Non-equilibrium Green's function theory for non-adiabatic effects in quantum transport: inclusion of electron-electron interactions

Non-equilibrium Green's function theory for non-adiabatic effects in quantum transport [Kershaw and Kosov, J.Chem. Phys. 2017, 147, 224109 and J. Chem. Phys. 2018, 149, 044121] is extended to the case of interacting electrons. We consider a general problem of quantum transport of interacting electrons through a central region with dynamically changing geometry. The approach is based on the separation of time scales in the non-equilibrium Green's functions and the use of Wigner transformation to solve the Kadanoff-Baym equations. The Green's functions and correlation self-energy are non-adiabatically expanded up to the second order central time derivatives. We produced expressions for Green's functions with non-adiabatic corrections and modified formula for electric current; both depend not only on instantaneous molecular junction geometry but also on nuclear velocities and accelerations. The theory is illustrated by the study of electron transport through a model single-resonant level molecular junction with local electron-electron repulsion and a dynamically changing geometry

Nonadiabatic corrections to electric current in molecular junction due to nuclear motion at the molecule-electrode interfaces

We present quantum electron transport theory that incorporates dynamical effects of motion of atoms on electrode-molecule interfaces in the calculations of the electric current. The theory is based on non-equilibrium Green's functions. We separate time scales in the Green's functions on fast relative time and slow central time. The derivative with respect to the central time serves as a small parameter in the theory. We solve the real-time Kadanoff-Baym equations for molecular Green's functions using Wigner representation and keep terms up to the second order with respect to the central time derivatives. Molecular Green's functions and consequently the electric current are expressed as functions of molecular junction coordinates as well as velocities and accelerations of molecule-electrode interface nuclei. We apply the theory to model a molecular system and study the effects of non-adiabatic nuclear motion on molecular junction conductivity

Learning High-Dimensional Markov Forest Distributions: Analysis of Error Rates

The problem of learning forest-structured discrete graphical models from i.i.d. samples is considered. An algorithm based on pruning of the Chow-Liu tree through adaptive thresholding is proposed. It is shown that this algorithm is both structurally consistent and risk consistent and the error probability of structure learning decays faster than any polynomial in the number of samples under fixed model size. For the high-dimensional scenario where the size of the model d and the number of edges k scale with the number of samples n, sufficient conditions on (n,d,k) are given for the algorithm to satisfy structural and risk consistencies. In addition, the extremal structures for learning are identified; we prove that the independent (resp. tree) model is the hardest (resp. easiest) to learn using the proposed algorithm in terms of error rates for structure learning.Comment: Accepted to the Journal of Machine Learning Research (Feb 2011

High-Dimensional Gaussian Graphical Model Selection: Walk Summability and Local Separation Criterion

We consider the problem of high-dimensional Gaussian graphical model selection. We identify a set of graphs for which an efficient estimation algorithm exists, and this algorithm is based on thresholding of empirical conditional covariances. Under a set of transparent conditions, we establish structural consistency (or sparsistency) for the proposed algorithm, when the number of samples n=omega(J_{min}^{-2} log p), where p is the number of variables and J_{min} is the minimum (absolute) edge potential of the graphical model. The sufficient conditions for sparsistency are based on the notion of walk-summability of the model and the presence of sparse local vertex separators in the underlying graph. We also derive novel non-asymptotic necessary conditions on the number of samples required for sparsistency

Performance of astrometric detection of a hotspot orbiting on the innermost stable circular orbit of the galactic centre black hole

The galactic central black hole Sgr A* exhibits outbursts of radiation in the near infrared (so-called IR flares). One model of these events consists in a hotspot orbiting on the innermost stable circular orbit (ISCO) of the hole. These outbursts can be used as a probe of the central gravitational potential. One main scientific goal of the second generation VLTI instrument GRAVITY is to observe these flares astrometrically. Here, the astrometric precision of GRAVITY is investigated in imaging mode, which consists in analysing the image computed from the interferometric data. The capability of the instrument to put in light the motion of a hotspot orbiting on the ISCO of our central black hole is then discussed. We find that GRAVITY's astrometric precision for a single star in imaging mode is smaller than the Schwarzschild radius of Sgr A*. The instrument can also demonstrate that a body orbiting on the last stable orbit of the black hole is indeed moving. It yields a typical size of the orbit, if the source is as bright as m_K=14. These results show that GRAVITY allows one to study the close environment of Sgr A*. Having access to the ISCO of the central massive black hole probably allows constraining general relativity in its strong regime. Moreover, if the hotspot model is appropriate, the black hole spin can be constrained.Comment: 13 pages, 11 figures ; accepted by MNRA

