In this doctoral thesis, we theoretically investigate the propagation of sound waves in dilute Bose gases, in both the collisionless and hydrodynamic regimes. The study of sound wave is a topic of high relevance for the understanding of dynamical properties of any fluid, classical or quantum, and further provides insightful information about the equation of state of the system. In our work, we focus in particular on the two-dimensional (2D) Bose gas, in which the sound wave is predicted to give useful information about the nature of the superfluid phase transition. Recently, experimental measurement of sound wave in a uniform 2D Bose gas has become available, and we show that the measured data are quantitatively well explained by our collisionless theory. Finally, we study the mixtures of weakly interacting Bose gases, by developing a beyond mean-field theory, which includes the effects of thermal and quantum fluctuations in both the density and spin channels. Our new theory allows for the investigation of sound dynamics, as well as the fundamental problem of phase- separation.

In der vorliegenden Arbeit wird eine einheitliche und allumfassende Theorie der Nicht-linearen Polarisationsspektroskopie in der Frequenzdomäne (NLPF) aufgestellt. Dies Methode basiert auf der in einer isotropen Farbstofflösung durch ein polarisiertes, monochromatisches Laserfeldes (pump) erzeugten Anisotropie, die mittels eines weiteren monochromatischen Laserfeldes (probe), mit einer um 45° gegenüber dem Pumpfeld gedrehten Polarisationsrichtung geprobt wird. Ausgehend von den grundlegenden Gleichungen für den nichtlinearen Respons molekularer Systeme auf elektromagnetische Felder wird das zweidimensional NLPF-spektrum hergeleitet, und zwar sowohl in der niedrigsten Ordnung Störungstheorie als auch unter Verwendung eines selbstkonsistenten Ansatzes für beliebige Pumpfeldstärken. In der niedrigsten Ordnung Störungstheorie können drei in ihrer Frequenzabhängigkeit sich unterscheidende Arten von Ausdrücke explizit angegeben werden. Diese sind drei Areten von Peaks im NLPF-spektrum zuzuordnen: Den T2-peaks, dem T1-peaks und den Zweiphotonen-peaks. Letztere sind unter Normalbedingungen im allgemeinen nicht beobachtbar und wurden daher nicht weiter behandelt. Die in dieser Arbeit erstmals gelungene, allgemeine und einheitliche theoretische Beschreibung der T1- und T2-peaks in NLPF-spektren von Mehrniveausystemen stellt einen Durchbruch hin zu einer allumfassenden Subbandenanalyse mittels NLPF dar. Durch Einbeziehung der teilweise bereits bekannten Auswirkungen homogener und inhomogener Linienverbreiterung und spektraler Diffusion auf NLPF-spektren, sowie deren Verallgemeinerung im Ramen der Theorie nichtmarkowscher Dissipationsprozesse, konnte eine Methodik entwickelt werden, die es erlaubt, NLPF-spektren molekularer und supramolekularer Systeme in Bezug auf das ihnen zugrundeliegende Termschema mit Übergangsfrequenzen und -dipolen, die homogenen und inhomogenen Linienbreiten, sowie dem zugeordneten Energierelaxations- und -transferpfad mitsamt zugehörigen Raten zu analysieren. Die in dieser Arbeit vorgestellte und über frühere rudimentäre Ansätze weit hinausgehende Theorie der NLPF bei starken Pumpfeldern, die auf einem selbstkonsistenten Ansatz für den Fourier-transformierten statistischen Operator beruhen, eröffnet ein komplett neues Feld von Anwendungen der NLPF. Für Zweiniveausysteme konnten die selbstkonsistenten Gleichung vollständig analytisch gelöst werden. Dabei konnten die Querverbindungen zur nichtlinearen Absorption und zum optischen Starkeffekt aufgezeigt werden. Aus der resultierenden Sättigungskurve für das NLPF-signal kann die Sättigungsintensität mit hoher Genauigkeit bestimmt werden. Diese kann unter Heranziehen der aus Analyse des T1-peaks bei niedrigen Intensitäten gewonnen