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Šiame darbe tiriamos naujo metodo, skirto funkcijų aproksimavimui baigtine eksponenčių suma galimybės, taikant šį metodą konkrečios diferencialinių lygčių sistemos, aprašančios mechaninius virpesius, sprendiniams. Viena iš galimų darbe pristatomos mechaninių virpesių sistemos taikymo sričių – jūros bangų arba vėjo sukeltus virpesius panaudoti kaip atsinaujinantį energijos šaltinį. Tokių mechanizmų veikimo principai prieš pradedant kurti realų veikiantį modelį analizuojami taikant matematinį modeliavimą. Sudėtingos lygčių sistemos sprendiniai, priklausomai nuo sprendimo metodo, gaunami laipsninių eilučių pavidale arba kaip taškų aibė, bet nei viena iš šių formų nėra patogi sprendinio kokybiniam tyrimui. Tačiau turint sprendinio išraišką eksponentinių funkcijų su kompleksiniais koeficientais suma, žinomi ir šį sprendinį sudarančių harmonikų dažniai – svarbi konkretaus virpesių sistemos režimo charakteristika. Atliekant skaitinius eksperimentus nustatyta, jog nusistovėjusį sistemos sprendinį galima įvertinti baigtine eksponenčių suma. Aproksimavimo paklaidos priklauso nuo žingsnio, aproksimuojamos funkcijos ir skaičiavimo paklaidos. / The aim of this work was to explore the possibilities of a new method, which gives an ability to approximate functions by a finite sum of exponential functions. This method was applied to the solutions of the concrete differential equations that describe the system of mechanical oscillations. One of the possible application areas of the system of oscillations presented in the paper is to use oscillations caused by the wind or water waves as a source of renewable energy. The action principles of such mechanisms are investigated using mathematical simulation before the real working model. The solutions of the sophisticated system of differential equations are obtained either in the form of power series or a set of points, depending of the solving method chosen. However, none of these forms is convenient for exploring properties of the solution. Therefore, we have a problem to approximate the solutions with linear formations of exponential functions. It is possible then to express the solutions as the linear formations of harmonics. It is demonstrated that a steady solution of the system can be expressed as a finite sum of exponential functions. Approximation errors vary depending on the distance between the points used, the function, which is being approximated, and the computation errors.

La connaissance précise des champs électromagnétiques rayonnés par les dispositifs hyperfréquences nécessite des outils instrumentaux permettant la mesure directe ou indirecte de ces champs. La technique du scan champ proche fait partie de ces outils. Ce manuscrit décrit les travaux de caractérisation des sondes électromagnétiques pour une plate-forme de scan champ proche développée au laboratoire LAPLACE. L’accent a été mis sur la simulation électromagnétique des dispositifs de test utilisés dans le travail de déconvolution du facteur d’antenne des sondes de champs magnétiques ou électriques. Ces dispositifs comprennent aussi bien des structures planaires telles que des interconnexions en ligne microruban que des composants en guide d’ondes tels que des guides ouverts de formes rectangulaire ou circulaire. Pour analyser ces structures des logiciels commerciaux basés sur la méthode des différences finis ont été utilisés. Dans le cas des structures rayonnantes un programme basé sur la méthode de l’opérateur transverse a été développé, permettant la détermination de l’admittance de rayonnement et les champs rayonnés en zones proche et lointaine. Les résultats obtenus ont été validés par des simulations avec des outils commerciaux, et par des mesures réalisés au laboratoire. / The accurate knowledge of electromagnetic fields radiated by microwave devices requires instrumental tools for direct or indirect measurement of these fields. Near-field scan technique is one of those tools. This manuscript describes the work done to characterize electromagnetic probes using a near field scan platform developed in the laboratory LAPLACE. We focused our work on the electromagnetic simulation of test devices that are used in the deconvolution of antenna factor of magnetic or electric probes. These devices include both planar structures such as microstrip line and also waveguide components such as rectangular or circular open-ended waveguides. To analyze these structures, commercial software based on finite element method was used. In case of radiating structures, a program based on transverse operator method was developed. It allows the determination of the admittance of radiation and the radiated electromagnetic fields in near-field and far-field regions. The results were validated by simulations with commercial tools, and measurements made in the laboratory.