A Geometric Model for Odd Differential K-theory

Odd $K$-theory has the interesting property that it admits an infinite number of inequivalent differential refinements. In this paper we provide a bundle theoretic model for odd differential $K$-theory using the caloron correspondence and prove that this refinement is unique up to a unique natural isomorphism. We characterise the odd Chern character and its transgression form in terms of a connection and Higgs field and discuss some applications. Our model can be seen as the odd counterpart to the Simons-Sullivan construction of even differential $K$-theory. We use this model to prove a conjecture of Tradler-Wilson-Zeinalian regarding a related differential extension of odd $K$-theoryComment: 36 page

Nonequilibrium Green's function theory for nonadiabatic effects in quantum electron transport

We develop nonequilibribrium Green's function based transport theory, which includes effects of nonadiabatic nuclear motion in the calculation of the electric current in molecular junctions. Our approach is based on the separation of slow and fast timescales in the equations of motion for the Green's functions by means of the Wigner representation. Time derivatives with respect to central time serves as a small parameter in the perturbative expansion enabling the computation of nonadiabatic corrections to molecular Green's functions. Consequently, we produce series of analytic expressions for non-adiabatic electronic Green's functions (up to the second order in the central time derivatives); which depend not solely on instantaneous molecular geometry but likewise on nuclear velocities and accelerations. Extended formula for electric current is derived which accounts for the non-adiabatic corrections. This theory is concisely illustrated by the calculations on a model molecular junction

Signature extension studies

The importance of specific spectral regions to signature extension is explored. In the recent past, the signature extension task was focused on the development of new techniques. Tested techniques are now used to investigate this spectral aspect of the large area survey. Sets of channels were sought which, for a given technique, were the least affected by several sources of variation over four data sets and yet provided good object class separation on each individual data set. Using sets of channels determined as part of this study, signature extension was accomplished between data sets collected over a six-day period and over a range of about 400 kilometers

A comparison and evaluation of satellite derived positions of tracking stations

A comparison is presented of sets of satellite tracking station coordinate values published in the past few years by a number of investigators, i.e. Goddard Space Flight Center, Smithsonian Astrophysical Observatory, Ohio State University, The Naval Weapons Laboratory, Air Force Cambridge Research Laboratories, and Wallops Island. The comparisons have been made in terms of latitude, longitude and height. The results of the various solutions have been compared directly and also with external standards such as local survey data and gravimetrically derived geoid heights. After taking into account systematic rotations, latitude and longitude agreement on a global basis is generally 15 meters or better, on the North American Datum agreement is generally better than 10 meters. Allowing for scale differences (of the order of 2 ppm) radial agreement is generally of the order of 10 meters

Learning Latent Tree Graphical Models

We study the problem of learning a latent tree graphical model where samples are available only from a subset of variables. We propose two consistent and computationally efficient algorithms for learning minimal latent trees, that is, trees without any redundant hidden nodes. Unlike many existing methods, the observed nodes (or variables) are not constrained to be leaf nodes. Our first algorithm, recursive grouping, builds the latent tree recursively by identifying sibling groups using so-called information distances. One of the main contributions of this work is our second algorithm, which we refer to as CLGrouping. CLGrouping starts with a pre-processing procedure in which a tree over the observed variables is constructed. This global step groups the observed nodes that are likely to be close to each other in the true latent tree, thereby guiding subsequent recursive grouping (or equivalent procedures) on much smaller subsets of variables. This results in more accurate and efficient learning of latent trees. We also present regularized versions of our algorithms that learn latent tree approximations of arbitrary distributions. We compare the proposed algorithms to other methods by performing extensive numerical experiments on various latent tree graphical models such as hidden Markov models and star graphs. In addition, we demonstrate the applicability of our methods on real-world datasets by modeling the dependency structure of monthly stock returns in the S&P index and of the words in the 20 newsgroups dataset