Nonlinear dynamical tunneling of optical whispering gallery modes in the presence of a Kerr nonlinearity

The effect of a Kerr nonlinearity on dynamical tunneling is studied, using coupled whispering gallery modes in an optical microcavity. The model system that we have chosen is the 'add-drop filter', which comprises an optical microcavity and two waveguide coupled to the cavity. Due to the evanescent field's scattering on the waveguide, the whispering gallery modes in the microcavity form doublets, which manifest themselves as splittings in the spectrum. As these doublets can be regarded as a spectral feature of dynamical tunneling between two different dynamical states with a spatial overlap, the effect of a Kerr nonlinearity on the doublets is numerically investigated in the more general context of the relationship between cubic nonlinearity and dynamical tunneling. Within the numerical realization of the model system, it is observed that the doublets shows a bistable transition in its transmission curve as the Kerr-nonlinearity in the cavity is increased. At the same time, one rotational mode gets dominant over the other one in the transmission, since the two states in the doublet have uneven linewidths. By using coupled mode theory, the underlying mode dynamics of the phenomena is theoretically modelled and clarified.Comment: 7 pages, 5 figure

Faraday instability and subthreshold Faraday waves: surface waves emitted by walkers

A walker is a fluid entity comprising a bouncing droplet coupled to the waves that it generates at the surface of a vibrated bath. Thanks to this coupling, walkers exhibit a series of wave-particle features formerly thought to be exclusive to the quantum realm. In this paper, we derive a model of the Faraday surface waves generated by an impact upon a vertically vibrated liquid surface. We then particularise this theoretical framework to the case of forcing slightly below the Faraday instability threshold. Among others, this theory yields a rationale for the dependence of the wave amplitude to the phase of impact, as well as the characteristic timescale and length scale of viscous damping. The theory is validated with experiments of bead impact on a vibrated bath. We finally discuss implications of these results for the analogy between walkers and quantum particles

Average analytic rank of elliptic curves with prescribed torsion

We show that average analytic rank of elliptic curves with prescribed torsion $G$ is bounded for every torsion group $G$ under GRH for elliptic curve $L$-functions.Comment: Major revision: now we consider all possible torsion subgroup

Association of Retinal Vascular Caliber and Age-Related Macular Degeneration in Patients With the Acquired Immunodeficiency Syndrome.

PurposeTo evaluate the relationship between retinal vascular caliber and AMD in patients with AIDS.MethodsParticipants enrolled in the Longitudinal Study of the Ocular Complications of AIDS had retinal photographs taken at enrollment. Retinal vascular caliber (central retinal artery equivalent [CRAE] and central retinal vein equivalent [CRVE]) and intermediate-stage AMD were determined from these retinal photographs. Photographs were evaluated by graders at a centralized reading center, using the Age-Related Eye Disease Study grading system for AMD and semiautomated techniques for evaluating retinal vascular caliber.ResultsOf the 1171 participants evaluated, 110 (9.4%) had AMD and 1061 (90.6%) did not. Compared with participants without AMD, participants with AMD had larger mean CRAEs (151 ± 16 μm versus 147 ± 16 μm; P = 0.009) and mean CRVEs (228 ± 24 μm versus 223 ± 25 μm; P = 0.02). The unadjusted differences were: CRAE, 4.3 μm (95% confidence interval [CI] 1.1-7.5; P = 0.009) and CRVE, 5.5 μm (95% CI 0.7-10.3; P = 0.02). After adjustment for age, race/ethnicity, sex, human immunodeficiency syndrome (HIV) transmission category, smoking, enrollment and nadir CD4+ T cells, and enrollment and maximum HIV load, the differences between patients with and without AMD were as follows: CRAE, 5.4 μm (95% CI 2.3-8.5; P = 0.001) and CRVE, 6.0 μm (95% CI 1.4-10.6; P = 0.01).ConclusionsIn patients with AIDS, AMD is associated with greater retinal arteriolar and venular calibers, suggesting a role for shared pathogenic mechanisms, such as persistent systemic inflammation

Quantum Repeaters using Coherent-State Communication

We investigate quantum repeater protocols based upon atomic qubit-entanglement distribution through optical coherent-state communication. Various measurement schemes for an optical mode entangled with two spatially separated atomic qubits are considered in order to nonlocally prepare conditional two-qubit entangled states. In particular, generalized measurements for unambiguous state discrimination enable one to completely eliminate spin-flip errors in the resulting qubit states, as they would occur in a homodyne-based scheme due to the finite overlap of the optical states in phase space. As a result, by using weaker coherent states, high initial fidelities can still be achieved for larger repeater spacing, at the expense of lower entanglement generation rates. In this regime, the coherent-state-based protocols start resembling single-photon-based repeater schemes.Comment: 11 pages, 8 figure

Measurement Model-Based Prediction of Correlated Flaw Signal

The Center for NDE, Iowa State University, has developed an ultrasonic pulse compression system using Golay codes, and demonstrated the enhanced signal-to-noise ratios (SNR) in highly energy absorbent materials such as rubber, plastics, corks, and some composites. Recently, an attempt has been made to theoretically predict ultrasonic pulse compression (correlated) flaw signals (e.g., voids) using the ultrasonic measurement model developed earlier at the same university. Predictions were made by the use of long coded waveforms (Golay codes) as inputs to the measurement model instead of the spike pulse in conventional ultrasonics. The results were then compared with experimentally measured conventional ultrasonic flaw signals. The results indicated that the ultrasonic pulse compression flaw signals can be predicted as accurate as conventional ultrasonic signals. In addition, the equivalent pulse of the Golay codes (delta-like pulse) was also used as an input to the measurement model to predict the same flaw signal, and it was demonstrated that the Golay codes and the equivalent pulse produce effectively the same results although the signal processing methods are significantly different

Retrospektivität im Rigveda: Aorist und Perfekt

Der Aufsatz diskutiert das Zusammenspiel von induktiver und deduktiver Methode bei der Funktionsbestimmung grammatischer Kategorien und führt das vorgeschlagene Verfahren anhand der Analyse der Funktionen von Aorist und Perfekt an ausgewählten Textstellen des Rigveda vor. Ergebnis: Aorist wie Perfekt drücken im Rigveda die retrospektive Perspektive aus. Der Aorist focussiert aber enger. Er lässt den Rückblick auf mittelbare – akkumulierte oder in grauer Vorzeit liegende – Ursachen nicht zu, und er bezeichnet auch nur einen aktuellen, keinen langanhaltenden Folgezustand. Das Perfekt, das diesen weiten Focus besitzt, kann nur unter speziellen Bedingungen für den engen aoristischen Focus gebraucht werden