Energierelaxationsrate und der analog aus T2-peakanalyse erhaltenen homogenen Linienbreite zur Bestimmung der Dipolstärke des Übergangs ohne Bestimmung der Farbstoffkonzentration verwendet werden. Dies erweist sich insbesondere bei der Analyse molekularer Aggregation als vorteilhaft. Durch Abbildung auf das gelöste Zweiniveauproblem konnte die Methodik auch auf spezielle Mehrniveausysteme übertragen werden. Eine analytische Lösung für allgemeine Mehrniveausysteme scheiterte jedoch an der komplizierten Orientierungsmittelung über die isotrope Verteilung der Übergangsdipole. Beide oben beschriebenen Methoden, Subbandanalyse bei niedrigen und Bestimmung der Übergangsdipolstärke bei hohen Pumpintensitäten, wurden in der vorliegenden Arbeit zur Untersuchung der Natur der angeregten Zustände in photosynthetischen Antennen von Purpurbakterien und höheren Pflanzen eingesetzt. Für die periphere lichtsammelnde Antenne LH2 des Purpurbakteriums Rhodobacter sphaeroides ergab die T2-peakanalyse der B850-absorptionsbande überraschenderweise zwei Subbanden, die im Absorptionsspektrum selbst bei tiefsten Temperaturen nicht aufzufinden gewesen wären. Eine Erklärung für die in Bezug auf die Oszilatorstärke asymmetrische Aufspaltung der B850-bande konnte allerdings nicht gefunden werden. Für den LH2 des sehr ähnliche Purpurbakterium Rhodospirillium molischianum konnte keine Aufspaltung der B850-bande festgestellt werden. Vielmehr liegt eine überwiegend homogen verbreiterte Bande mit einer homogener Linienbreite (FWHM) von 474±10 cm-1 und einem oberen limit für die inhomogene Linienbreite von 120 cm-1 vor. Daher wurde Rhodospirillium molischianum ausgewählt, um Delokalisation der Anregung im B850-aggregat mittels pumpintensitätsabhängiger NLPF zu untersuchen. Die Frage nach der Delokalisationslänge im B850-aggregat gab und gibt teilweise immer noch Anlass zu hitzigen Debatten. Das Ergebnis einer Ausdehnung der Anregung über 3-4 Bakteriochlorophylle des B850-aggregats der vorliegenden Arbeit unterstützt die aus Exciton-Exciton gewonnen Resultate. Weder eine vollständig lokalisierte noch vollständig delokalisierte Beschreibung war mit dem hier präsentierten Ergebnis in Übereinstimmung zu bringen. Auch im Hauptlichtsammelkomplex höherer Pflanzen LHC II konnte mittels pumpintensitätsabhängiger NLPF-spektren Delokalisation der Anregung über mindestens ein Chlì¥Á / In the work be presented a standard theory of non-linear polarization spectroscopy in the frequency domain (NLPF) will be established. The NLPF technique based on anisotropy induced in a dye-solution, which is isotropic elsewhere, by a polarized monochromatic pump laser field. This is probed by a second laser field, which polarization direction is turned of 45 degree in respect to that of the pump. From the fundamental equations describing the non-linear response of molecular systems on electromagnetic fields, the two-dimensional NLPF spectrum is deduced for arbitrary pump-intensities. At low pump-intensities a subband analysis by NLPF has been established. This allows one to study the term scheme and energy relaxation path of molecular and supra-molecular systems by their NLPF-spectra. This includes the determination of transition-frequencies and -dipole orientations, homogeneous and inhomogeneous linewidths, as well as energy relaxation rates. Furthermore, using a self-connsistent approach, the pump-fieled dependence of the NLPF-spectrum has been deduced for the two-level system in general and also for specific multi-level systems. This method allows one to determine the oscillator strength without knowledge of the concentration, what is quite useful for studying molecular aggregates. Applications are presented to the peripheral light harvesting antenna LH2 of purple bacteria and the light harvesting complexes LHC II and CP 29 of higher plants.

