Probing Phases and Quantum Criticality using Deviations from the Local Fluctuation-Dissipation Theorem

Introduction Cold atomic gases in optical lattices are emerging as excellent laboratories for testing models of strongly interacting particles in condensed matter physics. Currently, one of the major open questions is how to obtain the finite temperature phase diagram of a given quantum Hamiltonian directly from experiments. Previous work in this direction required quantum Monte Carlo simulations to directly model the experimental situation in order to extract quantitative information, clearly defeating the purpose of an optical lattice emulator. Here we propose a new method that utilizes deviations from a local fluctuation dissipation theorem to construct a finite temperature phase diagram, for the first time, from local observables accessible by in situ experimental observations. Our approach extends the utility of the fluctuation-dissipation theorem from thermometry to the identification of quantum phases, associated energy scales and the quantum critical region. We test our ideas using state-of-the-art large-scale quantum Monte Carlo simulations of the two-dimensional Bose Hubbard model.Comment: 7 pages; 4 figures; also see supplementary material of 7 pages with 3 figure

Extending the range of error estimates for radial approximation in Euclidean space and on spheres

We adapt Schaback's error doubling trick [R. Schaback. Improved error bounds for scattered data interpolation by radial basis functions. Math. Comp., 68(225):201--216, 1999.] to give error estimates for radial interpolation of functions with smoothness lying (in some sense) between that of the usual native space and the subspace with double the smoothness. We do this for both bounded subsets of R^d and spheres. As a step on the way to our ultimate goal we also show convergence of pseudoderivatives of the interpolation error.Comment: 10 page

An Empirical Test of Staw and Ross Prescriptions for the Management of Escalation of Commitment Behavior in organizations

Tests two major prescriptions of Staw and Ross about the management of escalation behavior in organizations. Since these prescriptions are primarily based on research using students in controlled settings, the efficacy of the prescriptions was tested in the context of a real, functioning organization. The results provide conditional support for separating initial decision responsibility from subsequent responsibility as a means of reducing escalation behavior. However, the findings did not support a reduction of project failure risk as a means of minimizing escalation of commitment to a failing course of action

Local 4/5-Law and Energy Dissipation Anomaly in Turbulence

A strong local form of the ``4/3-law'' in turbulent flow has been proved recently by Duchon and Robert for a triple moment of velocity increments averaged over both a bounded spacetime region and separation vector directions, and for energy dissipation averaged over the same spacetime region. Under precisely stated hypotheses, the two are proved to be proportional, by a constant 4/3, and to appear as a nonnegative defect measure in the local energy balance of singular (distributional) solutions of the incompressible Euler equations. Here we prove that the energy defect measure can be represented also by a triple moment of purely longitudinal velocity increments and by a mixed moment with one longitudinal and two tranverse velocity increments. Thus, we prove that the traditional 4/5- and 4/15-laws of Kolmogorov hold in the same local sense as demonstrated for the 4/3-law by Duchon-Robert.Comment: 14 page

Uniform generation in trace monoids

We consider the problem of random uniform generation of traces (the elements of a free partially commutative monoid) in light of the uniform measure on the boundary at infinity of the associated monoid. We obtain a product decomposition of the uniform measure at infinity if the trace monoid has several irreducible components-a case where other notions such as Parry measures, are not defined. Random generation algorithms are then examined.Comment: Full version of the paper in MFCS 2015 with the same titl

On thin plate spline interpolation

We present a simple, PDE-based proof of the result [M. Johnson, 2001] that the error estimates of [J. Duchon, 1978] for thin plate spline interpolation can be improved by $h^{1/2}$. We illustrate that ${\mathcal H}$-matrix techniques can successfully be employed to solve very large thin plate spline interpolation problem

Precision Pointing of IBEX-Lo Observations

Post-launch boresight of the IBEX-Lo instrument onboard the Interstellar Boundary Explorer (IBEX) is determined based on IBEX-Lo Star Sensor observations. Accurate information on the boresight of the neutral gas camera is essential for precise determination of interstellar gas flow parameters. Utilizing spin-phase information from the spacecraft attitude control system (ACS), positions of stars observed by the Star Sensor during two years of IBEX measurements were analyzed and compared with positions obtained from a star catalog. No statistically significant differences were observed beyond those expected from the pre-launch uncertainty in the Star Sensor mounting. Based on the star observations and their positions in the spacecraft reference system, pointing of the IBEX satellite spin axis was determined and compared with the pointing obtained from the ACS. Again, no statistically significant deviations were observed. We conclude that no systematic correction for boresight geometry is needed in the analysis of IBEX-Lo observations to determine neutral interstellar gas flow properties. A stack-up of uncertainties in attitude knowledge shows that the instantaneous IBEX-Lo pointing is determined to within \sim 0.1\degr in both spin angle and elevation using either the Star Sensor or the ACS. Further, the Star Sensor can be used to independently determine the spacecraft spin axis. Thus, Star Sensor data can be used reliably to correct the spin phase when the Star Tracker (used by the ACS) is disabled by bright objects in its field-of-view. The Star Sensor can also determine the spin axis during most orbits and thus provides redundancy for the Star Tracker.Comment: 22 pages, 18 figure

Navigability is a Robust Property

The Small World phenomenon has inspired researchers across a number of fields. A breakthrough in its understanding was made by Kleinberg who introduced Rank Based Augmentation (RBA): add to each vertex independently an arc to a random destination selected from a carefully crafted probability distribution. Kleinberg proved that RBA makes many networks navigable, i.e., it allows greedy routing to successfully deliver messages between any two vertices in a polylogarithmic number of steps. We prove that navigability is an inherent property of many random networks, arising without coordination, or even independence assumptions

On admissibility criteria for weak solutions of the Euler equations

We consider solutions to the Cauchy problem for the incompressible Euler equations satisfying several additional requirements, like the global and local energy inequalities. Using some techniques introduced in an earlier paper we show that, for some bounded compactly supported initial data, none of these admissibility criteria singles out a unique weak solution. As a byproduct we show bounded initial data for which admissible solutions to the p-system of isentropic gas dynamics in Eulerian coordinates are not unique in more than one space dimension.Comment: 33 pages, 1 figure; v2: 35 pages, corrected typos, clarified proof