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

Molecular epidemiology of complex heritable disease : applications in genomics and metabolomics

Modern high-throughput molecular technologies (collectively referred to as “omic” platforms) are generating unprecedented amounts of data on human variation. The four papers in this thesis each investigate and characterize associations between common, complex, heritable disease, and genetic or metabolomic markers from omic platforms. In paper I, we searched bipolar affective disorder (BPAD) pedigrees for genomic copy-number variants (CNVs, segmental deletions or duplications) segregating with disease. In one pedigree, a deletion in the gene MAGI1 was observed in six out of six affected members. Upon further inspection, another pedigree was found with two out of three affected members carrying a duplication in the same gene. A pooled association analysis was subsequently carried out using in-house and public data sets on CNVs in control subjects and cases of BPAD, schizophrenia (SZ), or schizoaffective disorder (SA). MAGI1 CNVs greater than 100 kb were found to be rare, nonsignificantly more common in BPAD cases than in controls, and significantly more common in the pooled case sample of BPAD, SZ, and SA than in controls. In paper II, we studied a rare single nucleotide polymorphism (SNP) in the gene HOXB13, which had been recently reported to be strongly associated with prostate cancer (PC) risk. We genotyped and analyzed the variant G84E (rs138213197) in the two large Swedish PC case-control samples CAPS and Stockholm-1 (in total 4,903 cases and 4,589 controls). G84E was less rare in the Swedish samples than in the United States population previously studied, with a carrier rate over 1% in Swedish population controls. The variant was associated with a more than threefold increased relative risk of PC in both Swedish samples. G84E carriers’ absolute lifetime risk to age 80 of PC was estimated to 33%. For G84E carriers in the uppermost quartile of a genetic risk score based on common risk SNPs, the same lifetime risk was estimated to 48%. In paper III, a replication study of previously reported genetic associations with testicular germ cell tumor (TGCT) risk was performed. SNPs in six genes (ATF7IP, BAK1, DMRT1, KITLG, SPRY4, and TERT) were genotyped and analyzed in a combined case-parent, case-control sample from Sweden and Norway. In total, 831 case-parent triads, 474 dyads, 712 singleton cases, and 3,919 control subjects were analyzed. Our results supported the previously reported association with TGCT risk for SNPs in all six genes. Tests of interaction effects revealed no allelic effect differences for the two major TGCT histological subtypes seminoma and non-seminoma. However, a variant in the gene SPRY4 was found to differ significantly in effect depending on the sex of the parent from which it was inherited. Only maternally inherited alleles were associated with TGCT risk. In paper IV, a large range of small molecules in human serum, collectively called the metabolome, were studied for association with PC risk and aggressiveness. Samples from 188 controls, 188 PC patients with indolent disease, and 99 PC patients with aggressive disease were analyzed by ultra-performance liquid chromatography coupled with mass spectrometry, generating 6,138 quantitative molecular features. All features were tested for association with PC status, adjusted for patient age and sample storage time. Two features were significantly associated after correction for multiple testing, but none of them could be identified as specific molecules. Testing the PC-associated features for association with 1.4 million SNPs genome-wide produced the strongest associations in variants in annotated genes, which may aid future molecular identification efforts. In conclusion, we have used omics platforms and modern computational tools to increase our knowledge about specific genetic risk factors and metabolomic markers for complex heritable disease. Our results may come of use in future etiological research as well as in genetic and molecular risk assessment

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

Energy exchange between nonlinear oscillators: An entropy foundation

In the field of vibrations of complex structures, energy methods like SEA and a series of mid-frequency methods, represent an important resource for computational analysis. All these methods are based in general on a linear formulation of the elastic problem. However, when nonlinearities are present, for example related to clearance or stiffening of joints, these methods, in principle, cannot be applied. This paper, on the basis of a theory presented recently by one of the authors, proposes a foundation of a new energy method able to deal with nonlinearities when studying the energy exchange between subsystems. The idea relies on the concept of a thermodynamic vibroacoustic temperature, that can be directly defined when introducing the entropy of a vibrating structure. The theory is introduced in general, and examples of calculation of the power flow between nonlinear resonators are presented introducing stiffening and clearences for systems with many degrees of freedom

