Syftet med denna licentiatuppsats är att undersöka aspekter i undervisningen som skapar förutsättningar för att elever i yngre åldrar (årskurs 2 och 3) ska engageras i ett algebraiskt arbete. Learning study har använts som metod (ansats) för att producera data. Ett forskarlag bestående av två grundskollärare i matematik och en lärarforskare har i  learning study-processen arbetat i en kolloborativ och intervenerande process.   I designen och analysen har Davydovs lärandeverksamhets teori, variationsteorin och Radfords definition av algebraiska mönstergeneraliseringar använts som teoretiska utgångspunkter. Det empiriska  datamaterialet består av (1) videoinspelade intervjuer med åtta elever samt transkriptioner av dessa; (2) videoinspelningar av tre forskningslektioner; (3) lektionsplaneringar; (4) synopsis av videoinspelade forskningslektioner; (5) transkriptioner av delar av forskningslektioner.   Resultatet består av tre identifierade kritiska aspekter som elever kan behöva urskilja för att kunna uttrycka och argumentera för en mönstergeneralisering algebraiskt: (a) att urskilja relationen mellan ett elements position och antalet komponenter; (b) att urskilja hur man kan använda relationen mellan ett elements position och antalet komponenter för att förutsäga ett godtyckligt element i mönstret; (c) att urskilja konstanten (den komponent som inte ändras utan är densamma i samtliga element) i mönstret.  Resultatet ger även exempel på vilka funktioner de lärandeverksamhetsteoretiska principerna (Davydov), problemsituation, lärandemodell och motsättningar, kan ha för att ett algebraiskt arbete ska etableras och upprätthållas. Vidare kan resultatet bidra till att fördjupa förståelsen gällande vad det innebär att kunna uttrycka och argumentera för mönstergeneraliseringar algebraiskt i yngre åldrar. Resultatet kan även bidra till kunskap som kan användas av lärare för att iscensätta och realisera en undervisning inom ramen för early algebra. / The purpose of this licentiate thesis is to study the aspects of the teaching that enable students of younger ages to be engaged in algebraic work. Learning study has been used as the method to produce data. A research team consisting of two primary school teachers in mathematics and a teacher researcher worked collaboratively, designing interventions iteratively during the learning study process.  In the design as well as analysis, Davydov's learning activity theory, Variation theory and Radford's definition of algebraic pattern generalizations have been used as theoretical starting points. The empirical data consists of (1) video-recorded interviews with eight students as well as transcriptions thereof; (2) video recordings of three research lessons; (3) lesson plans; (4) synopsis of video recordings of three research lessons; (5)  transcriptions of parts of video recorded research lessons. Results consists of three identified critical aspects that students may need to discern in order to express and justify for a pattern generalization algebraically: (a) to discern the relationship between the position of an element and the number of components; (b) to discern how to use the relationship between the position of an element and the number of components to predict an arbitrary element in the pattern; (c) to discern the constant (the component that does not change but is the same in all elements) in the pattern. Results give examples of what functions the theoretical principles of Davydov´s learning activity, problem situation, learning model and contradictions, may have for algebraic work to be established and maintained. Furthermore, the results may contribute to a deepened understanding of what it means to be able to express and justify for pattern generalizations algebraically at younger ages. The results may also contribute to knowledge that can be used by teachers to stage and carry out a teaching within the frame of early algebra.

