Partial self-consistency and analyticity in many-body perturbation theory: particle number conservation and a generalized sum rule

We consider a general class of approximations which guarantees the conservation of particle number in many-body perturbation theory. To do this we extend the concept of $\Phi$-derivability for the self-energy $\Sigma$ to a larger class of diagrammatic terms in which only some of the Green's function lines contain the fully dressed Green's function $G$. We call the corresponding approximations for $\Sigma$ partially $\Phi$-derivable. A special subclass of such approximations, which are gauge-invariant, is obtained by dressing loops in the diagrammatic expansion of $\Phi$ consistently with $G$. These approximations are number conserving but do not have to fulfill other conservation laws, such as the conservation of energy and momentum. From our formalism we can easily deduce if commonly used approximations will fulfill the continuity equation, which implies particle number conservation. We further show how the concept of partial $\Phi$-derivability plays an important role in the derivation of a generalized sum rule for the particle number, which reduces to the Luttinger-Ward theorem in the case of a homogeneous electron gas, and the Friedel sum rule in the case of the Anderson model. To do this we need to ensure that the Green's function has certain complex analytic properties, which can be guaranteed if the spectral function is positive semi-definite.The latter property can be ensured for a subset of partially $\Phi$-derivable approximations for the self-energy, namely those that can be constructed from squares of so-called half-diagrams. In case the analytic requirements are not fulfilled we highlight a number of subtle issues related to branch cuts, pole structure and multi-valuedness. We also show that various schemes of computing the particle number are consistent for particle number conserving approximations.Comment: Minor changes, corrected typo

Contour calculus for many-particle functions

In non-equilibrium many-body perturbation theory, Langreth rules are an efficient way to extract real-time equations from contour ones. However, the standard rules are not applicable in cases that do not reduce to simple convolutions and multiplications. We introduce a procedure for extracting real-time equations from general multi-argument contour functions with an arbitrary number of arguments. This is done for both the standard Keldysh contour, as well as the extended contour with a vertical track that allows for general initial states. This amounts to the generalization of the standard Langreth rules to much more general situations. These rules involve multi-argument retarded functions as key ingredients, for which we derive intuitive graphical rules. We apply our diagrammatic recipe to derive Langreth rules for the so-called double triangle structure and the general vertex function, relevant for the study of vertex corrections beyond the $GW$ approximation

The Generalized Kadanoff-Baym Ansatz with Initial Correlations

Within the non-equilibrium Green's function (NEGF) formalism, the Generalized Kadanoff-Baym Ansatz (GKBA) has stood out as a computationally cheap method to investigate the dynamics of interacting quantum systems driven out of equilibrium. Current implementations of the NEGF--GKBA, however, suffer from a drawback: real-time simulations require {\em noncorrelated} states as initial states. Consequently, initial correlations must be built up through an adiabatic switching of the interaction before turning on any external field, a procedure that can be numerically highly expensive. In this work, we extend the NEGF--GKBA to allow for {\em correlated} states as initial states. Our scheme makes it possible to efficiently separate the calculation of the initial state from the real-time simulation, thus paving the way for enlarging the class of systems and external drivings accessible by the already successful NEGF--GKBA. We demonstrate the accuracy of the method and its improved performance in a model donor-acceptor dyad driven out of equilibrium by an external laser pulse

Processes for isolating chitin and chitosan from fungal biomass

Methods of extracting chitin and chitosan from fungal biomass using a solution of one or more ammonia compounds, amines, and/or alkaline silicate compounds. The solution dissolves and extracts amino acids, fatty acids and other carbohydrates from the fungal cells leaving chitin and/or chitosan, and the extractant may be recovered from the liquid by simple phase changes such as heating or cooling, dissociation into volatile components, distillation and/or solidification and separation of immiscible extractants. Further lipid removal may be achieved with one or more organic solvents, which may also be recovered by distillation

Prohibited Floor Trading Activities Under the Commodity Exchange Act

In algorithmic graph theory, a classic open question is to determine the complexity of the Maximum Independent Set problem on Pt -free graphs, that is, on graphs not containing any induced path on t vertices. So far, polynomial-time algorithms are known only for t≤5 (Lokshtanov et al., in: Proceedings of the twenty-fifth annual ACM-SIAM symposium on discrete algorithms, SODA 2014, Portland, OR, USA, January 5–7, 2014, pp 570–581, 2014), and an algorithm for t=6 announced recently (Grzesik et al. in Polynomial-time algorithm for maximum weight independent set on P6 -free graphs. CoRR, arXiv:1707.05491, 2017). Here we study the existence of subexponential-time algorithms for the problem: we show that for any t≥1 , there is an algorithm for Maximum Independent Set on Pt -free graphs whose running time is subexponential in the number of vertices. Even for the weighted version MWIS, the problem is solvable in 2O(tnlogn√) time on Pt -free graphs. For approximation of MIS in broom-free graphs, a similar time bound is proved. Scattered Set is the generalization of Maximum Independent Set where the vertices of the solution are required to be at distance at least d from each other. We give a complete characterization of those graphs H for which d-Scattered Set on H-free graphs can be solved in time subexponential in the size of the input (that is, in the number of vertices plus the number of edges): If every component of H is a path, then d-Scattered Set on H-free graphs with n vertices and m edges can be solved in time 2O(|V(H)|n+m√log(n+m)) , even if d is part of the input. Otherwise, assuming the Exponential-Time Hypothesis (ETH), there is no 2o(n+m) -time algorithm for d-Scattered Set for any fixed d≥3 on H-free graphs with n-vertices and m-edges