The size and conformational complexity of proteins and other large systems represent major challenges for today's methods of quantum chemistry.This thesis is centered around the development of new computational tools to gain molecular-level insight into electronic transitions in such systems. To meet this challenge, we focus on the polarizable embedding (PE) model, which takes advantage of the fact that many electronic transitions are localized to a smaller part of the entire system.This motivates a partitioning of the large system into two regions that are treated at different levels of theory:The smaller part directly involved in the electronic process is described using accurate quantum-chemical methods, while the effects of the rest of the system, the environment, are incorporated into the Hamiltonian of the quantum region in an effective manner. This thesis presents extensions of the PE model with theaim of expanding its range of applicability to describe electronic transitions in large molecular systemsin the optical and X-ray regions. The developments cover both improvements with regardto the quantum region as well as the embedding potential representing the environment.Regarding the former, a damped linear response formulation has been implemented to allow for calculations of absorption spectra of large molecular systems acrossthe entire frequency range. A special feature of this development is its abilityto address core excitations that are otherwise not easily accessible.Another important development presented in this thesis is the coupling of the PE model to a multi-configuration self-consistent-field description of the quantum region and its further combination with response theory. In essence, this extends the PE model to the study of electronic transitions in large systems that are prone to static correlation --- a situation that is frequently encountered in biological systems. In addition to the direct environmental effects on the electronic structure of the quantum region, another important component of the description of electronic transitions in large molecular systems is an accurate account of the indirect effects of the environment, i.e., the geometrical distortions in the quantum region imposed by the environment. In thisthesis we have taken the first step toward the inclusion of geometry distortions in the PE frameworkby formulating and implementing molecular gradients for the quantum region. To identify critical points related to the environment description, we perform a theoretical analysis of the PE model starting from a full quantum-mechanicaltreatment of a composite system. Based on this, we present strategies for an accurate yet efficient construction of the embedding potentialcovering both the calculation of ground state and transition properties. The accurate representation of the environment makes it possible to reduce the size of the quantum region without compromising the overall accuracy of the final results. This further enables use of highly accurate quantum-chemical methods despite their unfavorable scaling with the size of the system. Finally, some examples of applications will be presented to demonstrate how the PE model may be applied as a tool to gain insight into and rationalize the factors influencing electronic transitions in large molecular systems of increasing complexity. / <p>The dissertation was awarded the best PhD thesis prize 2016 by the Danish Academy of Natural Sciences.</p><p></p><p>QC 20170209</p>

Dans la modélisation de la matière dense, et partiellement ionisée, une question importante concerne le traitement des électrons libres. Vis-à-vis des électrons liés, la nature délocalisée et non discrète de ces électrons est responsable d’une différence de traitement, qui est souvent effectuée dans les modélisations des propriétés radiatives des plasmas. Cependant, afin d’éviter les incohérences dans le calcul des spectres d’absorption, tous les électrons devraient, en principe, être décrits dans un même formalisme.Nous utilisons deux modèles variationnels d’atome-moyen : un modèle semi-classique, et un modèle quantique, qui permettent cette égalité de traitement pour tous les électrons. Nous calculons la section-efficace de photo-extinction, en appliquant le cadre de la théorie de la réponse linéaire dynamique à chacun de ces modèles d’atome dans un plasma. Pour cette étude, nous développons et utilisons une approche auto-cohérente, de type random-phase-approximation (RPA), qui, en allant au-delà de la réponse des électrons indépendants, permet d’évaluer les effets collectifs, par l’introduction de la polarisation dynamique. Cette approche s’inscrit dans le formalisme de la théorie de la fonctionnelle de la densité dépendant du temps (TDDFT), appliquée au cas d’un système atomique immergé dans un plasma.Pour les deux modèles, semi-classique et quantique, nous dérivons, et vérifions dans nos calculs, une nouvelle règle de somme, qui permet d’évaluer le dipôle atomique à partir d’un volume fini dans le plasma. Cette règle de somme s’avère être un outil de premier ordre pour le calcul des propriétés radiatives des atomes dans les plasmas denses. / In modeling dense and partially ionized matter, the treatment of the free electrons remains an important issue. Compared to bound electrons, the delocalized and non-discrete nature of these electrons is responsible to treat them differently, which is usually adopted in the modelings of radiative properties of plasmas. However, in order to avoid inconsistencies in the calculation of absorption spectra, all the electrons should be described in the same formalism.We use two variational average-atom models: a semi-classical and a quantum model, which allow this common treatment for all the electrons. We calculate the photo-extinction cross-section, by applying the framework of the linear dynamical response theory to each of these models of an atom in a plasma. For this study, we develop and use a self-consistent approach, of random-phase-approximation (RPA) type, which, while going beyond the independent electron response, permits to evaluate the collective effects by the introduction of the dynamical polarization. This approach uses the formalism of the time dependent density functional theory (TDDFT), applied in the case of an atomic system immersed in a plasma.For both models, semi-classical and quantum, we derive and verify in our calculations, a new sum rule, which allows the evaluation of the atomic dipole from a finite volume in the plasma. This sum rule turns out to be a crucial device in the calculation of radiative properties of atoms in dense plasmas.

