict to the simplest situation of an abelian group where the quotient geometry describes thermal AdS and also the non-spinning BTZ instanton. The bulk computation is explicitly done using the method of images and the answer can be encoded in a (Patterson-)Selberg zeta-function.Comment: 11 pages, published JPA versio

On Local Behavior of Holomorphic Functions Along Complex Submanifolds of C^N

In this paper we establish some general results on local behavior of holomorphic functions along complex submanifolds of \Co^{N}. As a corollary, we present multi-dimensional generalizations of an important result of Coman and Poletsky on Bernstein type inequalities on transcendental curves in \Co^{2}.Comment: minor changes in the formulation and the proof of Lemma 8.

Measuring frequency fluctuations in nonlinear nanomechanical resonators

Advances in nanomechanics within recent years have demonstrated an always expanding range of devices, from top-down structures to appealing bottom-up MoS$_2$ and graphene membranes, used for both sensing and component-oriented applications. One of the main concerns in all of these devices is frequency noise, which ultimately limits their applicability. This issue has attracted a lot of attention recently, and the origin of this noise remains elusive up to date. In this Letter we present a very simple technique to measure frequency noise in nonlinear mechanical devices, based on the presence of bistability. It is illustrated on silicon-nitride high-stress doubly-clamped beams, in a cryogenic environment. We report on the same $T/f$ dependence of the frequency noise power spectra as reported in the literature. But we also find unexpected {\it damping fluctuations}, amplified in the vicinity of the bifurcation points; this effect is clearly distinct from already reported nonlinear dephasing, and poses a fundamental limit on the measurement of bifurcation frequencies. The technique is further applied to the measurement of frequency noise as a function of mode number, within the same device. The relative frequency noise for the fundamental flexure $\delta f/f_0$ lies in the range $0.5 - 0.01~$ppm (consistent with literature for cryogenic MHz devices), and decreases with mode number in the range studied. The technique can be applied to {\it any types} of nano-mechanical structures, enabling progresses towards the understanding of intrinsic sources of noise in these devices.Comment: Published 7 may 201