Measuring Open Access uptake: Data sources, expectations, and misconceptions

In this paper we briefly introduce the concept of Open Access and review the many variants that have been presented in the literature. We then critically examine how OA variants are presented by data source and how they are operationalized in practice. The goal of the paper is to provide a set of guidelines on how to effectively interpret OA information. For this, we compare OA figures reported in different data sources at the institutional and journal level and dig into the potential explanations behind the differences observed on the figures each source provides. Policy highlights: 1) Open Access reporting in bibliometric reports is now possible due the proliferation of data sources which now provide information on the OA status of publications. 2) Unpaywall has become the main primary source on OA metadata for publications for the main bibliometric databases, however there are divergences on how this is reported and showed by each of them. 3) Understanding how OA variants are defined by each source and later operationalized is key to correctly report and interpret Open Access uptak

Fast Green's function method for ultrafast electron-boson dynamics

The interaction of electrons with quantized phonons and photons underlies the ultrafast dynamics of systems ranging from molecules to solids, and it gives rise to a plethora of physical phenomena experimentally accessible using time-resolved techniques. Green's function methods offer an invaluable interpretation tool since scattering mechanisms of growing complexity can be selectively incorporated in the theory. Currently, however, real-time Green's function simulations are either prohibitively expensive due to the cubic scaling with the propagation time or do neglect the feedback of electrons on the bosons, thus violating energy conservation. We put forward a computationally efficient Green's function scheme which overcomes both limitations. The numerical effort scales linearly with the propagation time while the simultaneous dressing of electrons and bosons guarantees the fulfillment of all fundamental conservation laws. We present a real-time study of the phonon-driven relaxation dynamics in an optically excited narrow band-gap insulator, highlighting the nonthermal behavior of the phononic degrees of freedom. Our formulation paves the way to first-principles simulations of electron-boson systems with unprecedented long propagation times.Comment: 7 pages, with additional supplementary material

Joint astrometric solution of Hipparcos and Gaia: A recipe for the Hundred Thousand Proper Motions project

The first release of astrometric data from Gaia is expected in 2016. It will contain the mean stellar positions and magnitudes from the first year of observations. For more than 100 000 stars in common with the Hipparcos Catalogue it will be possible to compute very accurate proper motions due to the time difference of about 24 years between the two missions. This Hundred Thousand Proper Motions (HTPM) project will be part of the first release. Our aim is to investigate how early Gaia data can be optimally combined with information from the Hipparcos Catalogue in order to provide the most accurate and reliable results for HTPM. The Astrometric Global Iterative Solution (AGIS) was developed to compute the astrometric core solution based on the Gaia observations and will be used for all releases of astrometric data from Gaia. We adapt AGIS to process Hipparcos data in addition to Gaia observations, and use simulations to verify and study the joint solution method. For the HTPM stars we predict proper motion accuracies between 14 and 134 muas/yr, depending on stellar magnitude and amount of Gaia data available. Perspective effects will be important for a significant number of HTPM stars, and in order to treat these effects accurately we introduce a scaled model of kinematics. We define a goodness-of-fit statistic which is sensitive to deviations from uniform space motion, caused for example by binaries with periods of 10-50 years. HTPM will significantly improve the proper motions of the Hipparcos Catalogue well before highly accurate Gaia- only results become available. Also, HTPM will allow us to detect long period binary and exoplanetary candidates which would be impossible to detect from Gaia data alone. The full sensitivity will not be reached with the first Gaia release but with subsequent data releases. Therefore HTPM should be repeated when more Gaia data become available.Comment: Revised manuscript following referee report. Accepted for publication in A&

Tool use for corpse cleaning in chimpanzees

For the first time, chimpanzees have been observed using tools to clean the corpse of a deceased group member. A female chimpanzee sat down at the dead body of a young male, selected a firm stem of grass, and started to intently remove debris from his teeth. This report contributes novel behaviour to the chimpanzee’s ethogram, and highlights how crucial information for reconstructing the evolutionary origins of human mortuary practices may be missed by refraining from developing adequate observation techniques to capture non-human animals’ death responses.Publisher PDFPeer reviewe