Spectral properties from Matsubara Green's function approach - application to molecules

We present results for many-body perturbation theory for the one-body Green's function at finite temperatures using the Matsubara formalism. Our method relies on the accurate representation of the single-particle states in standard Gaussian basis sets, allowing to efficiently compute, among other observables, quasiparticle energies and Dyson orbitals of atoms and molecules. In particular, we challenge the second-order treatment of the Coulomb interaction by benchmarking its accuracy for a well-established test set of small molecules, which includes also systems where the usual Hartree-Fock treatment encounters difficulties. We discuss different schemes how to extract quasiparticle properties and assess their range of applicability. With an accurate solution and compact representation, our method is an ideal starting point to study electron dynamics in time-resolved experiments by the propagation of the Kadanoff-Baym equations.Comment: 12 pages, 8 figure

An Underwater SLAM System using Sonar, Visual, Inertial, and Depth Sensor

This paper presents a novel tightly-coupled keyframe-based Simultaneous Localization and Mapping (SLAM) system with loop-closing and relocalization capabilities targeted for the underwater domain. Our previous work, SVIn, augmented the state-of-the-art visual-inertial state estimation package OKVIS to accommodate acoustic data from sonar in a non-linear optimization-based framework. This paper addresses drift and loss of localization -- one of the main problems affecting other packages in underwater domain -- by providing the following main contributions: a robust initialization method to refine scale using depth measurements, a fast preprocessing step to enhance the image quality, and a real-time loop-closing and relocalization method using bag of words (BoW). An additional contribution is the addition of depth measurements from a pressure sensor to the tightly-coupled optimization formulation. Experimental results on datasets collected with a custom-made underwater sensor suite and an autonomous underwater vehicle from challenging underwater environments with poor visibility demonstrate performance never achieved before in terms of accuracy and robustness

Ro-vibrational Quenching of CO (\u3cem\u3ev\u3c/em\u3e = 1) by He Impact in a Broad Range of Temperatures: A Benchmark Study Using Mixed Quantum/Classical Inelastic Scattering Theory

The mixed quantum/classical approach is applied to the problem of ro-vibrational energy transfer in the inelastic collisions of CO(v = 1) with He atom, in order to predict the quenching rate coefficient in a broad range of temperatures 5 \u3c T \u3c 2500 K. Scattering calculations are done in two different ways: direct calculations of quenching cross sections and, alternatively, calculations of the excitation cross sections plus microscopic reversibility. In addition, a symmetrized average-velocity method of Billing is tried. Combination of these methods allows reproducing experiment in a broad range of temperatures. Excellent agreement with experiment is obtained at 400 \u3c T \u3c 2500 K (within 10%), good agreement in the range 100 \u3c T \u3c 400 K (within 25%), and semi-quantitative agreement at 40 \u3c T \u3c 100 K(within a factor of 2). This study provides a stringent test of the mixed quantum/classical theory, because the vibrational quantum in CO molecule is rather large and the quencher is very light (He atom). For heavier quenchers and closer to dissociation limit of the molecule, the mixed quantum/classical theory is expected to work even better

A dynamic look-ahead Monte Carlo algorithm for pricing Bermudan options

Under the assumption of no-arbitrage, the pricing of American and Bermudan options can be casted into optimal stopping problems. We propose a new adaptive simulation based algorithm for the numerical solution of optimal stopping problems in discrete time. Our approach is to recursively compute the so-called continuation values. They are defined as regression functions of the cash flow, which would occur over a series of subsequent time periods, if the approximated optimal exercise strategy is applied. We use nonparametric least squares regression estimates to approximate the continuation values from a set of sample paths which we simulate from the underlying stochastic process. The parameters of the regression estimates and the regression problems are chosen in a data-dependent manner. We present results concerning the consistency and rate of convergence of the new algorithm. Finally, we illustrate its performance by pricing high-dimensional Bermudan basket options with strangle-spread payoff based on the average of the underlying assets.Comment: Published in at http://dx.doi.org/10.1214/105051607000000249 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org