BACKGROUND It is unknown whether warfarin or aspirin therapy is superior for patients with heart failure who are in sinus rhythm. METHODS We designed this trial to determine whether warfarin (with a target international normalized ratio of 2.0 to 3.5) or aspirin (at a dose of 325 mg per day) is a better treatment for patients in sinus rhythm who have a reduced left ventricular ejection fraction (LVEF). We followed 2305 patients for up to 6 years (mean [±SD], 3.5±1.8). The primary outcome was the time to the first event in a composite end point of ischemic stroke, intracerebral hemorrhage, or death from any cause. RESULTS The rates of the primary outcome were 7.47 events per 100 patient-years in the warfarin group and 7.93 in the aspirin group (hazard ratio with warfarin, 0.93; 95% confidence interval [CI], 0.79 to 1.10; P = 0.40). Thus, there was no significant overall difference between the two treatments. In a time-varying analysis, the hazard ratio changed over time, slightly favoring warfarin over aspirin by the fourth year of follow-up, but this finding was only marginally significant (P = 0.046). Warfarin, as compared with aspirin, was associated with a significant reduction in the rate of ischemic stroke throughout the follow-up period (0.72 events per 100 patient-years vs. 1.36 per 100 patient-years; hazard ratio, 0.52; 95% CI, 0.33 to 0.82; P = 0.005). The rate of major hemorrhage was 1.78 events per 100 patient-years in the warfarin group as compared with 0.87 in the aspirin group (P<0.001). The rates of intracerebral and intracranial hemorrhage did not differ significantly between the two treatment groups (0.27 events per 100 patient-years with warfarin and 0.22 with aspirin, P = 0.82). CONCLUSIONS Among patients with reduced LVEF who were in sinus rhythm, there was no significant overall difference in the primary outcome between treatment with warfarin and treatment with aspirin. A reduced risk of ischemic stroke with warfarin was offset by an increased risk of major hemorrhage. The choice between warfarin and aspirin should be individualized.

Spin-triplet superfluids can support exotic objects, such as half-quantum vortices characterized by the nontrivial winding of the spin structure. We present cantilever magnetometry measurements performed on mesoscopic samples of Sr(2)RuO(4), a spin-triplet superconductor. With micrometer-sized annular-shaped samples, we observed transitions between integer fluxoid states as well as a regime characterized by "half-integer transitions"--steps in the magnetization with half the height of the ones we observed between integer fluxoid states. These half-height steps are consistent with the existence of half-quantum vortices in superconducting Sr(2)RuO(4).

In circuit QED, protocols for quantum gates and readout of superconducting qubits often rely on the dispersive regime, reached when the qubit-photon detuning ∆ is large compared to the mutual coupling strength. For qubits including the Cooper-pair box and transmon, selection rules dramatically restrict the contributions to dispersive level shifts χ. By contrast, in the absence of selection rules many virtual transitions contribute to χ and can produce sizable dispersive shifts even at large detuning. We present theory for a generic multi-level qudit capacitively coupled to one or multiple harmonic modes, and give general expressions for the effective Hamiltonian in second and fourth order perturbation theory. Applying our results to the fluxonium system, we show that the absence of strong selection rules explains the surprisingly large dispersive shifts observed in experiments and leads to the prediction of a two-photon vacuum Rabi splitting. Quantitative predictions from our theory are in good agreement with experimental data over a wide range of magnetic flux and reveal that fourth-order resonances are important for the phase modulation observed in fluxonium spectroscopy.

A recent theoretical proposal suggests that a simple circuit utilizing two superinductors may produce a qubit with ground-state degeneracy [Brooks, Phys. Rev. A 87, 052306 (2013)]. We perform a full circuit analysis along with exact diagonalization of the circuit Hamiltonian to elucidate the nature of the spectrum and low-lying wave functions of this 0-π device. We show that the ground-state degeneracy is robust to disorder in charge, flux, and critical current as well as insensitive to modest variations in the circuit parameters. Our treatment is nonperturbative, provides access to excited states and matrix elements, and is immediately applicable also to intermediate parameter regimes of experimental interest.

In this work, we present theoretical tools suitable for quantitative modeling of large superconducting circuits that include one-dimensional Josephson-junction arrays. The large number of low-energy degrees of freedom and the peculiar interactions between them induced by flux quantization present a considerable challenge to the detailed modeling of such circuits. For the concrete example of the fluxonium device, we show how to address this challenge. Starting from the complete degrees of freedom of the circuit, we employ the relevant collective modes and circuit symmetries to obtain a systematic approximation scheme. Important circuit symmetries include approximate invariance under the symmetric group and lead to considerable simplifications of the theory. Selection rules restrict the possible coupling among different collective modes and help explain the remarkable accuracy of previous simplified models. Using this strategy, we obtain new predictions for the energy spectrum of the fluxonium device that can be tested with current experimental technology.