Forskningsprojektet Matematikundervisningens innehåll byggdes upp som ett kollaborativt projekt där forskare och lärare arbetade med att analysera innehållet i strävansmålen (mål att sträva mot) i kursplanen för matematik. Ett syfte var att forskare och lärare i samverkan skulle utveckla kunskaper om de förmågor som eleverna förväntas utveckla i matematik. Det kollaborativa arbetet mellan lärarna och forskarna startade höstterminen 2004 och pågick under två läsår. Projektet genomfördes under det första året tillsammans med åtta lärare från fyra Farstaskolor i år 1-6. Det andra projektåret deltog sex lärare från tre Farstaskolor – år 7-9. Under det första projektåret handlade det matematiska innehållet om mätning av volym och under det andra ekvationer. Centralt för projektet var frågan om vad det är man kan när man är kunnig (innehållsanalys) och i vilket sammanhang detta kunnande efterfrågas. För att organisera en undervisning där strävansmålen kan realiseras arbetade lärarna och forskarna tillsammans med att genomföra innehållsanalyser och konstruera sådana uppgifter som gör det möjligt för eleverna att utforska kunskapsinnehållet. / <p>Projektrapporten är elektroniskt publicerad som PDF</p>

The aim of the research reported in this licentiate thesis was to create an environment that could support students’ learning about logarithms. To develop such a learning environment, Davydov’s ‘learning activity’ was used as a theoretical framework for the design. A new tool was created, that was used by the students to unfold and single out some of the unique properties of logarithms when solving different learning tasks. The construction of the model was inspired by Napiers original idea from 1614, i.e. exactly 400 years ago, by using two number lines; one arithmetic (i.e. based on addition) and one geometric (i.e. based on multiplication). The research approach used was learning study where teachers and researcher worked collaboratively in an iterative process to refine the research lesson. The study was conducted in six groups with six teachers in upper secondary school in a major city in Sweden. The sample comprised about 150 students and data were collected by filming lessons and by interviews with some of the students. The data were analysed using an analytic framework derived from ‘learning activity’ and the results show what supports, but also what does not support, the creation of an environment for supporting students’ learning of logarithms. The results from the study are related to former research regarding instrumental/procedural vis-à-vis relational/conceptual understanding and also about research about students’ ‘errors and misconceptions’. It is argued that the formal definition of logarithms, y = 10x &lt;-&gt; x = lgy (y &gt; 0), should not be used to introduce the concept, instead a new way is proposed. One conclusion is that it is possible to reconstruct logarithms without using the definition as a tool. The results from the analysed lessons show how students looked for ways to solve learning tasks using the new tool. The definition and the identities regarding logarithms appear as bi-products of the students learning activity. When analysing students actions, they rarely over-generalised mathematical rules, e.g. used the distributive law, or separated log-expressions, e.g. adding log expressions part by part, that seemed to be an issue according to former research.

Den här licentiatuppsatsen handlar om hur en undervisning kan främja elevers förståelse av tiobassystemet genom att de bjuds in till en undervisning där de kan delta i ett kollektivt utforskande av bassystemet, som en övergripande nivå av tiobassystemet. Syftet är att exemplifiera och diskutera hur en undervisning, som främjar elevernas möjligheter att utveckla ett tänkande om tiobassystemet på en generell eller övergripande nivå, kan utformas. Vidare är syftet att studera vad i en undervisning, designad enligt principerna för lärandeverksamhet, som kan förstås som förebyggande i specialpedagogisk mening. Studien bygger på resultatet av två artiklar med följande frågeställningar: 1) Vilka aspekter i uppgifternas utformning och genomförande främjar elevers möjligheter att pröva relationen mellan olika bastal och övergång till successivt större respektive mindre talenheter? 