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

Parametric analysis of diffuser requirements for high expansion ratio space engine

A supersonic diffuser ejector design computer program was developed. Using empirically modified one dimensional flow methods the diffuser ejector geometry is specified by the code. The design code results for calculations up to the end of the diffuser second throat were verified. Diffuser requirements for sea level testing of high expansion ratio space engines were defined. The feasibility of an ejector system using two commonly available turbojet engines feeding two variable area ratio ejectors was demonstrated

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

Quasi-Particles in Two-Dimensional Hubbard Model: Splitting of Spectral Weight

It is shown that the energy $(\varepsilon)$ and momentum $(k)$ dependences of the electron self-energy function $\Sigma (k, \varepsilon + i0) \equiv \Sigma^{R}(k, \varepsilon)$ are, ${\rm Im} \Sigma^{R} (k, \varepsilon) = -a\varepsilon^{2}|\varepsilon - \xi_{k}|^{- \gamma (k)}$ where $a$ is some constant, $\xi_{k} = \varepsilon(k)-\mu, \varepsilon(k)$ being the band energy, and the critical exponent $\gamma(k)$, which depends on the curvature of the Fermi surface at $k$, satisfies, $0 \leq \gamma(k) \leq 1$. This leads to a new type of electron liquid, which is the Fermi liquid in the limit of $\varepsilon, \xi_{k} \rightarrow 0$ but for $\xi_{k} \neq 0$ has a split one-particle spectra as in the Tomonaga-Luttinger liquid.Comment: 8 pages (LaTeX) 4 figures available upon request will be sent by air mail. KomabaCM-preprint-O

One-Particle Excitation of the Two-Dimensional Hubbard Model

The real part of the self-energy of interacting two-dimensional electrons has been calculated in the t-matrix approximation. It is shown that the forward scattering results in an anomalous term leading to the vanishing renormalization factor of the one-particle Green function, which is a non-perturbative effect of the interaction U. The present result is a microscopic demonstration of the claim by Anderson based on the conventional many-body theory. The effect of the damping of the interacting electrons, which has been ignored in reaching above conclusion, has been briefly discussed.Comment: 7 pages, LaTeX, 1 figure, uses jpsj.sty, to be published in J. Phys. Soc. Jpn. 66 No. 3 (1997

Recommendation Subgraphs for Web Discovery

Recommendations are central to the utility of many websites including YouTube, Quora as well as popular e-commerce stores. Such sites typically contain a set of recommendations on every product page that enables visitors to easily navigate the website. Choosing an appropriate set of recommendations at each page is one of the key features of backend engines that have been deployed at several e-commerce sites. Specifically at BloomReach, an engine consisting of several independent components analyzes and optimizes its clients' websites. This paper focuses on the structure optimizer component which improves the website navigation experience that enables the discovery of novel content. We begin by formalizing the concept of recommendations used for discovery. We formulate this as a natural graph optimization problem which in its simplest case, reduces to a bipartite matching problem. In practice, solving these matching problems requires superlinear time and is not scalable. Also, implementing simple algorithms is critical in practice because they are significantly easier to maintain in production. This motivated us to analyze three methods for solving the problem in increasing order of sophistication: a sampling algorithm, a greedy algorithm and a more involved partitioning based algorithm. We first theoretically analyze the performance of these three methods on random graph models characterizing when each method will yield a solution of sufficient quality and the parameter ranges when more sophistication is needed. We complement this by providing an empirical analysis of these algorithms on simulated and real-world production data. Our results confirm that it is not always necessary to implement complicated algorithms in the real-world and that very good practical results can be obtained by using heuristics that are backed by the confidence of concrete theoretical guarantees

Approaching the Problem of Time with a Combined Semiclassical-Records-Histories Scheme

I approach the Problem of Time and other foundations of Quantum Cosmology using a combined histories, timeless and semiclassical approach. This approach is along the lines pursued by Halliwell. It involves the timeless probabilities for dynamical trajectories entering regions of configuration space, which are computed within the semiclassical regime. Moreover, the objects that Halliwell uses in this approach commute with the Hamiltonian constraint, H. This approach has not hitherto been considered for models that also possess nontrivial linear constraints, Lin. This paper carries this out for some concrete relational particle models (RPM's). If there is also commutation with Lin - the Kuchar observables condition - the constructed objects are Dirac observables. Moreover, this paper shows that the problem of Kuchar observables is explicitly resolved for 1- and 2-d RPM's. Then as a first route to Halliwell's approach for nontrivial linear constraints that is also a construction of Dirac observables, I consider theories for which Kuchar observables are formally known, giving the relational triangle as an example. As a second route, I apply an indirect method that generalizes both group-averaging and Barbour's best matching. For conceptual clarity, my study involves the simpler case of Halliwell 2003 sharp-edged window function. I leave the elsewise-improved softened case of Halliwell 2009 for a subsequent Paper II. Finally, I provide comments on Halliwell's approach and how well it fares as regards the various facets of the Problem of Time and as an implementation of QM propositions.Comment: An improved version of the text, and with various further references. 25 pages, 4 figure

On the Stability and Single-Particle Properties of Bosonized Fermi Liquids

We study the stability and single-particle properties of Fermi liquids in spatial dimensions greater than one via bosonization. For smooth non-singular Fermi liquid interactions we obtain Shankar's renormalization- group flows and reproduce well known results for quasi-particle lifetimes. We demonstrate by explicit calculation that spin-charge separation does not occur when the Fermi liquid interactions are regular. We also explore the relationship between quantized bosonic excitations and zero sound modes and present a concise derivation of both the spin and the charge collective mode equations. Finally we discuss some aspects of singular Fermi liquid interactions.Comment: 13 pages plus three postscript figures appended; RevTex 3.0; BUP-JBM-

Feasibility of Experimental Realization of Entangled Bose-Einstein Condensation

We examine the practical feasibility of the experimental realization of the so-called entangled Bose-Einstein condensation (BEC), occurring in an entangled state of two atoms of different species. We demonstrate that if the energy gap remains vanishing, the entangled BEC persists as the ground state of the concerned model in a wide parameter regime. We establish the experimental accessibility of the isotropic point of the effective parameters, in which the entangled BEC is the exact ground state, as well as the consistency with the generalized Gross-Pitaevskii equations. The transition temperature is estimated. Possible experimental implementations are discussed in detail.Comment: 6 pages, published versio