Observations of the binary pulsar system PSR B1718-19 -- The Role of Tidal Circularisation

We present optical and infrared observations taken with the Very Large Telescope of the eclipsing binary pulsar system PSR B1718-19. The candidate companion of the pulsar, identified earlier in Hubble Space Telescope observations, has been detected in all three bands, R, I, and J. These detections allowed us to derive constraints on temperature, radius, and mass, pointing to a companion that has expanded to a radius between one of a main sequence star and one at the Roche-limit. We focus on the role of tidal circularisation in the system, which will have transformed the initially eccentric orbit expected from formation scenarios into the nearly circular orbit presently observed. Based on simple energy balance arguments, we are able to draw a picture of the companion's evolution resulting from the energy deposition in the star due to circularisation. In this picture, our measurement of the companion's parameters is consistent with the expected initial eccentricity. However, with the present understanding of tidal dissipation it remains difficult to account for the short time in which the system was circularised.Comment: 10 pages, 6 figures, accepted for publication in Astronomy and Astrophysic

Scaling regimes and critical dimensions in the Kardar-Parisi-Zhang problem

We study the scaling regimes for the Kardar-Parisi-Zhang equation with noise correlator R(q) ~ (1 + w q^{-2 \rho}) in Fourier space, as a function of \rho and the spatial dimension d. By means of a stochastic Cole-Hopf transformation, the critical and correction-to-scaling exponents at the roughening transition are determined to all orders in a (d - d_c) expansion. We also argue that there is a intriguing possibility that the rough phases above and below the lower critical dimension d_c = 2 (1 + \rho) are genuinely different which could lead to a re-interpretation of results in the literature.Comment: Latex, 7 pages, eps files for two figures as well as Europhys. Lett. style files included; slightly expanded reincarnatio

Correlation of eigenstates in the critical regime of quantum Hall systems

We extend the multifractal analysis of the statistics of critical wave functions in quantum Hall systems by calculating numerically the correlations of local amplitudes corresponding to eigenstates at two different energies. Our results confirm multifractal scaling relations which are different from those occurring in conventional critical phenomena. The critical exponent corresponding to the typical amplitude, $\alpha_0\approx 2.28$, gives an almost complete characterization of the critical behavior of eigenstates, including correlations. Our results support the interpretation of the local density of states being an order parameter of the Anderson transition.Comment: 17 pages, 9 Postscript figure

On Lerch's transcendent and the Gaussian random walk

Let $X_1,X_2,...$ be independent variables, each having a normal distribution with negative mean $-\beta<0$ and variance 1. We consider the partial sums $S_n=X_1+...+X_n$, with $S_0=0$, and refer to the process $\{S_n:n\geq0\}$ as the Gaussian random walk. We present explicit expressions for the mean and variance of the maximum $M=\max\{S_n:n\geq0\}.$ These expressions are in terms of Taylor series about $\beta=0$ with coefficients that involve the Riemann zeta function. Our results extend Kingman's first-order approximation [Proc. Symp. on Congestion Theory (1965) 137--169] of the mean for $\beta\downarrow0$. We build upon the work of Chang and Peres [Ann. Probab. 25 (1997) 787--802], and use Bateman's formulas on Lerch's transcendent and Euler--Maclaurin summation as key ingredients.Comment: Published at http://dx.doi.org/10.1214/105051606000000781 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Short- and long-term experience in pulmonary vein segmental ostial ablation for paroxysmal atrial fibrillation*

Introduction: Segmental ostial pulmonary vein isolation (PVI) is considered a potentially curative therapeutic approach in the treatment of paroxysmal atrial fibrillation (PAF). There is only limited data available on the long-term effect of this procedure. Methods: Patients (Pts) underwent a regular clinical follow up visit at 3, 6 and 24 months after PVI. Clinical success was classified as complete (i.e. no arrhythmia recurrences, no antiarrhythmic drug), partial (i.e. no/only few recurrences, on drug) or as a failure (no benefit). The clinical responder rate (CRR) was determined by combining complete and partial success. Results: 117 patients (96 male, 21 female), aged 51±11 years (range 25 to 73) underwent a total of 166 procedures (1.4/patient) in 2-4 pulmonary veins (PV). 115 patients (98%) had AF, 2 patients presented with regular PV atrial tachycardia. ,109/115 patients. exhibited PAF as the primary arrhythmia (versus persistent AF). A total of 113 patients with PVI in the years 2001 to 2003 were evaluated for their CRR after 6 (3) months. A single intervention was carried out in 63 patients (55.8%), two interventions were performed in 45 patients (39.8%) and three interventions in 5 patients (4.4%). The clinical response demonstrated a complete success of 52% (59 patients), a partial success of 26% (29 patients) and a failure rate of 22% (25 patients), leading to a CRR of 78% (88 patients). Ostial PVI in all 4 PVs exhibited a tendency towards higher curative success rates (54% versus 44% in patients with 3 PVs ablated for the 6 month follow up). Long-term clinical outcome was evaluated in 39 patients with an ablation attempt at 3 PVs only (excluding the right inferior PV in our early experience) and a mean clinical follow up of 21±6 months. At this point in time the success rate was 41% (complete, 16 patients) and 21% (partial, 8 patients), respectively, adding up to a CRR of 62% (24 patients). In total, 20 patients (17.1%) had either a single or 2 (3 patients, 2.6%) complications independent of the number of procedures performed with PV stenosis as the leading cause (7.7%). Conclusion: The CRR of patients with medical refractory PAF in our patient cohort is 78% at the 6 month follow up. PV stenosis is the main cause for procedure-related complications. Ablation of all 4 PV exhibits a tendency towards higher complete success rates despite equal CRR. Calculation of the clinical response after a mid- to long-term follow of 21±6 months in those patients with an ostial PVI in only 3 pulmonary veins (sparing the right inferior PV) shows a further reduction to 62%, exclusively caused by a drop in patients with a former partial success. To evaluate the long-term clinical benefit of segmental ostial PVI in comparison with other ablation techniques, more extended follow up periods are mandatory, including a larger study cohort and a detailed description of procedural parameters

Finite-size scaling of directed percolation above the upper critical dimension

We consider analytically as well as numerically the finite-size scaling behavior in the stationary state near the non-equilibrium phase transition of directed percolation within the mean field regime, i.e., above the upper critical dimension. Analogous to equilibrium, usual finite-size scaling is valid below the upper critical dimension, whereas it fails above. Performing a momentum analysis of associated path integrals we derive modified finite-size scaling forms of the order parameter and its higher moments. The results are confirmed by numerical simulations of corresponding high-dimensional lattice models.Comment: 4 pages, one figur

Casimir Energy for a Wedge with Three Surfaces and for a Pyramidal Cavity

Casimir energy calculations for the conformally coupled massless scalar field for a wedge defined by three intersecting planes and for a pyramid with four triangular surfaces are presented. The group generated by reflections are employed in the formulation of the required Green functions and the wave functions.Comment: Latex, 9 page