2) Vad i elevernas resonemang och arbete med speciellt designade uppgifter kan ses som tecken på teoretiskt tänkande om bassystemet? Learning study har använts som forskningsramverk och genererat data för uppsatsens två artiklar. Learning studyn genomfördes i årskurs 4, tillsammans med tre matematiklärare. Design och analys är inspirerad av El’konins och Davydovs matematiska program och några principer från lärandeverksamhet. Analysen i de bägge artiklarna är genomförd med stöd av teoretiska principer för lärandeverksamhet. Datamaterialet består av videoinspelningar från tre lektioner (totalt cirka 420 minuter), transkriptioner och datasammanställningar av uppgifter, transkriptioner och anteckningar från utvärderingarna i det iterativa arbetet med lektionerna. Resultatet består av tre aspekter som behöver synliggöras genom uppgifternas utformning och genomförande för att eleverna ska kunna arbeta teoretiskt med bassystemets struktur: (1) Bastalet, (2) Tal som mätetal, och (3) Talenheternas representationer. Eleverna behöver urskilja aspekterna för att kunna identifiera att det fattas en lämplig talenhet och för att kunna pröva och reflektera över relationen mellan bastalet och övergången till successivt större respektive mindre talenheter i olika baser. Resultatet består också av ett antal exempel på tecken på teoretiskt tänkande inom tre identifierade kategorier: 1) basens funktion för det värde som siffrorna anger i talet, 2) positionsväxling, och (3 entalet som ett av en kvantitet. I analysen har Davydovs definition av teoretiskt tänkande, som något som kan komma till uttryck i form av teoretisk reflektion, analys och planering samt reproduktion av grundläggande principer för ett specifikt ämnesinnehåll, använts. Resultatet ger ett bidrag till den matematikdidaktiska forskningen och till den specialpedagogiska forskningen med inriktning mot matematik genom beskrivningar av de tre aspekterna och av tecken på teoretiskt tänkande. Vidare kan beskrivningarna av uppgifternas utformning och genomförande användas i undervisning och i fortsatta studier. I diskussionen behandlas hur en undervisning kan utformas som främjar elevernas möjligheter att utveckla ett teoretiskt tänkande om bassystemet. Diskussionen behandlar också vad i en undervisning designad enligt principerna för lärandeverksamhet som kan förstås som förebyggande i specialpedagogisk mening genom att skapa möjligheter för elever att redan tidigt i grundskolan kollektivt utforska och förstå hela positionssystemet som en struktur. Slutligen diskuteras implikationer för specialundervisning och studiens bidrag. / The subject of this licentiate thesis is about how a teaching can promote students' understanding of the base-ten system by inviting them to a teaching where they can collectively explore the base system, as an overall level of the base-ten system. The aim is to exemplify and discuss how teaching, which affords students opportunities to develop thinking about the base-ten system on a general or overall level, can be designed. Furthermore, the aim is to study teaching designed according to the principles of learning activity in terms of how it can be preventive from a special pedagogical perspective. The study is based on the results of two articles with the following questions: 1) Which aspects in the design and implementation of the tasks afford students opportunities to explore the relationship between different base numbers and the transition to successively larger and smaller number units? 2) What in the students' reasoning and work with specially designed tasks can be seen as signs of theoretical thinking about the base system? Learning study has been used as a research framework and generated data for the two articles. The learning study was carried out in year 4, together with three mathematics teachers. Design and analysis are inspired by El’konin’s and Davydov’s mathematical program and some principles from learning activity. The theoretical principles for learning activity were used as tools for analysis. Data consists of video recordings from three lessons (in total approximately 420 minutes), transcriptions and data compilations of tasks, transcriptions, and notes from the evaluations in the iterative work with the lessons. The results consist of three aspects that need to be made visible through the design and implementation of the tasks so that the students can work theoretically with the structure of the base system: (1) The base number, (2) Number as a measurement number, and (3) The representations of the number units. The students need to distinguish the aspects in order to discern that a bigger or smaller number unit is missing and to test and reflect on the relationship between the base number and the transition to successively larger and smaller number units, constructed in different bases. The result also includes several examples of signs of emerging theoretical thinking within three identified categories: 1) the bases function to the digits´ value in the number, 2) position switching, and (3) the unit as one of a quantity. In the analysis, Davydov's definition of theoretical thinking, as something that can be expressed in the form of theoretical reflection, analysis, and planning as well as the reproduction of fundamental principles for specific subject content, has been used. The results contribute to mathematics didactic research and to special educational research with a focus on mathematics through descriptions of the three aspects and signs of theoretical thinking. Further the descriptions of how tasks can be designed and carried out be used in teaching and continued research. The discussion deals with how teaching can be designed that afford student opportunities to develop theoretical thinking about the base system. The discussion also deals with what in a teaching designed according to the principles of learning activity can be understood as preventive in a special pedagogical perspective, by creating opportunities for students to collectively explore and understand the entire position system as a structure already early in elementary school. Finally, implications for special education and the contribution of the study are discussed. / <p>Sammanläggningen i Pdf innehåller båda artiklarna. </p>