Tous les systèmes biologiques sont formés d’atomes et de molécules qui interagissent et dont émergent des propriétés subtiles et complexes. Par ces interactions, les organismes vivants peuvent subvenir à toutes leurs fonctions vitales. Ces propriétés apparaissent dans tous les systèmes biologiques à des niveaux différents, du niveau des molécules et gènes jusqu’aux niveau des cellules et tissus. Ces dernières années, les physiciens se sont impliqués dans la compréhension de ces aspects particulièrement intrigants, en particulier en étudiant les systèmes vivants dans le cadre de la théorie des réseaux, théorie qui offre des outils d’analyse très puissants. Il est possible aujourd’hui d’identifier deux classes d’approches qui sont utilisée pour étudier ces types de systèmes complexes : les méthodes directes de modélisation et les approches inverses d’inférence. Dans cette thèse, mon travail est basé sur les deux types d’approches appliquées à trois niveaux de systèmes biologiques. Dans la première partie de la thèse, je me concentre sur les premières étapes du développement des tissus biologiques des plantes. Je propose un nouveau modèle pour comprendre la dynamique collective des transporteurs de l’hormone auxine et qui permet la croissance non-homogène des tissu dans l’espace et le temps. Dans la deuxième partie de la thèse, j’analyse comment l’évolution contraint la diversité́ de séquence des protéines tout en conservant leur fonction dans différents organismes. En particulier, je propose une nouvelle méthode pour inférer les sites essentiels pour la fonction ou la structure de protéines à partir d’un ensemble de séquences biologiques. Finalement, dans la troisième partie de la thèse, je travaille au niveau cellulaire et étudie les réseaux de signalisation associés à l’auxine. Dans ce contexte, je reformule un modèle préexistant et propose une nouvelle technique qui permet de définir et d’étudier la réponse du système aux signaux externes pour des topologies de réseaux différentes. J’exploite ce cadre théorique pour identifier le rôle fonctionnel de différentes topologies dans ces systèmes. / All biological systems are made of atoms and molecules interacting in a non- trivial manner. Such non-trivial interactions induce complex behaviours allow- ing organisms to fulfill all their vital functions. These features can be found in all biological systems at different levels, from molecules and genes up to cells and tissues. In the past few decades, physicists have been paying much attention to these intriguing aspects by framing them in network approaches for which a number of theoretical methods offer many powerful ways to tackle systemic problems. At least two different ways of approaching these challenges may be considered: direct modeling methods and approaches based on inverse methods. In the context of this thesis, we made use of both methods to study three different problems occurring on three different biological scales. In the first part of the thesis, we mainly deal with the very early stages of tissue development in plants. We propose a model aimed at understanding which features drive the spontaneous collective behaviour in space and time of PINs, the transporters which pump the phytohormone auxin out of cells. In the second part of the thesis, we focus instead on the structural properties of proteins. In particular we ask how conservation of protein function across different organ- isms constrains the evolution of protein sequences and their diversity. Hereby we propose a new method to extract the sequence positions most relevant for protein function. Finally, in the third part, we study intracellular molecular networks that implement auxin signaling in plants. In this context, and using extensions of a previously published model, we examine how network structure affects network function. The comparison of different network topologies provides insights into the role of different modules and of a negative feedback loop in particular. Our introduction of the dynamical response function allows us to characterize the systemic properties of the auxin signaling when external stimuli are applied.