The aim of this work is to investigate projection operator method of deriva- tion of equations of motion for reduced density matrix and apply it to a model open quantum system. We gradually pass from quantum mechanical model of a molecule with one vibrational degree of freedom to an example of open quantum system relevant in the theory of nonlinear spectroscopy. In the thesis we present results of numerical simulations of the time evolution of the open quantum system performed with a program written for this purpose. We are specially concerned with simulations of the solution of the time-convolutionless generalized master equation up to the a second order of the perturbation expan- sion, and we show that under certain conditions it provides an exact solution of the problem. The text also contains derivation of the recurrence relations for the Franck-Condon factors for the most general case of two quantum harmonic oscillators in one space dimension, i. e. transformation matrix between two bases of the L2 (R) space determined by the solutions of the time-independent Schrödinger equation appropriate for these oscillators. 1

In this work we investigate some aspects of the physics of strongly correlated systems by taking into account both electron-electron and electron-phonon interactions as basic mechanisms for reproducing electronic correlations in real materials. The relevance of the electron-electron interactions is discussed in the first part of this thesis in the framework of a self-consistent theoretical approach, named Composite Operator Method (COM), which accounts for the relevant quasi-particle excitations in terms of a set of composite operators that appear as a result of the modification imposed by the interactions on the canonical electronic fields. We show that the COM allows the calculation of all the relevant Green s and correlation functions in terms of a number of unknown internal parameters to be determined self-consistently. Therefore, depending on the balance between unknown parameters and self-consistent equations, exact and approximate solutions can be obtained. By way of example, we discuss the application of the COM to the extended t-U-J-h model in the atomic limit, and to the two-dimensional single-band Hubbard model. In the former case, we show that the COM provides the exact solution of the model in one dimension. We study the effects of electronic correlations as responsible for the formation of a plethora of different charge and/or spin orderings. We report the phase diagram of the model, as well as a detailed analysis of both zero and finite temperature single-particle and thermodynamic properties. As far as the single-band Hubbard model is concerned, we illustrate an approximated self-consistent scheme based on the choice of a two-field basis. We report a detailed analysis of many unconventional features that arise in single-particle properties, thermodynamics and system's response functions. We emphasize that the accuracy of the COM in describing the effects of electronic correlations strongly relies on the choice of the basis, paving the way for possible multi-pole extensions to the two-field theory. To this purpose, we also study a three-field approach to the single-band Hubbard model, showing a significant step forward in the agreements with numerical data with respect to the two-pole results. The role of the electron-phonon interaction in the physics of strongly correlated systems is discussed in the second part of this thesis. We show that in highly polarizable lattices the competition between unscreened Coulomb and Fröhlich interactions results in a short-range polaronic exchange term Jp that favours the formation of local and light pairs of bosonic nature, named bipolarons, which condense with a critical temperature well in excess of hundred kelvins. These findings, discussed in the framework of the so-called polaronic t-Jp model, are further investigated in the presence of a finite on-site potential U, coming from the competition between on-site Coulomb and Fröhlich interactions. We discuss the role of U as the driving parameter for a small-to-large bipolaron transition, providing a possible explanation of the BEC-BCS crossover in terms of the properties of the bipolaronic ground state. Finally, we show that a hard-core bipolarons gas, studied as a charged Bose-Fermi mixture, allows for the description of many non Fermi liquid behaviours, allowing also for a microscopic explanation of pseudogap features in terms of a thermal-induced recombination of polarons and bipolarons, without any assumption on preexisting order or broken symmetries.

