Persistent current in superconducting nanorings

The superconductivity in very thin rings is suppressed by quantum phase slips. As a result the amplitude of the persistent current oscillations with flux becomes exponentially small, and their shape changes from sawtooth to a sinusoidal one. We reduce the problem of low-energy properties of a superconducting nanoring to that of a quantum particle in a sinusoidal potential and show that the dependence of the current on the flux belongs to a one-parameter family of functions obtained by solving the respective Schrodinger equation with twisted boundary conditions.Comment: 5 pages, 1 figur

Topological entropy of realistic quantum Hall wave functions

The entanglement entropy of the incompressible states of a realistic quantum Hall system are studied by direct diagonalization. The subdominant term to the area law, the topological entanglement entropy, which is believed to carry information about topologic order in the ground state, was extracted for filling factors 1/3, 1/5 and 5/2. The results for 1/3 and 1/5 are consistent with the topological entanglement entropy for the Laughlin wave function. The 5/2 state exhibits a topological entanglement entropy consistent with the Moore-Read wave function.Comment: 6 pages, 6 figures; improved computations and graphics; added reference

Anomalous Hall Effect in Ferromagnetic Semiconductors in the Hopping Transport Regime

We present a theory of the Anomalous Hall Effect (AHE) in ferromagnetic (Ga,Mn)As in the regime when conduction is due to phonon-assisted hopping of holes between localized states in the impurity band. We show that the microscopic origin of the anomalous Hall conductivity in this system can be attributed to a phase that a hole gains when hopping around closed-loop paths in the presence of spin-orbit interactions and background magnetization of the localized Mn moments. Mapping the problem to a random resistor network, we derive an analytic expression for the macroscopic anomalous Hall conductivity $\sigma_{xy}^{AH}$. We show that $\sigma_{xy}^{AH}$ is proportional to the first derivative of the density of states $\varrho(\epsilon)$ and thus can be expected to change sign as a function of impurity band filling. We also show that $\sigma_{xy}^{AH}$ depends on temperature as the longitudinal conductivity $\sigma_{xx}$ within logarithmic accuracy.Comment: 4 pages, 1 eps figure, final versio

Random Unitaries Give Quantum Expanders

We show that randomly choosing the matrices in a completely positive map from the unitary group gives a quantum expander. We consider Hermitian and non-Hermitian cases, and we provide asymptotically tight bounds in the Hermitian case on the typical value of the second largest eigenvalue. The key idea is the use of Schwinger-Dyson equations from lattice gauge theory to efficiently compute averages over the unitary group.Comment: 14 pages, 1 figur

Stochastic methods for solving high-dimensional partial differential equations

We propose algorithms for solving high-dimensional Partial Differential Equations (PDEs) that combine a probabilistic interpretation of PDEs, through Feynman-Kac representation, with sparse interpolation. Monte-Carlo methods and time-integration schemes are used to estimate pointwise evaluations of the solution of a PDE. We use a sequential control variates algorithm, where control variates are constructed based on successive approximations of the solution of the PDE. Two different algorithms are proposed, combining in different ways the sequential control variates algorithm and adaptive sparse interpolation. Numerical examples will illustrate the behavior of these algorithms

Use of Most Bothersome Symptom as a Coprimary Endpoint in Migraine Clinical Trials: A Post-Hoc Analysis of the Pivotal ZOTRIP Randomized, Controlled Trial.

ObjectiveTo better understand the utility of using pain freedom and most bothersome headache-associated symptom (MBS) freedom as co-primary endpoints in clinical trials of acute migraine interventions.BackgroundAdhesive dermally applied microarray (ADAM) is an investigational system for intracutaneous drug administration. The recently completed pivotal Phase 2b/3 study (ZOTRIP), evaluating ADAM zolmitriptan for the treatment of acute moderate to severe migraine, was one of the first large studies to incorporate MBS freedom and pain freedom as co-primary endpoints per recently issued guidance by the US Food and Drug Administration. In this trial, the proportion of patients treated with ADAM zolmitriptan 3.8 mg, who were pain-free and MBS-free at 2 hours post-dose, was significantly higher than for placebo.MethodsWe undertook a post-hoc analysis of data from the ZOTRIP trial to examine how the outcomes from this trial compare to what might have been achieved using the conventional co-primary endpoints of pain relief, nausea, photophobia, and phonophobia.ResultsOf the 159 patients treated with ADAM zolmitriptan 3.8 mg or placebo, prospectively designated MBS were photophobia (n = 79), phonophobia (n = 43), and nausea (n = 37). Two-hour pain free rates in those with photophobia as the MBS were 36% for ADAM zolmitriptan 3.8 mg and 14% for placebo (P = .02). Corresponding rates for those with phonophobia as the MBS were 14% and 41% (P = .05). For those whose MBS was nausea, corresponding values were 56% and 16%, respectively (P = .01). Two-hour freedom from the MBS for active drug vs placebo were 67% vs 35% (P < .01) for photophobia, 55% vs 43% (P = .45) for phonophobia, and 89% vs 58% for nausea (P = .04). MBS freedom but not pain freedom was achieved in 28%. Only 1 patient (1%) achieved pain freedom, but not MBS freedom. The proportion with both pain and MBS freedom was highest (56%) among those whose MBS was nausea.ConclusionIn this study, the use of MBS was feasible and seemed to compare favorably to the previously required 4 co-primary endpoints