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批判卡爾波普之批判理性 / The criticism of Popper's rational criticism.

Glycosaminoglycans (GAGs) play an important role in many biological processes in the extracellular matrix. In a theoretical approach, structures of monosaccharide building blocks of natural GAGs and their sulfated derivatives were optimized by a B3LYP6311ppdd//B3LYP/ 6-31+G(d) method. The dependence of the observed conformational properties on the applied methodology is described. NMR chemical shifts and proton-proton spin-spin coupling constants were calculated using the GIAO approach and analyzed in terms of the method's accuracy and sensitivity towards the influence of sulfation, O1-methylation, conformations of sugar ring, and ω dihedral angle. The net sulfation of the monosaccharides was found to be correlated with the 1H chemical shifts in the methyl group of the N-acetylated saccharides both theoretically and experimentally. The ω dihedral angle conformation populations of free monosaccharides and monosaccharide blocks within polymeric GAG molecules were calculated by a molecular dynamics approach using the GLYCAM06 force field and compared with the available NMR and quantum mechanical data. Qualitative trends for the impact of sulfation and ring conformation on the chemical shifts and proton-proton spin-spin coupling constants were obtained and discussed in terms of the potential and limitations of the computational methodology used to be complementary to NMR experiments and to assist in experimental data assignment.

A measurement-independent formulation of quantum mechanics called ‘regular histories’ (RH) is presented, able to reproduce the predictions of the standard formalism without the need to for a quantum-classical divide or the presence of an observer. It applies to closed systems and features no wave-function collapse. Weights are assigned only to histories satisfying a criterion called ‘regularity’. As the set of regular histories is not closed under the Boolean operations this requires a new con- cept of weight, called ‘likelihood’. Remarkably, this single change is enough to overcome many of the well-known obstacles to a sensible interpretation of quantum mechanics. For example, Bell’s theorem, which makes essential use of probabilities, places no constraints on the locality properties of a theory based on likelihoods. Indeed, RH is both counter- factually definite and free from action-at-a-distance. Moreover, in RH the meaningful histories are exactly those that can be witnessed at least in principle. Since it is especially difficult to make sense of the concept of probability for histories whose occurrence is intrinsically indeterminable, this makes likelihoods easier to justify than probabilities. Interaction with the environment causes the kinds of histories relevant at the macroscopic scale of human experience to be witnessable and indeed to generate Boolean algebras of witnessable histories, on which likelihoods reduce to ordinary probabilities. Further- more, a formal notion of inference defined on regular histories satisfies, when restricted to such Boolean algebras, the classical axioms of implication, explaining our perception of a largely classical world. Even in the context of general quantum histories the rules of reasoning in RH are remark- ably intuitive. Classical logic must only be amended to reflect the fundamental premise that one cannot meaningfully talk about the occurrence of unwitnessable histories. Crucially, different histories with the same ‘physical content’ can be interpreted in the same way and independently of the family in which they are expressed. RH thereby rectifies a critical flaw of its inspiration, the consistent histories (CH) approach, which requires either an as yet unknown set selection rule or a paradigm shift towards an un- conventional picture of reality whose elements are histories-with-respect-to-a-framework. It can be argued that RH compares favourably with other proposed interpretations of quantum mechanics in that it resolves the measurement problem while retaining an essentially classical worldview without parallel universes, a framework-dependent reality or action-at-a-distance.

L'approximation adiabatique en mécanique quantique stipule que si un système quantique évolue assez lentement, alors il demeurera dans le même état propre. Récemment, une faille dans l'application de l'approximation adiabatique a été découverte. Les limites du théorème seront expliquées lors de sa dérivation. Ce mémoire à pour but d'optimiser la probabilité de se maintenir dans le même état propre connaissant le système initial, final et le temps d'évolution total. Cette contrainte sur le temps empêche le système d'être assez lent pour être adiabatique. Pour solutionner ce problème, une méthode variationnelle est utilisée. Cette méthode suppose connaître l'évolution optimale et y ajoute une petite variation. Par après, nous insérons cette variation dans l'équation de la probabilité d'être adiabatique et développons en série. Puisque la série est développée autour d'un optimum, le terme d'ordre un doit nécessairement être nul. Ceci devrait nous donner un critère sur l'évolution la plus adiabatique possible et permettre de la déterminer. Les systèmes quantiques dépendants du temps sont très complexes. Ainsi, nous commencerons par les systèmes ayant des énergies propres indépendantes du temps. Puis, les systèmes sans contrainte et avec des fonctions d'onde initiale et finale libres seront étudiés. / The adiabatic approximation in quantum mechanics states that if the Hamiltonian of a physical system evolves slowly enough, then it will remain in the instantaneous eigenstate related to the initial eigenstate. Recently, two researchers found an inconsistency in the application of the approximation. A discussion about the limit of this idea will be presented. Our goal is to optimize the probability to be in the instantaneous eigenstate related to the initial eigenstate knowing the initial and final system, with the total time of the experiment fixed to $T$. This last condition prevents us from being slow enough to use the adiabatic approximation. To solve this problem, we turn to the calculus of variation. We suppose the ideal evolution is known and we add a small variation to it. We take the result, put it in the probability to be adiabatic and expand in powers of the variation. The first order term must be zero. This enables us to derive a criterion which will give us conditions on the ideal Hamiltonian. Those conditions should define the ideal Hamiltonian. Time dependent quantum systems are very complicated. To simplify the problem, we will start by considering systems with time independent energies. Afterward, the general case will be treated.