Made available in DSpace on 2016-06-02T20:15:30Z (GMT). No. of bitstreams: 1 5738.pdf: 3104025 bytes, checksum: 27f8126e91dc4b23ddd37a2e733a23fa (MD5) Previous issue date: 2014-01-29 / Universidade Federal de Sao Carlos / In the present thesis, we realize a computational modeling of semiconductor structures based on multiple quantum wells with filter barriers and on quantum wells with semiconductor diluted magnetic layers. We numerically solve the time-dependent Schrödinger s equation within the effective mass approximation, using the Split Operator method. Through the time evolved wave functions we access the dynamics quantities as the light assisted couplings of the states, in which the light is described by the inclusion of an oscillating electric field in the Hamiltonian. Then we determine the probabilities of absorption, oscillator strengths of the intersubband transitions induced by the light. Moreover we analyze the transmission probabilities and, in special, the system s photocurrent. The eigenstates and the eigenfunctions of the stationary states are also obtained within the method by simply making an imaginary time evolution. In the first work, the photocurrent of a multiple quantum well structure with filter barriers modulating the continuum above the wells was analyzed as a function of the applied bias. We find out an interesting dependence of the photocurrent with the applied field, as a differential negative photoconductance controlled by the field. We attribute this negative conductance to the interaction between the localized and extended states in the continuum, expressed by anticrossings between these states and the enhancement of the photocurrent at the crossings by the Landau-Zener-Stückelberg-Majorama like transitions. In the second work, it was evaluated the spin polarized photocurrent arising from quantum well s structures of GaMnAs, under light, electric and magnetic fields of few teslas. The study shows the existence of spectral domains in the THz ranges for which the proposed structure is strongly spin selective. For such photon frequencies, the photocurrent is spin polarized and the application of the external electric field reverts the polarization s signal. This behavior suggests the possibility of conveniently simple switching mechanisms. The physics underlying these results is studied and understood in terms of the spin-dependent coupling strengths emerging from the particular potential profiles of the heterostructures. We present two additional works related to the main ones. In the first additional one, we evaluated the dark current of the multiple quantum well structure with and without filter barriers. For doing this, we add totally the transmission probability through the structure in the Levine s model for the dark current. We observe that dark current is considerably reduced for the structure with the filter barriers when compared to the structure without these barriers. In the second additional work, we calculate the photocurrent in a ZnMnSe structure. We observe the generation of a spin polarized photocurrent controlled by the external electric field, as in the case of the GaMnAs structures. / Na presente tese, realizamos a modelagem computacional de estruturas semicondutoras baseadas em poços quânticos múltiplos com barreiras de filtro e em poços quânticos com camadas de material semicondutor magnético diluído. Para tanto, resolvemos numericamente a equação de Schrödinger dependente do tempo na aproximação de massa efetiva, por meio da evolução temporal das funções de onda do sistema, utilizando o chamado método do Split- Operator. Com as funções de onda evoluídas no tempo temos acesso às variáveis dinâmicas do sistema, como os acoplamentos entre os estados pela presença de luz, descrita na forma de um campo elétrico oscilante. Determinamos assim as probabilidades de absorção, forças de oscilador das transições intersubbandas geradas por essa excitação com luz, as probabilidades de transmissão através da estrutura e, em especial, o espectro de fotocorrente proveniente desses sistemas semicondutores. As autofunções e as autoenergias dos estados estacionários dos sistemas são obtidas pelo mesmo método realizando a evolução em tempo imaginário. No primeiro trabalho, a fotocorrente da estrutura de poços quânticos múltiplos com barreiras de filtro foi analisada em função do campo elétrico aplicado à estrutura. Foi encontrada uma dependência da fotocorrente com o campo elétrico bastante interessante, na forma de uma fotocondutância negativa controlada pelo campo elétrico aplicado à heteroestrutura. Atribuímos essa condutância negativa à interação entre estados localizados e estendidos no continuo se manifestando na forma de anticrossings e o aumento da fotocorrente para os valores de campo elétrico nos quais ocorrem esses crossings foi associado a transições de dois níveis do tipo Landau-Zener-Stückelberg-Majorama. No segundo trabalho, foi calculada a fotocorrente polarizada em spin de estruturas de poços quânticos de GaMnAs, na presença de um campo elétrico varável e um campo magnético de poucos teslas. O estudo mostrou a existência de domínios espectrais na região de THz do espectro eletromagnético, para os quais as estruturas propostas são altamente seletivas em spin. Para tais frequências, encontramos que a fotocorrente é polarizada em spin e a aplicação do campo elétrico é capaz de reverter forma muito eficiente o sinal da polarização. O comportamento observado sugere a possibilidade de mecanismos simples de controle sobre a fotocorrente e a Física por trás de tais efeitos foi entendida em termos dos acoplamentos dependentes de spin dos estados da estrutura, emergentes do perfil de potencial particular das heteroestruturas. Apresentamos dois trabalhos adicionais diretamente relacionados aos trabalhos principais. No primeiro trabalho, calculamos a corrente de escuro proveniente da estrutura de poços quânticos múltiplos com e sem barreiras de filtro, adicionando de forma integral a probabilidade de transmissão através da estrutura no modelo de Levine que determina essa corrente. Observamos que a presença das barreiras de filtro diminui significativamente a corrente de escuro dessa estrutura no regime de altos valores de campo elétrico. No segundo trabalho adicional, foi calculada a fotocorrente de uma estrutura de PQ com camada DMS, composta por ZnMnSe. Observamos a possibilidade de controle da polarização de spin com o campo elétrico, assim como no caso da estrutura composta de GaMnAs.