Bowen Measure From Heteroclinic Points

We present a new construction of the entropy-maximizing, invariant probability measure on a Smale space (the Bowen measure). Our construction is based on points that are unstably equivalent to one given point, and stably equivalent to another: heteroclinic points. The spirit of the construction is similar to Bowen's construction from periodic points, though the techniques are very different. We also prove results about the growth rate of certain sets of heteroclinic points, and about the stable and unstable components of the Bowen measure. The approach we take is to prove results through direct computation for the case of a Shift of Finite type, and then use resolving factor maps to extend the results to more general Smale spaces

Laser cooling and control of excitations in superfluid helium

Superfluidity is an emergent quantum phenomenon which arises due to strong interactions between elementary excitations in liquid helium. These excitations have been probed with great success using techniques such as neutron and light scattering. However measurements to-date have been limited, quite generally, to average properties of bulk superfluid or the driven response far out of thermal equilibrium. Here, we use cavity optomechanics to probe the thermodynamics of superfluid excitations in real-time. Furthermore, strong light-matter interactions allow both laser cooling and amplification of the thermal motion. This provides a new tool to understand and control the microscopic behaviour of superfluids, including phonon-phonon interactions, quantised vortices and two-dimensional quantum phenomena such as the Berezinskii-Kosterlitz-Thouless transition. The third sound modes studied here also offer a pathway towards quantum optomechanics with thin superfluid films, including femtogram effective masses, high mechanical quality factors, strong phonon-phonon and phonon-vortex interactions, and self-assembly into complex geometries with sub-nanometre feature size.Comment: 6 pages, 4 figures. Supplementary information attache

Microphotonic Forces From Superfluid Flow

In cavity optomechanics, radiation pressure and photothermal forces are widely utilized to cool and control micromechanical motion, with applications ranging from precision sensing and quantum information to fundamental science. Here, we realize an alternative approach to optical forcing based on superfluid flow and evaporation in response to optical heating. We demonstrate optical forcing of the motion of a cryogenic microtoroidal resonator at a level of 1.46 nN, roughly one order of magnitude larger than the radiation pressure force. We use this force to feedback cool the motion of a microtoroid mechanical mode to 137 mK. The photoconvective forces demonstrated here provide a new tool for high bandwidth control of mechanical motion in cryogenic conditions, and have the potential to allow efficient transfer of electromagnetic energy to motional kinetic energy.Comment: 5 pages, 6 figure

Subset currents on free groups

We introduce and study the space of \emph{subset currents} on the free group $F_N$. A subset current on $F_N$ is a positive $F_N$-invariant locally finite Borel measure on the space $\mathfrak C_N$ of all closed subsets of $\partial F_N$ consisting of at least two points. While ordinary geodesic currents generalize conjugacy classes of nontrivial group elements, a subset current is a measure-theoretic generalization of the conjugacy class of a nontrivial finitely generated subgroup in $F_N$, and, more generally, in a word-hyperbolic group. The concept of a subset current is related to the notion of an "invariant random subgroup" with respect to some conjugacy-invariant probability measure on the space of closed subgroups of a topological group. If we fix a free basis $A$ of $F_N$, a subset current may also be viewed as an $F_N$-invariant measure on a "branching" analog of the geodesic flow space for $F_N$, whose elements are infinite subtrees (rather than just geodesic lines) of the Cayley graph of $F_N$ with respect to $A$.Comment: updated version; to appear in Geometriae Dedicat

The Dust Content of Galaxy Clusters

We report on the detection of reddening toward z ~ 0.2 galaxy clusters. This is measured by correlating the Sloan Digital Sky Survey cluster and quasar catalogs and by comparing the photometric and spectroscopic properties of quasars behind the clusters to those in the field. We find mean E(B-V) values of a few times 10^-3 mag for sight lines passing ~Mpc from the clusters' center. The reddening curve is typical of dust but cannot be used to distinguish between different dust types. The radial dependence of the extinction is shallow near the cluster center suggesting that most of the detected dust lies at the outskirts of the clusters. Gravitational magnification of background z ~ 1.7 sources seen on Mpc (projected) scales around the clusters is found to be of order a few per cent, in qualitative agreement with theoretical predictions. Contamination by different spectral properties of the lensed quasar population is unlikely but cannot be excluded.Comment: 4 pages, 3 figure

Cavity Optomechanical Magnetometer

A cavity optomechanical magnetometer is demonstrated where the magnetic field induced expansion of a magnetostrictive material is transduced onto the physical structure of a highly compliant optical microresonator. The resulting motion is read out optically with ultra-high sensitivity. Detecting the magnetostrictive deformation of Terfenol-D with a toroidal whispering gallery mode (TWGM) resonator a peak sensitivity of 400 nT/Hz^.5 was achieved with theoretical modelling predicting that sensitivities of up to 500 fT/Hz^.5 may be possible. This chip-based magnetometer combines high-sensitivity and large dynamic range with small size and room temperature operation

Crystal truncation rods in kinematical and dynamical x-ray diffraction theories

Crystal truncation rods calculated in the kinematical approximation are shown to quantitatively agree with the sum of the diffracted waves obtained in the two-beam dynamical calculations for different reflections along the rod. The choice and the number of these reflections are specified. The agreement extends down to at least $\sim 10^{-7}$ of the peak intensity. For lower intensities, the accuracy of dynamical calculations is limited by truncation of the electron density at a mathematically planar surface, arising from the Fourier series expansion of the crystal polarizability

Dietary patterns and non-communicable disease risk in Indian adults : secondary analysis of Indian Migration Study data

Acknowledgements The authors thank the IMS study team members and field staff involved in the generation and processing of IMS data. Financial support: This study forms part of the Sustainable and Healthy Diets in India (SAHDI) project supported by the Wellcome Trust ‘Our Planet, Our Health’ programme (grant number 103932). The Wellcome Trust had no role in the design, analysis or writing of this article. The IMS was funded by Wellcome Trust (grant number GR070797MF). L.A.’s PhD studentship is funded by the Leverhulme Centre for Integrative Research on Agriculture and Health (LCIRAH).Peer reviewedPublisher PD