Made available in DSpace on 2014-06-11T19:24:51Z (GMT). No. of bitstreams: 0 Previous issue date: 2014-01-29Bitstream added on 2014-06-13T20:13:16Z : No. of bitstreams: 1 000740583.pdf: 772759 bytes, checksum: 5bc332bc8f38186ade4166fa30c09c72 (MD5) / Esta pesquisa tem por objetivo compreender e investigar as inter-relações do uso das Tecnologias de Informação e Comunicação e alguns conceitos da teoria de Vasili Davydov, que propõe o desenvolvimento do pensamento teórico de um determinado conteúdo/fenômeno em estudo. Este pensamento caracteriza-se por priorizar a essência dos conteúdos/fenômenos por meio da análise das condições de sua origem e desenvolvimento. A pesquisa, que é de cunho bibliográfico, procura compreender a proposta do autor para o ensino de Matemática. Para alcançarmos o objetivo da pesquisa nos propomos a desenvolver exemplos que mostram a possibilidade de desenvolver um trabalho voltando o olhar para a essência de conceitos por meio do uso de tecnologias, em especial, o computador com software. Destacamos a importância do papel do professor como mediador dos processos de ensino e aprendizagem pautados na teoria de Davydov, conduzindo e proporcionando o desenvolvimento dos conceitos científicos por meio de atividades de ensino orientadas para a observação da essência dos conceitos / This research aims to understand and investigate the interrelationships of the use of Information and Communication Technologies and some concepts of the theory of Vasili Davydov, which proposes the development of theoretical thinking of a particular content/phenomenon under study. This thought is characterized by prioritizing the essence of the contents/phenomena through the analysis of the conditions of its origin and development. The research, which is a bibliographical nature, the proposal seeks to understand the author for teaching mathematics. To achieve the research objective, we propose to develop examples that show the possibility of developing a job turning his gaze to the essence of concepts through the use of technology, in particular computer with software. We stress the importance of the teacher's role as mediator of the teaching and learning guided theory of Davydov, leading and encouraging the development of scientific concepts through targeted education activities to observe the essence of concepts

We utilize the multi Davydov-Ansatz, an Ansatz of the bosonic many-body wave function in terms of moving Gaussian basis functions, to illuminate several aspects of open quantum system dynamics and quantum many-body theory. By two artifices alongside the time-dependent variational principle we extract from this Ansatz, commonly considered ill-behaved and not converging, a highly stable and converging method. Its extremely favourable scaling of the numerical effort with the number of degrees of freedom facilitates exploration of the zero and non-zero temperature physics of both system and environment of open quantum systems in the strong coupling regime, even in cases where the system is laser-driven. The discovery that strongly coupling a system to an environment may, apart from the introduction of dissipation and decoherence also serve as a resource for the system has fuelled the research on strongly correlated open quantum systems. Although the advent of ultra powerful data processors enables advanced methods to tackle these systems, their explicit treatment without further assumptions remains an eminently challenging task. With the multi Davydov-Ansatz we numerically exactly calculate the dynamics of various open systems coupled strongly to an environment. In particular, we illuminate diverse aspects of laser-driven molecular dynamics in dissipative environments. Based on a rigorous investigation of the time-dependent variational principle for moving Gaussian basis functions, we systematically develop a linear algebra formulation of the system of equations of motion for the Ansatz parameters. On its basis we precisely isolate the origin of the issues related to the multi Davydov-Ansatz and solve the long-standing convergence problem of the method by a regularization termed apoptosis. We show exemplary for the ohmic and sub-ohmic Spin-Boson model that apoptosis renders the multi Davydov-Ansatz a highly stable method with an outstanding speed of convergence, suited to numerically exactly reproduce the dynamics of the model at surprisingly humble numerical effort even for strong coupling strengths. Furthermore, since they are not suited to efficiently reproduce Fock number states in many-body systems, we shed some