ATCA: Its Performance and Application for Real Time Systems

The Advanced Telecom Computing Architecture (ATCA), describes a high bandwidth, high connectivity, chassis based architecture designed principally to appeal to the telecommunications industry. The object of the exercise was to closely connect compute engines within the chassis to multiple user services brought in at the front panel. This maps closely to the needs of real time systems and the main points of the architecture are reviewed and discussed in that light. The performance of an ATCA backplane has been tested and measured using a Backplane Tester developed within a 10 Gb/s Ethernet switch project that was an early adopter of the ATCA standard. Some results from these tests are presented

Passage efficiency and migration behavior for adult Atlantic salmon at a Half-Ice Harbor fish ladder

Due to exploitation of the world’s rivers, the upstream migration of anadromous species is frequently delayed or even prevented. To mitigate these problems and allow fish to migrate past obstacles, structures such as fish ladders have been developed. However, recent studies show that many of the present fish passage facilities are deficient. Monitoring and evaluation of passage facilities is therefore crucial to enable necessary adjustments. In this study I have examined the passage efficiency and the migration behavior for upstream migrating Atlantic salmon (Salmo salar L.) passing a recently built fish ladder in the river Umeälven. 104 salmon were caught, tagged and released in the spillway close to the fish way entrance during the 2012 spawning run. Tagged fish were monitored with several radio telemetry loggers and PIT-antennas (Passive Integrated Transponder). The result revealed a passage efficiency of 78% and a mean delay of 30 days, post-tagging, before passage. Salmon tagged earlier in the season delayed longer before passing the fish way. The majority of salmon visited the entrance pool several times (mean 11.3 visits) before ascending and the time spent in the entrance pool were in general high (mean 2.4 days). The activity in and out from the entrance pool followed a diel rhythmicity but was independent of discharge in the bypass channel. The ladder was visited in average 1.5 times before the final ascent, which took on average 17.7 hours. A delay was observed in the upper part of the ladder in front of the VAKI-system, used to count passing fish. Once past the VAKI-system, there seems to be no problem for the fish to reach river Vindelälven. I also report that the migration pattern passed the fish way did not differ between native salmons from the Ume/Vindelälven stock and strayers with a genetic origin from the Luleälven stock.Till följd av exploatering av världens vattendrag, blir uppströms migrerande fiskar ofta uppehållna eller till och med hindrade. För att minska problemen och möjligöra för fisk att passera förbi antropogena hinder har anordningar som fisktrappor byggts. Emellertid, så visar ny forskning att många av dessa fiskpassageanläggningar är bristfälliga. Uppföljning och utvärdering av nämnda anläggningar är därför avgörande för att möjliggöra nödvändiga justeringar. I denna studie har jag utvärderat passageeffektiviteten och rörelsemönstret under en vandringssäsong för uppströms migrerande lax (Salmo salar L.) i en fisktrappa belägen i Umeälvens nedre del. 104 laxar fångades, märktes och släpptes i närheten av fisktrappans entré under lekvandringen 2012. Märkt fisk följdes därefter bland annat med hjälp av flera radio-telemetriloggrar och PIT-antenner (Passiva Integrerade märken). Resultatet visade en passageeffektiviteten på 78 % och en 30 dagars (medeltal) fördröjning mellan märkning och passage av fisk trappan. Fisk som märktes tidigt under säsongen uppvisade längst fördröjning. Majoriteten av laxarna som passerade trappan besökte entré-poolen flera gånger (medeltal 11.3 besök) innan den slutgiltiga forceringen och generellt så spenderade laxarna mycket tid i entré-poolen (medeltal 2.4 dagar). Passage in och ut från entré-poolen följde en daglig rytm men var däremot oberoende av om det spilldes i utskovet. Trappan besöktes i medeltal 1.5 gånger före den slutgiltiga forceringen, vilket i medeltal tog 17.7 timmar. En fördröjning kunde ses i trappans övre del framför VAKI-utrustningen som installerats för att automatiskt räkna passerande fisk. Jag fann även att det inte fanns någon signifikant skillnad i beteendet och passage mönstret för älvsegen fisk kontra fisk av annan stamtillhörighet