Critical Behavior of the Schwinger Model with Wilson Fermions

We present a detailed analysis, in the framework of the MFA approach, of the critical behaviour of the lattice Schwinger model with Wilson fermions on lattices up to $24^2$, through the study of the Lee-Yang zeros and the specific heat. We find compelling evidence for a critical line ending at $\kappa = 0.25$ at large $\beta$. Finite size scaling analysis on lattices $8^2,12^2,16^2, 20^2$ and $24^2$ indicates a continuous transition. The hyperscaling relation is verified in the explored $\beta$ region.Comment: 12 pages LaTeX file, 10 figures in one uuencoded compressed postscript file. Report LNF-95/049(P

Radiation from the non-extremal fuzzball

The fuzzball proposal says that the information of the black hole state is distributed throughout the interior of the horizon in a `quantum fuzz'. There are special microstates where in the dual CFT we have `many excitations in the same state'; these are described by regular classical geometries without horizons. Jejjala et.al constructed non-extremal regular geometries of this type. Cardoso et. al then found that these geometries had a classical instability. In this paper we show that the energy radiated through the unstable modes is exactly the Hawking radiation for these microstates. We do this by (i) starting with the semiclassical Hawking radiation rate (ii) using it to find the emission vertex in the CFT (iii) replacing the Boltzman distributions of the generic CFT state with the ones describing the microstate of interest (iv) observing that the emission now reproduces the classical instability. Because the CFT has `many excitations in the same state' we get the physics of a Bose-Einstein condensate rather than a thermal gas, and the usually slow Hawking emission increases, by Bose enhancement, to a classically radiated field. This system therefore provides a complete gravity description of information-carrying radiation from a special microstate of the nonextremal hole.Comment: corrected typo

Calculation of the unitary part of the Bures measure for N-level quantum systems

We use the canonical coset parameterization and provide a formula with the unitary part of the Bures measure for non-degenerate systems in terms of the product of even Euclidean balls. This formula is shown to be consistent with the sampling of random states through the generation of random unitary matrices

Route Planning in Transportation Networks

We survey recent advances in algorithms for route planning in transportation networks. For road networks, we show that one can compute driving directions in milliseconds or less even at continental scale. A variety of techniques provide different trade-offs between preprocessing effort, space requirements, and query time. Some algorithms can answer queries in a fraction of a microsecond, while others can deal efficiently with real-time traffic. Journey planning on public transportation systems, although conceptually similar, is a significantly harder problem due to its inherent time-dependent and multicriteria nature. Although exact algorithms are fast enough for interactive queries on metropolitan transit systems, dealing with continent-sized instances requires simplifications or heavy preprocessing. The multimodal route planning problem, which seeks journeys combining schedule-based transportation (buses, trains) with unrestricted modes (walking, driving), is even harder, relying on approximate solutions even for metropolitan inputs.Comment: This is an updated version of the technical report MSR-TR-2014-4, previously published by Microsoft Research. This work was mostly done while the authors Daniel Delling, Andrew Goldberg, and Renato F. Werneck were at Microsoft Research Silicon Valle

One machine, one minute, three billion tetrahedra

This paper presents a new scalable parallelization scheme to generate the 3D Delaunay triangulation of a given set of points. Our first contribution is an efficient serial implementation of the incremental Delaunay insertion algorithm. A simple dedicated data structure, an efficient sorting of the points and the optimization of the insertion algorithm have permitted to accelerate reference implementations by a factor three. Our second contribution is a multi-threaded version of the Delaunay kernel that is able to concurrently insert vertices. Moore curve coordinates are used to partition the point set, avoiding heavy synchronization overheads. Conflicts are managed by modifying the partitions with a simple rescaling of the space-filling curve. The performances of our implementation have been measured on three different processors, an Intel core-i7, an Intel Xeon Phi and an AMD EPYC, on which we have been able to compute 3 billion tetrahedra in 53 seconds. This corresponds to a generation rate of over 55 million tetrahedra per second. We finally show how this very efficient parallel Delaunay triangulation can be integrated in a Delaunay refinement mesh generator which takes as input the triangulated surface boundary of the volume to mesh