light on possible extensions of the Gaussian basis functions in the multi Davydov-Ansatz in terms of displaced number states and in terms of squeezed states. In particular we argue that due to the emergence of an inappropriate number of equations of motion, there is no straightforward generalization of the multi Davydov-Ansatz by displaced number states. For the purpose of further optimization of the multi Davydov-Ansatz, we investigate in detail the impact on the numerical effort of different representations of an open system's environment. In particular, different frequency discretizations for given continuous spectral densities are examined with respect to the speed of convergence of the system dynamics to the continuum limit. We utilize a Windowed Fourier Transform as an a priori measure for the quality of the discretized representation of bath correlations. Furthermore, efficient representations of the environment for shifted initial conditions in general and non-zero temperature in particular are found systematically. As an alternative representation of an environment of mutually uncoupled harmonic oscillators, we investigate an environment represented in terms of a linear chain of effective modes. In this context we detail how to consistently reformulate the effective mode representation in second quantization, removing inadvertent double excitations introduced by the original formulation. We show that the alternative representation is beneficial in cases where the bath spectral density is highly structured, while for the ohmic and sub-ohmic spectral density of the Spin-Boson model it is of no advantage. Once we have identified the numerically most efficient representation of the environment, we apply the multi Davydov-Ansatz in order to illuminate several aspects of open quantum system dynamics whose investigation has previously remained occlusive. In particular, the access to the exact dynamics of the environmental degrees of freedom allows to shed light on the question for the channels through which energy can be interchanged between system and environment in the considered systems. Firstly, in a system-bath setup we survey the vibrational relaxation dynamics of deuterium dimers at a silicon surface. The investigation of the relaxation dynamics requires the quantum mechanical treatment of multiple system levels, which in turn prohibits a treatment of the environmental dynamics on a perturbative level. We demonstrate that the multi Davydov-Ansatz allows for a numerically exact calculation of the system dynamics with multiple system levels and a huge number of surface vibrations explicitly taken into account. Furthermore, due to the structure of the spectral density of the environment, the effective mode representation allows for this system to dramatically reduce the numerical effort. Secondly we shall investigate in detail the relaxation dynamics of an exciton in a one-dimensional molecular crystal. Since the strong coupling regime renders highly complicated the phonon dynamics, apoptosis turns out to be inevitably required in order to reliably converge the system dynamics. We show that the multi Davydov-Ansatz equipped with apoptosis allows for an extremely efficient calculation of the exciton and phonon dynamics, for both large hopping integrals and large molecular crystals. Furthermore we illuminate diverse aspects of laser-driven molecular dynamics in a dissipative environment. By restriction to two electronic energy levels we determine the channels through which system and environment interchange energy in the vicinity of an avoided crossing in a dissipative Landau-Zener model. In particular, we reveal that the final transition probability can be tuned by coupling to the environment for both diagonal and off-diagonal coupling. By appropriately adjusting the initial excitation of the system, the final transition probability is shown to converge to a fixed value for increasing coupling. Finally, we investigate in detail laser-induced population transfer by rapid adiabatic passage in a dissipative environment. By application of the multi Davydov-Ansatz it is shown for zero as well as for non-zero temperature that strongly coupling the system to an environment can serve as a resource for the population inversion. In particular, we shall examine how the coupling to the environment compensates for the decay channels in the system even if the laser pulse is only weakly chirped.:1. Introduction 2. Prerequisites 2.1. Harmonic oscillator basics 2.2. Canonical coherent states of the harmonic oscillator 2.3. Overcompleteness of CS and the Segal-Bargmann transformation 2.4. Density operator representation in terms of CS 2.5. Ideal squeezed states 2.6. Displaced number states 2.7. On the variational principle 3. Real time propagation with CS 3.1. Variational principle with CS 3.1.1. Gauge freedom in the vMCG Ansatz 3.1.2. Equations of motion for the vMCG Ansatz 3.2. Standard form of the linear system 3.3. Regularity of the coefficient matrix 3.3.1. Regularization in the case of vanishing