Orientador: Glaucia Amorim Faria / Resumo: Considerando que a intensidade de infestação (I.I.%) é um importante dado sobre o dano causado pela Diatraea saccharalis em cana-de-açúcar e que existem poucos trabalhos na literatura relacionados ao tamanho de ótimo de parcela para este tipo de amostragem, o objetivo deste trabalho foi estimar o tamanho ótimo de parcela em hectares e número de colmos que deverá ser utilizado no processo de amostragem de modo que represente a intensidade de infestação causada pelo ataque da D. saccharalis em cana-de-açúcar. Para os cálculos relativos ao tamanho da área a ser amostrada foram utilizados quatro métodos para o cálculo do tamanho de parcela: método de inspeção visual da curvatura máxima, método da máxima curvatura modificado, modelo linear segmentado com platô e modelo quadrático segmentado com platô. Para os cálculos referentes ao número de entrenós foi utilizado o método da estimativa da suficiência amostral. O método da máxima curvatura modificado foi o que proporcionou melhores resultados. De acordo com os resultados encontrados neste trabalho, podemos concluir que o número mínimo a ser amostrado é o de 36 entrenós por hectare e a área máxima a ser amostrada é a de 27,5 hectares. / Abstract: Infestation intensity (II%) is an important data on the damage caused by Diatraea saccharalis in sugarcane. There are few studies in the literature related to the optimal plot size for this type of sampling. The objective of this work is to estimate the optimal plot size in hectares and number of stems to be used in the sampling process to represent the intensity of infestation caused by D. saccharalis attack on sugarcane. For the calculation of the size of the minimum sampled area, four methods were used: 1. visual inspection method of maximum curvature; 2. modified maximum curvature method; 3. segmented linear model with plateau and; 4. quadratic segmented model with plateau. For the calculations referring to the number of internodes, the method of estimating the sample adequacy was used. The modified maximum curvature method presented the best results. According this study, the minimum number to be sampled is 36 trains per hectare and the maximum area to be sampled is 27.5 hectares. / Mestre

<p>The ability to accurately predict binding free energies from computer simulations is an invaluable resource in understanding biochemical processes and drug action. Several methods based on microscopic molecular dynamics simulations exist, and in this thesis the validation, application, and development of the linear interaction energy (LIE) method is presented.</p><p>For a test case of several hydrophobic ligands binding to P450cam it is found that the LIE parameters do not change when simulations are performed with three different force fields. The nonpolar contribution to binding of these ligands is best reproduced with a constant offset and a previously determined scaling of the van der Waals interactions.</p><p>A new methodology for prediction of binding free energies of protein-protein complexes is investigated and found to give excellent agreement with experimental results. In order to reproduce the nonpolar contribution to binding, a different scaling of the van der Waals interactions is neccesary (compared to small ligand binding) and found to be, in part, due to an electrostatic preorganization effect not present when binding small ligands.</p><p>A new treatment of the electrostatic contribution to binding is also proposed. In this new scheme, the chemical makeup of the ligand determines the scaling of the electrostatic ligand interaction energies. These scaling factors are calibrated using the electrostatic contribution to hydration free energies and proposed to be applicable to ligand binding.</p><p>The issue of codon-anticodon recognition on the ribosome is adressed using LIE. The calculated binding free energies are in excellent agreement with experimental results, and further predict that the Leu2 anticodon stem loop is about 10 times more stable than the Ser stem loop in complex with a ribosome loaded with the Phe UUU codon. The simulations also support the previously suggested roles of A1492, A1493, and G530 in the codon-anticodon recognition process.</p>

