An improved method for obtaining a normalized junction temperature for semiconductors: A concept

Failure rate for given semiconductor device is simply determined by reading value of normalized junction temperature from printout for any given combination of ambient temperature, stress ratio, and maximum rated junction temperature, and obtaining corresponding failure rate from graph

Bosons in a double-well potential: Understanding the interplay between disorder and interaction in a simple model

We propose an exactly solvable model to reveal the physics of the interplay between interaction and disorder in bosonic systems. Considering interacting bosons in a double-well potential, in which disorder is mimicked by taking the energy level mismatch between the two wells to be randomly distributed, we find "two negatives make a positive" effect. While disorder or interaction by itself suppresses the phase coherence between the two wells, both together enhance the phase coherence. This model also captures several striking features of the disordered Bose-Hubbard model found in recent numerical simulations. Results at finite temperatures may help explain why a recent experiment did not find any evidence for the enhancement of phase coherence in a disordered bosonic system.Comment: Published version, 4 pages, 4 figure

Radiative interactions in laminar duct flows

Analyses and numerical procedures are presented for infrared radiative energy transfer in gases when other modes of energy transfer occur simultaneously. Two types of geometries are considered, a parallel plate duct and a circular duct. Fully developed laminar incompressible flows of absorbing-emitting species in black surfaced ducts are considered under the conditions of uniform wall heat flux. The participating species considered are OH, CO, CO2, and H2O. Nongray as well as gray formulations are developed for both geometries. Appropriate limiting solutions of the governing equations are obtained and conduction-radiation interaction parameters are evaluated. Tien and Lowder's wide band model correlation was used in nongray formulation. Numerical procedures are presented to solve the integro-differential equations for both geometries. The range of physical variables considered are 300 to 2000 K for temperature, 0.1 to 100.0 atm for pressure, and 0.1 to 100 cm spacings between plates/radius of the tube. An extensive parametric study based on nongray formulation is presented. Results obtained for different flow conditions indicate that the radiative interactions can be quite significant in fully developed incompressible flows

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

Antiferromagnetism and phase separation in the t-J model at low doping: a variational study

Using Gutzwiller-projected wave functions, I estimate the ground-state energy of the t-J model for several variational states relevant for high-temperature cuprate superconductors. The results indicate antiferromagnetism and phase separation at low doping both in the superconducting state and in the staggered-flux normal state proposed for the vortex cores. While phase separation in the underdoped superconducting state may be relevant for the stripe formation mechanism, the results for the normal state suggest that similar charge inhomogeneities may also appear in vortex cores up to relatively high doping values.Comment: 4 pages, 3 figures, reference adde

High Tc Superconductors -- A Variational Theory of the Superconducting State

We use a variational approach to gain insight into the strongly correlated d-wave superconducting state of the high Tc cuprates at T=0. We show that strong correlations lead to qualitatively different trends in pairing and phase coherence: the pairing scale decreases monotonically with hole doping while the SC order parameter shows a non-monotonic dome. We obtain detailed results for the doping-dependence of a large number of experimentally observable quantities, including the chemical potential, coherence length, momentum distribution, nodal quasiparticle weight and dispersion, incoherent features in photoemission spectra, optical spectral weight and superfluid density. Most of our results are in remarkable quantitative agreement with existing data and some of our predictions, first reported in Phys. Rev. Lett. {\bf 87}, 217002 (2001), have been recently verified.Comment: (Minor revisions, 1 figure added, version to appear in PRB) 23 RevTeX pages, 11 eps figs, long version of cond-mat/0101121, contains detailed comparisons with experiments, analytical insights, technical aspects of the calculation, and comparison with slave boson MF

Repulsive Fermions in Optical Lattices: Phase separation versus Coexistence of Antiferromagnetism and d-Superfluidity

We investigate a system of fermions on a two-dimensional optical square lattice in the strongly repulsive coupling regime. In this case, the interactions can be controlled by laser intensity as well as by Feshbach resonance. We compare the energetics of states with resonating valence bond d-wave superfluidity, antiferromagnetic long range order and a homogeneous state with coexistence of superfluidity and antiferromagnetism. We show that the energy density of a hole $e_{hole}(x)$ has a minimum at doping $x=x_c$ that signals phase separation between the antiferromagnetic and d-wave paired superfluid phases. The energy of the phase-separated ground state is however found to be very close to that of a homogeneous state with coexisting antiferromagnetic and superfluid orders. We explore the dependence of the energy on the interaction strength and on the three-site hopping terms and compare with the nearest neighbor hopping {\it t-J} model

Estimation of Parameters of Misclassified Size Biased Borel Distribution

A misclassified size-biased Borel Distribution (MSBBD), where some of the observations corresponding to x = c + 1 are wrongly reported as x = c with probability α, is defined. Various estimation methods like the method of maximum likelihood (ML), method of moments, and the Bayes estimation for the parameters of the MSBB distribution are used. The performance of the estimators are studied using simulated bias and simulated risk. Simulation studies are carried out for different values of the parameters and sample size

Classification of Lipschitz simple function germs

It was shown by Henry and Parusiński in 2003 that the bi-Lipschitz right equivalence of function germs admits moduli. In this article, we introduce the notion of Lipschitz simple function germ and present the complete classification in the complex case. For this, we present several bi-Lipschitz invariants associated to functions germs. In particular, we prove that the lowest degree homogeneous part of a function germ is a bi-Lipschitz invariant and use this to show a weak version of the splitting lemma for bi-Lipschitz equivalence. We improve upon earlier results on bi-Lipschitz triviality of families to show that several families of germs in Arnold's list of unimodal singularities are bi-Lipschitz trivial. A surprising consequence of our result is that a function germ is Lipschitz modal if and only if it deforms to the smooth unimodal family of singularities called (Formula presented.) in Arnold's list