Optimally Convergent Quantum Jump Expansion

A method for deriving accurate analytic approximations for Markovian open quantum systems was recently introduced in [F. Lucas and K. Hornberger, Phys. Rev. Lett. 110, 240401 (2013)]. Here, we present a detailed derivation of the underlying non-perturbative jump expansion, which involves an adaptive resummation to ensure optimal convergence. Applying this to a set of exemplary master equations, we find that the resummation typically leads to convergence within the lowest two to five orders. Besides facilitating analytic approximations, the optimal jump expansion thus provides a numerical scheme for the efficient simulation of open quantum systems.Comment: 13 pages, 3 figure

Adaptive Resummation of Markovian Quantum Dynamics

We introduce a method for obtaining analytic approximations to the evolution of Markovian open quantum systems. It is based on resumming a generalized Dyson series in a way that ensures optimal convergence even in the absence of a small parameter. The power of this approach is demonstrated by two benchmark examples: the spatial detection of a free particle and the Landau-Zener problem in the presence of dephasing. The derived approximations are asymptotically exact and exhibit errors on the per mil level over the entire parameter range.Comment: 5 pages, 2 figures - minor changes, typos correcte

Scheduling Monotone Moldable Jobs in Linear Time

A moldable job is a job that can be executed on an arbitrary number of processors, and whose processing time depends on the number of processors allotted to it. A moldable job is monotone if its work doesn't decrease for an increasing number of allotted processors. We consider the problem of scheduling monotone moldable jobs to minimize the makespan. We argue that for certain compact input encodings a polynomial algorithm has a running time polynomial in n and log(m), where n is the number of jobs and m is the number of machines. We describe how monotony of jobs can be used to counteract the increased problem complexity that arises from compact encodings, and give tight bounds on the approximability of the problem with compact encoding: it is NP-hard to solve optimally, but admits a PTAS. The main focus of this work are efficient approximation algorithms. We describe different techniques to exploit the monotony of the jobs for better running times, and present a (3/2+{\epsilon})-approximate algorithm whose running time is polynomial in log(m) and 1/{\epsilon}, and only linear in the number n of jobs

Catheter ablation of atrial fibrillation : radiofrequency catheter ablation for redo procedures after cryoablation

Aim: To evaluate the effectiveness of two different strategies using radiofrequency catheter ablation for redo procedures after cryoablation of atrial fibrillation. Methods: Thirty patients (paroxysmal atrial fibrillation: 22 patients, persistent atrial fibrillation: 8 patients) had to undergo a redo procedure after initially successful circumferential pulmonary vein (PV) isolation with the cryoballoon technique (Arctic Front Balloon, CryoCath Technologies/Medtronic). The redo ablation procedures were performed using a segmental approach or a circumferential ablation strategy (CARTO; Biosense Webster) depending on the intra-procedural findings. After discharge, patients were scheduled for repeated visits at the arrhythmia clinic. A 7-day Holter monitoring was performed at 3, 12 and 24 mo after the ablation procedure. Results: During the redo procedure, a mean number of 2.9 re-conducting pulmonary veins (SD ± 1.0 PVs) were detected (using a circular mapping catheter). In 20 patients, a segmental approach was sufficient to eliminate the residual pulmonary vein conduction because there were only a few recovered pulmonary vein fibres. In the remaining 10 patients, a circumferential ablation strategy was used because of a complete recovery of the PV-LA conduction. All recovered pulmonary veins could be isolated successfully again. At 2-year follow-up, 73.3% of all patients were free from an arrhythmia recurrence (22/30). There were no major complications. Conclusion: In patients with an initial circumferential pulmonary vein isolation using the cryoballoon technique, a repeat ablation procedure can be performed safely and effectively using radiofrequency catheter ablation

Content-Aware DataGuides for Indexing Large Collections of XML Documents

XML is well-suited for modelling structured data with textual content. However, most indexing approaches perform structure and content matching independently, combining the retrieved path and keyword occurrences in a third step. This paper shows that retrieval in XML documents can be accelerated significantly by processing text and structure simultaneously during all retrieval phases. To this end, the Content-Aware DataGuide (CADG) enhances the wellknown DataGuide with (1) simultaneous keyword and path matching and (2) a precomputed content/structure join. Extensive experiments prove the CADG to be 50-90% faster than the DataGuide for various sorts of query and document, including difficult cases such as poorly structured queries and recursive document paths. A new query classification scheme identifies precise query characteristics with a predominant influence on the performance of the individual indices. The experiments show that the CADG is applicable to many real-world applications, in particular large collections of heterogeneously structured XML documents