The origin of phase in the interference of Bose-Einstein condensates

We consider the interference of two overlapping ideal Bose-Einstein condensates. The usual description of this phenomenon involves the introduction of a so-called condensate wave functions having a definite phase. We investigate the origin of this phase and the theoretical basis of treating interference. It is possible to construct a phase state, for which the particle number is uncertain, but phase is known. However, how one would prepare such a state before an experiment is not obvious. We show that a phase can also arise from experiments using condensates in Fock states, that is, having known particle numbers. Analysis of measurements in such states also gives us a prescription for preparing phase states. The connection of this procedure to questions of ``spontaneously broken gauge symmetry'' and to ``hidden variables'' is mentioned.Comment: 22 pages 4 figure

Electronic structure of strongly correlated d-wave superconductors

We study the electronic structure of a strongly correlated d-wave superconducting state. Combining a renormalized mean field theory with direct calculation of matrix elements, we obtain explicit analytical results for the nodal Fermi velocity, v_F, the Fermi wave vector, k_F, and the momentum distribution, n_k, as a function of hole doping in a Gutzwiller projected d-wave superconductor. We calculate the energy dispersion, E_k, and spectral weight of the Gutzwiller-Bogoliubov quasiparticles, and find that the spectral weight associated with the quasiparticle excitation at the antinodal point shows a non monotonic behavior as a function of doping. Results are compared to angle resolved photoemission spectroscopy (ARPES) of the high temperature superconductors.Comment: final version, comparison to experiments added, 4+ pages, 4 figure

Generic Connectivity-Based CGRA Mapping via Integer Linear Programming

Coarse-grained reconfigurable architectures (CGRAs) are programmable logic devices with large coarse-grained ALU-like logic blocks, and multi-bit datapath-style routing. CGRAs often have relatively restricted data routing networks, so they attract CAD mapping tools that use exact methods, such as Integer Linear Programming (ILP). However, tools that target general architectures must use large constraint systems to fully describe an architecture's flexibility, resulting in lengthy run-times. In this paper, we propose to derive connectivity information from an otherwise generic device model, and use this to create simpler ILPs, which we combine in an iterative schedule and retain most of the exactness of a fully-generic ILP approach. This new approach has a speed-up geometric mean of 5.88x when considering benchmarks that do not hit a time-limit of 7.5 hours on the fully-generic ILP, and 37.6x otherwise. This was measured using the set of benchmarks used to originally evaluate the fully-generic approach and several more benchmarks representing computation tasks, over three different CGRA architectures. All run-times of the new approach are less than 20 minutes, with 90th percentile time of 410 seconds. The proposed mapping techniques are integrated into, and evaluated using the open-source CGRA-ME architecture modelling and exploration framework.Comment: 8 pages of content; 8 figures; 3 tables; to appear in FCCM 2019; Uses the CGRA-ME framework at http://cgra-me.ece.utoronto.ca

Research pressure instrumentation for NASA space shuttle main engine

The breadboard feasibility model of a silicon piezoresistive pressure transducer suitable for space shuttle main engine (SSME) applications was demonstrated. The development of pressure instrumentation for the SSME was examined. The objective is to develop prototype pressure transducers which are targeted to meet the SSME performance design goals and to fabricate, test and deliver a total of 10 prototype units. Effective utilization of the many advantages of silicon piezoresistive strain sensing technology to achieve the objectives of advanced state-of-the-art pressure sensors for reliability, accuracy and ease of manufacture is analyzed. Integration of multiple functions on a single chip is the key attribute of the technology

Research pressure instrumentation for NASA Space Shuttle main engine, modification no. 5

The advantages of silicon piezoresistive strain sensing technology are being used to achieve the objectives of state of the art pressure sensors for SSME applications. The integration of multiple functions on a single chip is the key attribute being exploited. Progress is reported in transducer packaging and materials; silicon resistor characterization at cryogenic temperatures; chip mounting; and frequency response optimization

Ignorance is Almost Bliss: Near-Optimal Stochastic Matching With Few Queries

The stochastic matching problem deals with finding a maximum matching in a graph whose edges are unknown but can be accessed via queries. This is a special case of stochastic $k$-set packing, where the problem is to find a maximum packing of sets, each of which exists with some probability. In this paper, we provide edge and set query algorithms for these two problems, respectively, that provably achieve some fraction of the omniscient optimal solution. Our main theoretical result for the stochastic matching (i.e., $2$-set packing) problem is the design of an \emph{adaptive} algorithm that queries only a constant number of edges per vertex and achieves a $(1-\epsilon)$ fraction of the omniscient optimal solution, for an arbitrarily small $\epsilon>0$. Moreover, this adaptive algorithm performs the queries in only a constant number of rounds. We complement this result with a \emph{non-adaptive} (i.e., one round of queries) algorithm that achieves a $(0.5 - \epsilon)$ fraction of the omniscient optimum. We also extend both our results to stochastic $k$-set packing by designing an adaptive algorithm that achieves a $(\frac{2}{k} - \epsilon)$ fraction of the omniscient optimal solution, again with only $O(1)$ queries per element. This guarantee is close to the best known polynomial-time approximation ratio of $\frac{3}{k+1} -\epsilon$ for the \emph{deterministic} $k$-set packing problem [Furer and Yu, 2013] We empirically explore the application of (adaptations of) these algorithms to the kidney exchange problem, where patients with end-stage renal failure swap willing but incompatible donors. We show on both generated data and on real data from the first 169 match runs of the UNOS nationwide kidney exchange that even a very small number of non-adaptive edge queries per vertex results in large gains in expected successful matches

Research pressure instrumentation for NASA Space Shuttle main engine, modification no. 6

Research concerning the utilization of silicon piezoresistive strain sensing technology for space shuttle main engine applications is reported. The following specific topics were addressed: (1) transducer design and materials, (2) silicon piezoresistor characterization at cryogenic temperatures, (3) chip mounting characterization, and (4) frequency response optimization