The ability to accurately predict binding free energies from computer simulations is an invaluable resource in understanding biochemical processes and drug action. Several methods based on microscopic molecular dynamics simulations exist, and in this thesis the validation, application, and development of the linear interaction energy (LIE) method is presented. For a test case of several hydrophobic ligands binding to P450cam it is found that the LIE parameters do not change when simulations are performed with three different force fields. The nonpolar contribution to binding of these ligands is best reproduced with a constant offset and a previously determined scaling of the van der Waals interactions. A new methodology for prediction of binding free energies of protein-protein complexes is investigated and found to give excellent agreement with experimental results. In order to reproduce the nonpolar contribution to binding, a different scaling of the van der Waals interactions is neccesary (compared to small ligand binding) and found to be, in part, due to an electrostatic preorganization effect not present when binding small ligands. A new treatment of the electrostatic contribution to binding is also proposed. In this new scheme, the chemical makeup of the ligand determines the scaling of the electrostatic ligand interaction energies. These scaling factors are calibrated using the electrostatic contribution to hydration free energies and proposed to be applicable to ligand binding. The issue of codon-anticodon recognition on the ribosome is adressed using LIE. The calculated binding free energies are in excellent agreement with experimental results, and further predict that the Leu2 anticodon stem loop is about 10 times more stable than the Ser stem loop in complex with a ribosome loaded with the Phe UUU codon. The simulations also support the previously suggested roles of A1492, A1493, and G530 in the codon-anticodon recognition process.

The charge and spin density correlations in a one dimensional electron gas (1DEG) confined in a semiconductor quantum wire structure at zero temperature are studied. The dielectric formulation of the many--body problem is employed and the longitudinal dielectric function, local-field correction, static structure factor, pair correlation function, ground state energy, compressibility, spin-dependent effective interaction potentials, paramagnon dispersion and static spin response function of the 1DEG are computed within the self-consistent field approximations of Singwi et al., known as the STLS and SSTL. The results are compared with those of other groups, and those obtained for two-dimensional electron gas systems whenever it is possible. It is observed that the SSTL satisfies the compressibility sum rule better than the STLS. Calculating the ground state energy of the 1DEG in unpolarized and fully polarized states, it is shown that both STLS and SSTL predict a Bloch transition for 1DEG systems at low electron densities. Finally, the coupled plasmon-phonon modes in semiconductor quantum wires are calculated within the Fermi and Luttinger liquid theories. The coupling of electrons to bulk longitudinal optical phonons without dispersion and to acoustic phonons via deformation potential with a linear dispersion are considered. Using the dielectric formalism, a unified picture of the collective coupled plasmon-phonon modes is presented. Considerable differences between the predictions of the Fermi and Luttinger liquid approaches at large wave vector values, which may be observed experimentally, are found.

Networked dynamical systems, i.e., systems of dynamical units coupled via nontrivial interaction topologies, constitute models of broad classes of complex systems, ranging from gene regulatory and metabolic circuits in our cells to pandemics spreading across continents. Most of such systems are driven by irregular and distributed fluctuating input signals from the environment. Yet how networked dynamical systems collectively respond to such fluctuations depends on the location and type of driving signal, the interaction topology and several other factors and remains largely unknown to date. As a key example, modern electric power grids are undergoing a rapid and systematic transformation towards more sustainable systems, signified by high penetrations of renewable energy sources. These in turn introduce significant fluctuations in power input and thereby pose immediate challenges to the stable operation of power grid systems. How power grid systems dynamically respond to fluctuating power feed-in as well as other temporal changes is critical for ensuring a reliable operation of power grids yet not well understood. In this work, we systematically introduce a linear response theory (LRT) for fluctuation-driven networked dynamical systems. The derivations presented not only provide approximate analytical descriptions of the dynamical responses of networks, but more importantly, also allow to extract key qualitative features about spatio-temporally distributed response patterns. Specifically, we provide a general formulation of a LRT for perturbed networked dynamical systems, explicate how dynamic network response patterns arise from the solution of the linearised response dynamics, and emphasise the role of LRT in predicting and comprehending power grid responses on different temporal and spatial scales and to various types of disturbances. Understanding such patterns from a general, mathematical perspective enables to estimate network responses quickly and intuitively, and to develop guiding principles for, e.g., power grid operation, control and design.