Critical fluctuations of noisy period-doubling maps

We extend the theory of quasipotentials in dynamical systems by calculating, within a broad class of period-doubling maps, an exact potential for the critical fluctuations of pitchfork bifurcations in the weak noise limit. These far-from-equilibrium fluctuations are described by finite-size mean field theory, placing their static properties in the same universality class as the Ising model on a complete graph. We demonstrate that the effective system size of noisy period-doubling bifurcations exhibits universal scaling behavior along period-doubling routes to chaos.Comment: 11 pages, 5 figure

Does Music Therapy Decrease Anxiety Levels in Pre-operative Cesarean Section Patients?

Objective stated as follows: The objective of this selective EBM review is to determine whether or not music therapy decreases anxiety levels in pre-operative cesarean section patients. Study Design: A systematic review of 3 randomized controlled trials (RCT) published in 2012, 2012, and 2018; all in the English language. Data sources: All three RCT’s were from peer-reviewed journals, found on the PubMed database. These articles were chosen based on their relevance to the chosen topic and included patient-oriented outcomes. Outcome(s) Measured: Patient outcomes were measured using a Visual Analog scale (VAS), Mood State Scale, and the Zung Self Rating Anxiety Scale (SAS). All of the aforementioned are patient reported. Results: All three RCTs showed statistically significant improvement in anxiety levels in the experimental group after interventional music therapy. This was based on the patient reported scales with Kushnir et. Al showing a p-value \u3c0.01, Eren et al. with a p-value of \u3c0.002, and Li et al. with a p-value \u3c0.01 (Birth, vol. 39, no. 2, 2012, pp. 121–127., doi:10.1111/j.1523-536x.2012.00532.x.) (Journal of the College of Physicians and Surgeons Pakistan, vol. 28, no. 3, 2018, pp. 247–249., doi:10.29271/jcpsp.2018.03.247.) ( Obstetric Anesthesia Digest, vol. 33, no. 4, 2013, pp. 221–222. PubMed, doi:10.1097/01.aoa.0000436341.61510.7e.) The control groups in all three trials showed no real change in anxiety levels in the absence of musical intervention. Conclusions: This systemic review has concluded based on evidence from various studies that music therapy administered to cesarean section patients pre-operatively can effectively reduce anxiety levels. Based on its efficacy and ease of accessibility it should be further studied and considered as an acceptable first line conservative method or adjunct therapy to ease anxiety in these patients

Atom interferometry with Bose-Einstein condensates in a double-well potential

A trapped-atom interferometer was demonstrated using gaseous Bose-Einstein condensates coherently split by deforming an optical single-well potential into a double-well potential. The relative phase between the two condensates was determined from the spatial phase of the matter wave interference pattern formed upon releasing the condensates from the separated potential wells. Coherent phase evolution was observed for condensates held separated by 13 $\mu$m for up to 5 ms and was controlled by applying ac Stark shift potentials to either of the two separated condensates.Comment: 4 pages, 4 figure

Group Theory of Chiral Photonic Crystals with 4-fold Symmetry: Band Structure and S-Parameters of Eight-Fold Intergrown Gyroid Nets

The Single Gyroid, or srs, nanostructure has attracted interest as a circular-polarisation sensitive photonic material. We develop a group theoretical and scattering matrix method, applicable to any photonic crystal with symmetry I432, to demonstrate the remarkable chiral-optical properties of a generalised structure called 8-srs, obtained by intergrowth of eight equal-handed srs nets. Exploiting the presence of four-fold rotations, Bloch modes corresponding to the irreducible representations E- and E+ are identified as the sole and non-interacting transmission channels for right- and left-circularly polarised light, respectively. For plane waves incident on a finite slab of the 8-srs, the reflection rates for both circular polarisations are identical for all frequencies and transmission rates are identical up to a critical frequency below which scattering in the far field is restricted to zero grating order. Simulations show the optical activity of the lossless dielectric 8-srs to be large, comparable to metallic metamaterials, demonstrating its potential as a nanofabricated photonic material

Group Theory of Circular-Polarization Effects in Chiral Photonic Crystals with Four-Fold Rotation Axes, Applied to the Eight-Fold Intergrowth of Gyroid Nets

We use group or representation theory and scattering matrix calculations to derive analytical results for the band structure topology and the scattering parameters, applicable to any chiral photonic crystal with body-centered cubic symmetry I432 for circularly-polarised incident light. We demonstrate in particular that all bands along the cubic [100] direction can be identified with the irreducible representations E+/-,A and B of the C4 point group. E+ and E- modes represent the only transmission channels for plane waves with wave vector along the ? line, and can be identified as non-interacting transmission channels for right- (E-) and left-circularly polarised light (E+), respectively. Scattering matrix calculations provide explicit relationships for the transmission and reflectance amplitudes through a finite slab which guarantee equal transmission rates for both polarisations and vanishing ellipticity below a critical frequency, yet allowing for finite rotation of the polarisation plane. All results are verified numerically for the so-called 8-srs geometry, consisting of eight interwoven equal-handed dielectric Gyroid networks embedded in air. The combination of vanishing losses, vanishing ellipticity, near-perfect transmission and optical activity comparable to that of metallic meta-materials makes this geometry an attractive design for nanofabricated photonic materials

Distillation of Bose-Einstein condensates in a double-well potential

Bose-Einstein condensates of sodium atoms, prepared in an optical dipole trap, were distilled into a second empty dipole trap adjacent to the first one. The distillation was driven by thermal atoms spilling over the potential barrier separating the two wells and then forming a new condensate. This process serves as a model system for metastability in condensates, provides a test for quantum kinetic theories of condensate formation, and also represents a novel technique for creating or replenishing condensates in new locations

Dynamics and control of orbiting grid and the synchronously deployable beam

The dynamic analysis of a grid structure hung from the ceiling by two steel wires is described. The method of approach uses the discrete mass model system. The concept of the bifilar pendulum is used in writing the equation of motion. Assumptions are made with regard to the bar stiffnesses in the vertical and horizontal planes. The discrete mases are assumed to be connected by inextensible massless strings that do not provide any torsion or bending. The modal frequencies obtained by this method are compared with those obtained from the finite element model

Optical Weak Link between Two Spatially Separate Bose-Einstein Condensates

Two spatially separate Bose-Einstein condensates were prepared in an optical double-well potential. A bidirectional coupling between the two condensates was established by two pairs of Bragg beams which continuously outcoupled atoms in opposite directions. The atomic currents induced by the optical coupling depend on the relative phase of the two condensates and on an additional controllable coupling phase. This was observed through symmetric and antisymmetric correlations between the two outcoupled atom fluxes. A Josephson optical coupling of two condensates in a ring geometry is proposed. The continuous outcoupling method was used to monitor slow relative motions of two elongated condensates and characterize the trapping potential.Comment: 4 pages, 5 figure

Quantum reflection of atoms from a solid surface at normal incidence

We observed quantum reflection of ultracold atoms from the attractive potential of a solid surface. Extremely dilute Bose-Einstein condensates of ^{23}Na, with peak density 10^{11}-10^{12}atoms/cm^3, confined in a weak gravito-magnetic trap were normally incident on a silicon surface. Reflection probabilities of up to 20 % were observed for incident velocities of 1-8 mm/s. The velocity dependence agrees qualitatively with the prediction for quantum reflection from the attractive Casimir-Polder potential. Atoms confined in a harmonic trap divided in half by a solid surface exhibited extended lifetime due to quantum reflection from the surface, implying a reflection probability above 50 %.Comment: To appear in Phys. Rev. Lett. (December 2004)5 pages, 4 figure