Knot Complement Problem for L-space ZHS3\mathbb{Z} HS^3

In this paper we look at the knot complement problem for L-space $\mathbb{Z}$-homology spheres. We show that an L-space $\mathbb{Z}$-homology sphere $Y$ cannot be obtained as a non-trivial surgery along a knot $K\subset Y$. As a consequence, we prove that knots in an L-space $\mathbb{Z}$-homology sphere are determined by their complements.Comment: The comment after Theorem 1.2 has been corrected, the adjective irreducible has been added. "The Poincare sphere {\Sigma}(2, 3, 5) is the only known irreducible L-space Z-homology sphere apart from S^3.

See a Black Hole on a Shoestring

The modes of vibration of hanging and partially supported strings provide useful analogies to scalar fields travelling through spacetimes that admit conformally flat spatial sections. This wide class of spacetimes includes static, spherically symmetric spacetimes. The modes of a spacetime where the scale factor depends as a power-law on one of the coordinates provide a useful starting point and yield a new classification of these spacetimes on the basis of the shape of the string analogue. The family of corresponding strings follow a family of curves related to the cycloid, denoted here as hypercycloids (for reasons that will become apparent). Like the spacetimes that they emulate these strings exhibit horizons, typically at their bottommost points where the string tension vanishes; therefore, hanging strings may provide a new avenue for the exploration of the quantum mechanics of horizons.Comment: 5 pages, 1 figure, extensive changes to refect version accepted to PR

Vortex ring refraction at large Froude numbers

We have experimentally studied the impact of an initially planar axisymmetric vortex ring, incident at an oblique angle, upon a gravity-induced interface separating two fluids of differing densities. After impact, the vortex ring was found to exhibit a variety of subsequent trajectories, which we organize according to both the incidence angle, $\theta_i$, and the interface strength, defined as the ratio of the Atwood and Froude numbers, $A/F$. For grazing incidence angles ($\theta_i \gtrsim 70$ deg.) vortices either penetrate or reflect from the interface, depending on whether the interface is weak or strong. In some cases, reflected vortices execute damped oscillations before finally disintegrating. For smaller incidence angles ($\theta_i \lesssim 70$ deg.) vortices penetrate the interface. When there is a strong interface, these vortices are observed to curve back up toward the interface. When there is a weak interface, these vortices are observed to refract downward, away from the interface. The critical interface strength below which vortex ring refraction is observed is given by $\log_{10}{(A/F)}= -2.38 \pm 0.05$.Comment: 26 pages, 11 figures; Submitted to Physical Review

Phase synchronization from noisy univariate signals

We present methods for detecting phase synchronization of two unidirectionally coupled, self-sustained noisy oscillators from a signal of the driven oscillator alone. One method detects soft, another hard phase locking. Both are applied to the problem of detecting phase synchronization in von Karman vortex flow meters.Comment: 4 pages, 4 figure

NMR implementation of Quantum Delayed-Choice Experiment

We report the first experimental demonstration of quantum delayed-choice experiment via nuclear magnetic resonance techniques. An ensemble of molecules each with two spin-1/2 nuclei are used as target and the ancilla qubits to perform the quantum circuit corresponding the delayed-choice setup. As expected in theory, our experiments clearly demonstrate the continuous morphing of the target qubit between particle-like and wave-like behaviors. The experimental visibility of the interference patterns shows good agreement with the theory.Comment: Revised text, more figures adde

The time resolution of the St. Petersburg paradox

A resolution of the St. Petersburg paradox is presented. In contrast to the standard resolution, utility is not required. Instead, the time-average performance of the lottery is computed. The final result can be phrased mathematically identically to Daniel Bernoulli's resolution, which uses logarithmic utility, but is derived using a conceptually different argument. The advantage of the time resolution is the elimination of arbitrary utility functions.Comment: 20 pages, 1 figur

Controlling light-with-light without nonlinearity

According to Huygens' superposition principle, light beams traveling in a linear medium will pass though one another without mutual disturbance. Indeed, it is widely held that controlling light signals with light requires intense laser fields to facilitate beam interactions in nonlinear media, where the superposition principle can be broken. We demonstrate here that two coherent beams of light of arbitrarily low intensity can interact on a metamaterial layer of nanoscale thickness in such a way that one beam modulates the intensity of the other. We show that the interference of beams can eliminate the plasmonic Joule losses of light energy in the metamaterial or, in contrast, can lead to almost total absorbtion of light. Applications of this phenomenon may lie in ultrafast all-optical pulse-recovery devices, coherence filters and THz-bandwidth light-by-light modulators

Discretely guided electromagnetic effective medium

A material comprised of an array of subwavelength coaxial waveguides decomposes incident electromagnetic waves into spatially discrete wave components, propagates these components without frequency cut-off, and reassembles them on the far side of the material. The propagation of these wave components is fully controlled by the physical properties of the waveguides and their geometrical distribution in the array. This allows for an exceptional degree of control over the electromagnetic response of this effective medium, with numerous potential applications. With the development of nanoscale subwavelength coaxial waveguides, these applications (including metamaterial functionality) can be enabled in the visible frequency range