Ce mémoire est une poursuite de l’étude de la superintégrabilité classique et quantique dans un espace euclidien de dimension deux avec une intégrale du mouvement d’ordre trois. Il est constitué d’un article. Puisque les classifications de tous les Hamiltoniens séparables en coordonnées cartésiennes et polaires sont déjà complétées, nous apportons à ce tableau l’étude de ces systèmes séparables en coordonnées paraboliques. Premièrement, nous dérivons les équations déterminantes d’un système en coordonnées paraboliques et ensuite nous résolvons les équations obtenues afin de trouver les intégrales d’ordre trois pour un potentiel qui permet la séparation en coordonnées paraboliques. Finalement, nous démontrons que toutes les intégrales d’ordre trois pour les potentiels séparables en coordonnées paraboliques dans l’espace euclidien de dimension deux sont réductibles. Dans la conclusion de l’article nous analysons les différences entre les potentiels séparables en coordonnées cartésiennes et polaires d’un côté et en coordonnées paraboliques d’une autre côté. Mots clés: intégrabilité, superintégrabilité, mécanique classique, mécanique quantique, Hamiltonien, séparation de variable, commutation. / This thesis is a contribution to the study of classical and quantum superintegrability in a two-dimensional Euclidean space involving a third order integral of motion. It consists of an article. Because the classifications of all separable hamiltonians into Cartesian and polar coordinates are already complete, we bring to this picture the study of those systems in parabolic coordinates. First, we derive the determinating equations of a system into parabolic coordinates, after which we solve the obtained equations in order to find integrals of order three for potentials, which allow the separations of variables into the parabolic coordinates. Finally, we prove that all the third order integrals for separable potentials in parabolic coordinates in the Euclidean space of dimension two are reducible. In the conclusion of this article, we analyze the differences between the separable potentials in Cartesian and polar coordinates and the separable potentials in parabolic coordinates. Keywords: integrability, superintegrability, classical mechanics, quantum mechanics, Hamiltonian, separation of variables, commutation.

Studies of Lanthanide Complexes by a Combination of Spectroscopic Methods Monika Krupová (Department of Physical and Macromoecular Chemistry, Faculty of Science, Charles University in Prague) Since conventional structural analysis offers rather limited means for the chirality detection, a series of lanthanide tris-(β-diketonates) are investigated as effective receptors for a better chirality sensing in biomolecular substrates. These lanthanide complexes containing β-diketonate ligands are electrically neutral; they can further coordinate with various small organic molecules such as chiral alcohols, amino alcohols or amino acids in organic solvents and produce a strong chiral signal. Previously, a resonance in Raman scattering was observed in the studied systems due to the correspondence of europium electronic transition energy to the laser excitation wavelength, about a 100-fold signal enhancement if compared to non-resonant vibrational ROA was observed. This enabled shorter detection times as well as lower sample concentrations. In the current work, interaction of the Eu(FOD) complex with (R)- and (S)- enantiomer of 1-phenylethanol in n-hexane was studied using IR spectroscopy, Raman spectroscopy and Raman optical activity (ROA), UV-Vis spectroscopy and ultraviolet circular dichroism (UVCD). Only...

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Este trabalho consiste em um estudo teórico da coexistência de condensados de Bose-Einstein atômicos acoplados. Esta mistura de condensados pode consistir em átomos de um mesmo elemento em vários estados hiperfinos (estado interno). Outra situação em que esta mistura ocorre é quando um átomo em um único estado interno pode ocupar mais de um estados externo. As semelhanças e diferenças entre condensados de Bose-Einstein com vários estados internos e externos serão analisadas cuidadosamente. Somente na aproximação de Bose-Hubbard os estados externos serão tratados como internos. Condensados envolvendo duas ou mais espécies serão estudados com a aproximação de Thomas-Fermi com estados coerentes. Esta aproximação implica em desprezar o termo de energia cinética. Muitos resultados analíticos serão exibidos para a condição em que todos os comprimentos de espalhamento são iguais entre si. Esta condição é bastante próxima da observada em um condensado de vários estados internos. Além disso serão apresentados alguns resultados anaíticos onde o comprimento de espalhamento para espécies diferentes é zero. Esta condição é verificada para a aproximação de Bose-Hubbard para misturas de condensados com estados externos. O objetivo principal destes cálculos é estudar o papel da fase relativa entre as funções de onda nas soluções estacionárias e na evolução temporal destes sistemas. / This work consists of a theoretical study of the coexistance of coupled atomic Bose-Einstein condensates. These mixed condensates can consist of atoms of the same element in different hyperfine internal states. A different situation is that in which an atom in one internal state can ocupate different single particle external states. The similarities and differences between mixed Bose-Einstein condensates involving internal and external states will be analysed carefully. Only in the Bose-Hubbard approximation the external states can be treated like internal states. Condensates involving two or more species will be studied with in a Thomas- Fermi\'s approximation with coherent states. This approximation involves in discarding of the Hamiltonian the kinetic energy term. A number of analytical results are given for the case in which the different channel scatering lenghts are equal to each other. This condition is which well approximated in condensates involving many internal states. Beside some results will also be given for situations where the scatering lenghts for different species vanishes. This condiction is verified for the Bose-Hubbard approximation to externally mixed condensates. The principal goal of this calculations is to study the role of relative phase between the wave functions in the stationary solutions and in the time evolution of the systems.