coefficients 3.3.2. Apoptosis of CS 3.4. The route to Semiclassics 3.5. Variational principle with DNS and squeezed states 3.6. The multi Davydov-Ansatz 3.7. The multi Davydov-Ansatz at non-zero temperature 4. Open Quantum Systems 4.1. System-Bath Hamiltonian 4.2. The road to classical dissipation 4.3. The impact of apoptosis and regularization of the 𝜌-matrix 4.3.1. Multi Davydov-Ansatz for the Quantum Rabi model 4.3.2. Multi Davydov-Ansatz and the Spin-Boson model 4.3.2.1. Spin-Boson model in the ohmic regime 4.3.2.2. Spin-Boson model in the sub-ohmic regime 4.4. The Windowed Fourier Transform 4.5. The sub-ohmic case and the problem of oversampling 4.5.1. On the polarized initial condition 4.5.2. On the treatment of non-zero temperature 4.6. The Effective Mode Representation 5. Applications 5.1. Vibrational relaxation dynamics at surfaces 5.2. Relaxation dynamics of the Holstein polaron 5.3. The dissipative Landau Zener Model 5.3.1. Coupling to a single environmental mode 5.3.2. Coupling to multiple environmental modes 5.4. Rapid Adiabatic Passage with a dissipative environment 6. Summary And Outlook List of abbreviations Appendix A. Closure relation of displaced number states B. Hamilton equations: classical vs. CCS for a Morse oscillator C. Equations of motion for the multi Davydov-Ansatz C.1. D2-Ansatz C.2. D1-Ansatz D. Details of implementation E. Calculation of the BCF F. Calculation of the polarized initial condition for 𝑇 = 0 Bibliography List of publications

This thesis deals with exciton relaxation processes in thin polycrystalline films and matrix-isolated molecules of the perylene derivatives PTCDA (3,4,9,10-perylenetetracarboxylic dianhydride) and MePTCDI (N,N'-dimethylperylene-3,4,9,10-dicarboximide). Using femtosecond pump-probe spectroscopy, transient absorption spectra, excitonic relaxation in the lowest excited state subsequent to excitation, and exciton-exciton interaction and annihilation at high excitation densities have been addressed. Transient absorption spectroscopy in the range 1.2eV-2.6eV has been applied to thin polycrystalline films of PTCDA and MePTCDI and to solid solutions of PTCDA and MePTCDI molecules (monomers) in a SiO2 matrix. We are able to ascribe the respective signal contributions to ground state bleaching, stimulated emission, and excited state absorption. Both systems exhibit broad excited-state absorption features below 2.0eV, with dominant peaks between 1.8eV and 2.0eV. The monomer spectra can be consistently explained by the results of quantum-chemical calculations on single molecules, and the respective experimental polarization anisotropies for the two major transitions agree with the calculated polarizations. Dimer calculations allow to qualitatively understand the trends visible in the experimental results from monomers to thin films. The broad excited state absorption band between 1.8eV and 2.0eV allows to probe the population dynamics in the first excited state of thin films. We show that excitons created at the Gamma point relax towards the border of the Brillouin zone on a 100fs time scale in both systems. Excitonic relaxation is accelerated by increase of temperature and/or excitation density, which is attributed to stimulated phonon emission during relaxation in k-space. Lower and upper limits of the intraband relaxation time constants are 25fs (resolution limit) and 250fs (100fs) for PTCDA (MePTCDI). These values agree with the upper limit for the intraband relaxation time of 10ps, evaluated from time-resolved luminescence measurements. While the luminescence anisotropy is in full accordance with the predictions made by a luminescence anisotropy model being consistent with the exciton model of Davydov-split states, the pump-probe anisotropy calls for an explanation beyond the models presently available. At excitation densities 10^(19)cm^(-3), the major de-excitation mechanism for the relaxed excitons is exciton-exciton annihilation, resulting in a strongly reduced exciton life time. Three different models for the microscopic behavior have been tested: a diffusion-limited annihilation model in both three and one dimensions (with diffusion constant D as fit parameter) as well as a long-range single-step Förster-type annihilation model (with Förster radius RF as fit parameter). For PTCDA, the latter two, being structurally equivalent, allow to fit a set of multiexponential decay curves for multiple initial exciton densities with high precision. In contrast, the three-dimensional diffusion-limited model is clearly inferior. For all three models, we extract annihilation rates, diffusion constants and diffusion lengths (or Förster radii), for both room and liquid helium temperature. Temperature dependence and orders of magnitude of the obtained parameters D or RF correspond to the expectations. For MePTCDI, the 1D and the Förster model are in good agreement for a smaller interval of excitation densities. For a initial exciton densities higher than 5 x 10^(19)cm^(-3), the 3D model performs significantly better than the other two.