Nesta tese estudamos dois problemas diferentes na área de átomos ultra frios: Ondas de choque em condensados de Bose-Einstein e Espalhamento inelástico de átomos em um potencial de dois poços. No primeiro problema, estudamos o fluxo supersônico de um condensado de Bose-Einstein (BEC) através de um obstáculo macroscópico impenetrável delgado no sistema da equação de Schrödinger não-linear (NLS) bidimensional. Assumindo-se que a velocidade do fluxo é suficientemente alta, reduzimos assintoticamente o problema bidimensional original de valor de contorno para o fluxo estacionário através de um obstáculo alongado ao problema do pistão dispersivo unidimensional descrito pela NLS 1D dependente do tempo, no qual a coordenada original x reescalonada faz o papel de tempo e o movimento do pistão está vinculado à geometria do obstáculo. Duas ondas de choque dispersivas (DSWs) são geradas no fluxo, cada uma sendo formada em uma extremidade (frontal e traseira) do obstáculo. A DSW frontal é descrita analiticamente construindo-se soluções de modulação exatas para as equações de Whitham e a para a DSW traseira, empregamos a regra de quantização de Bohr-Sommerfeld generalizada para descrever a distribuição dos sólitons escuros. Propomos uma extensão da solução de modulação tradicional, a fim de incluir o padrão de ship-wave linear formado fora da região da DSW frontal. Realizamos simulações numéricas 2D completas e verificamos a validade das previsões analíticas. Os resultados deste problema podem ser relevantes para experimentos recentes sobre o fluxo de BECs através de obstáculos. No segundo problema, estudamos uma mistura atômica de dois átomos fermiônicos leves de spin 1/2 e dois átomos pesados em um potencial de dois poços. Processos de espalhamento inelástico entre ambas as espécies atômicas excitam os átomos pesados e renormalizam a taxa de tunelamento e a interação entre os átomos leves (efeito polarônico). A interação efetiva dos átomos leves muda de sinal e se torna atrativa quando o espalhamento inelástico é forte. Observamos também o cruzamento de níveis de energia, de um estado onde cada poço contém apenas um férmion (espalhamento inelástico fraco) para um estado onde um poço contém um par de férmions e ou outra está vazio (espalhamento inelástico forte). Identificamos o efeito polarônico e o cruzamento dos níveis de energia estudando-se a dinâmica quântica do sistema. / In this thesis we study two different problems in the field of ultracold atoms: Shock waves in Bose-Einstein condensates and Inelastic scattering of atoms in a double well. In the first problem, we study the supersonic flow of a Bose-Einstein condensate (BEC) past a slender impenetrable macroscopic obstacle in the framework of the twodimensional (2D) defocusing nonlinear Schr¨odinger equation (NLS). Assuming the oncoming flow speed sufficiently high, we asymptotically reduce the original boundary-value problem for a steady flow past a slender body to the one-dimensional dispersive piston problem described by the nonstationary NLS equation, in which the role of time is played by the stretched x-coordinate and the piston motion curve is defined by the spatial body profile. Two steady oblique spatial dispersive shock waves (DSWs) spreading from the pointed ends of the body are generated in both half-planes. These are described analytically by constructing appropriate exact solutions of the Whitham modulation equations for the front DSW and by using a generalized Bohr-Sommerfeld quantization rule for the oblique dark soliton fan in the rear DSW. We propose an extension of the traditional modulation description of DSWs to include the linear ship-wave pattern forming outside the nonlinear modulation region of the front DSW. Our analytic results are supported by direct 2D unsteady numerical simulations and are relevant to recent experiments on Bose-Einstein condensates freely expanding past obstacles. In the second problem, we study a mixture of two light spin-1/2 fermionic atoms and two heavy atoms in a double well potential. Inelastic scattering processes between both atomic species excite the heavy atoms and renormalize the tunneling rate and the interaction of the light atoms (polaron effect). The effective interaction of the light atoms changes its sign and becomes attractive for strong inelastic scattering. This is accompanied by a crossing of the energy levels from singly occupied sites at weak inelastic scattering to a doubly occupied and an empty site for stronger inelastic scattering. We are able to identify the polaron effect and the level crossing in the quantum dynamics.