This thesis deals with exciton relaxation processes in thin polycrystalline films and matrix-isolated molecules of the perylene derivatives PTCDA (3,4,9,10-perylenetetracarboxylic dianhydride) and MePTCDI (N,N'-dimethylperylene-3,4,9,10-dicarboximide). Using femtosecond pump-probe spectroscopy, transient absorption spectra, excitonic relaxation in the lowest excited state subsequent to excitation, and exciton-exciton interaction and annihilation at high excitation densities have been addressed. Transient absorption spectroscopy in the range 1.2eV-2.6eV has been applied to thin polycrystalline films of PTCDA and MePTCDI and to solid solutions of PTCDA and MePTCDI molecules (monomers) in a SiO2 matrix. We are able to ascribe the respective signal contributions to ground state bleaching, stimulated emission, and excited state absorption. Both systems exhibit broad excited-state absorption features below 2.0eV, with dominant peaks between 1.8eV and 2.0eV. The monomer spectra can be consistently explained by the results of quantum-chemical calculations on single molecules, and the respective experimental polarization anisotropies for the two major transitions agree with the calculated polarizations. Dimer calculations allow to qualitatively understand the trends visible in the experimental results from monomers to thin films. The broad excited state absorption band between 1.8eV and 2.0eV allows to probe the population dynamics in the first excited state of thin films. We show that excitons created at the Gamma point relax towards the border of the Brillouin zone on a 100fs time scale in both systems. Excitonic relaxation is accelerated by increase of temperature and/or excitation density, which is attributed to stimulated phonon emission during relaxation in k-space. Lower and upper limits of the intraband relaxation time constants are 25fs (resolution limit) and 250fs (100fs) for PTCDA (MePTCDI). These values agree with the upper limit for the intraband relaxation time of 10ps, evaluated from time-resolved luminescence measurements. While the luminescence anisotropy is in full accordance with the predictions made by a luminescence anisotropy model being consistent with the exciton model of Davydov-split states, the pump-probe anisotropy calls for an explanation beyond the models presently available. At excitation densities 10^(19)cm^(-3), the major de-excitation mechanism for the relaxed excitons is exciton-exciton annihilation, resulting in a strongly reduced exciton life time. Three different models for the microscopic behavior have been tested: a diffusion-limited annihilation model in both three and one dimensions (with diffusion constant D as fit parameter) as well as a long-range single-step Förster-type annihilation model (with Förster radius RF as fit parameter). For PTCDA, the latter two, being structurally equivalent, allow to fit a set of multiexponential decay curves for multiple initial exciton densities with high precision. In contrast, the three-dimensional diffusion-limited model is clearly inferior. For all three models, we extract annihilation rates, diffusion constants and diffusion lengths (or Förster radii), for both room and liquid helium temperature. Temperature dependence and orders of magnitude of the obtained parameters D or RF correspond to the expectations. For MePTCDI, the 1D and the Förster model are in good agreement for a smaller interval of excitation densities. For a initial exciton densities higher than 5 x 10^(19)cm^(-3), the 3D model performs significantly better than the other two.

Au cours de ce projet, nous avons utilisé la microspectroscopie Raman et de photoluminescence pour étudier des matériaux bidimensionnels (graphène et dichalcogénures de métaux de transition) et des hétérostructures de van der Waals. Tout d’abord, à l’aide de transistors de graphène munis d’une grille électrochimique, nous montrons que la spectroscopie Raman est un outil extrêmement performant pour caractériser précisément des échantillons de graphène. Puis, nous explorons l’évolution des propriétés physiques de N couches de dichalcogénures de métaux de transition semi-conducteurs, en particulier de ditellurure de molybdène (MoTe2) et de diséléniure de molybdène (MoSe2). Dans ces structures lamellaires, nous observons la séparation de Davydov des phonons optiques au centre de la première zone de Brillouin, que nous décrivons à l’aide d’un modèle de chaîne linéaire. Enfin, nous présentons une étude toute optique du transfert de charge et d’énergie dans des hétérostructures de van der Waals constituées de monocouches de graphène et de MoSe2. Ce travail de thèse met en évidence la riche photophysique de ces matériaux atomiquement fins et leur potentiel en vue de la réalisation de nouveaux dispositifs optoélectroniques. / In this project, we have used micro-Raman and micro-photoluminescence spectroscopy to study two-dimensional materials (graphene and transition metal dichalcogenides) and van der Waals heterostructures. First, using electrochemically-gated graphene transistors, we show that Raman spectroscopy is an extremely sensitive tool for advanced characteri-zations of graphene samples. Then, we investigate the evolution of the physical properties of N-layer semiconducting transition metal dichalcogenides, in particular molybdenum ditelluride (MoTe2) and molybdenum diselenide (MoSe2). In these layered structures, theDavydov splitting of zone-center optical phonons is observed and remarkably well described by a ‘textbook’ force constant model. We then describe an all-optical study of interlayer charge and energy transfer in van der Waals heterostructures made of graphene and MoSe2 monolayers. This work sheds light on the very rich photophysics of these atomically thin two-dimensional materials and on their potential in view of optoelectronic applications.

Thèse numérisée par la Direction des bibliothèques de l'Université de Montréal.