Symmetry breaking in small rotating clouds of trapped ultracold Bose atoms

We study the signatures of rotational and phase symmetry breaking in small rotating clouds of trapped ultracold Bose atoms by looking at rigorously defined condensate wave function. Rotational symmetry breaking occurs in narrow frequency windows, where energy degeneracy between the lowest energy states of different total angular momentum takes place. This leads to a complex condensate wave function that exhibits vortices clearly seen as holes in the density, as well as characteristic local phase patterns, reflecting the appearance of vorticities. Phase symmetry (or gauge symmetry) breaking, on the other hand, is clearly manifested in the interference of two independent rotating clouds.

Pattern selection in a lattice of pulse-coupled oscillators

We study spatio-temporal pattern formation in a ring of N oscillators with inhibitory unidirectional pulselike interactions. The attractors of the dynamics are limit cycles where each oscillator fires once and only once. Since some of these limit cycles lead to the same pattern, we introduce the concept of pattern degeneracy to take it into account. Moreover, we give a qualitative estimation of the volume of the basin of attraction of each pattern by means of some probabilistic arguments and pattern degeneracy, and show how they are modified as we change the value of the coupling strength. In the limit of small coupling, our estimative formula gives a pefect agreement with numerical simulations.

Collineations of a symmetric 2-covariant tensor: Ricci collineations

The infinitesimal transformations that leave invariant a two-covariant symmetric tensor are studied. The interest of these symmetry transformations lays in the fact that this class of tensors includes the energy-momentum and Ricci tensors. We find that in most cases the class of infinitesimal generators of these transformations is a finite dimensional Lie algebra, but in some cases exhibiting a higher degree of degeneracy, this class is infinite dimensional and may fail to be a Lie algebra. As an application, we study the Ricci collineations of a type B warped spacetime.

Computing the diameter of Coxeter groups

This thesis addresses the problem of computing the minimal and maximal diameter of the Cayley graph of Coxeter groups. We first present and assert relevant parts of polytope theory and related Coxeter theory. After this, a method of contracting the orthogonal projections of a polytope from Rd onto R2 and R3, d ¸ 3 is presented. This method is the Equality Set Projection algorithm that requires a constant number of linearprogramming problems per facet of the projection in the absence of degeneracy. The ESP algorithm allows us to compute also projected geometric diameters of high-dimensional polytopes. A representation set of projected polytopes is presented to illustrate the methods adopted in this thesis.

Uma introdução à espectroscopia atômica: II - o espectro do sódio

The present article is devoted to Chemistry or Physics undergraduate students, given their difficulty to understand fundamental concepts and technical language used in atomic spectroscopy and quantum mechanics. An easy approach is shown in the treatment of the emission spectrum of the sodium atom without any involved calculations. In a previous article, the hydrogen spectrum was considered and the energy degeneracy of the angular momentum quantum number was observed. For the sodium spectrum, due to the valence electron penetration into internal shells, a breakdown of this degeneracy occurs and a dependence of this penetration on the angular momentum quantum number is observed. The eigenvalues are determined introducing the quantum defect correction (Rydberg correction) in the denominator of the Balmer equation, and the energy diagram is obtained. The intensity ratio for the observed doublets is explained by introducing new wave functions, containing the magnetic quantum number of the total angular momentum.

Sobre uma degenerescência acidental nos deslocamentos químicos de RMN de 31P{¹H} em complexos difosfínicos de rutênio

The [RuCl(bipy)(dppb)(4-pic)]PF6 complex was prepared and fully characterized. The X-ray crystal structure of this complex was determined in order to make an unambiguous distinction between the two possible positions of the 4-methylpyridine ligand (4-pic) in the compound: trans to phosphorus atom or trans to nitrogen atom. The [RuCl(bipy)(dppb)(4-pic)]PF6 complex exhibits an unusual temperature-dependent accidental degeneracy of the 31P chemical shifts in its solution NMR spectrum.

Magnetic Resonance Experiments with Atomic Hydrogen

In this thesis three experiments with atomic hydrogen (H) at low temperatures T<1 K are presented. Experiments were carried out with two- (2D) and three-dimensional (3D) H gas, and with H atoms trapped in solid H2 matrix. The main focus of this work is on interatomic interactions, which have certain specific features in these three systems considered. A common feature is the very high density of atomic hydrogen, the systems are close to quantum degeneracy. Short range interactions in collisions between atoms are important in gaseous H. The system of H in H₂ differ dramatically because atoms remain fixed in the H₂ lattice and properties are governed by long-range interactions with the solid matrix and with H atoms. The main tools in our studies were the methods of magnetic resonance, with electron spin resonance (ESR) at 128 GHz being used as the principal detection method. For the first time in experiments with H in high magnetic fields and at low temperatures we combined ESR and NMR to perform electron-nuclear double resonance (ENDOR) as well as coherent two-photon spectroscopy. This allowed to distinguish between different types of interactions in the magnetic resonance spectra. Experiments with 2D H gas utilized the thermal compression method in homogeneous magnetic field, developed in our laboratory. In this work methods were developed for direct studies of 3D H at high density, and for creating high density samples of H in H₂. We measured magnetic resonance line shifts due to collisions in the 2D and 3D H gases. First we observed that the cold collision shift in 2D H gas composed of atoms in a single hyperfine state is much smaller than predicted by the mean-field theory. This motivated us to carry out similar experiments with 3D H. In 3D H the cold collision shift was found to be an order of magnitude smaller for atoms in a single hyperfine state than that for a mixture of atoms in two different hyperfine states. The collisional shifts were found to be in fair agreement with the theory, which takes into account symmetrization of the wave functions of the colliding atoms. The origin of the small shift in the 2D H composed of single hyperfine state atoms is not yet understood. The measurement of the shift in 3D H provides experimental determination for the difference of the scattering lengths of ground state atoms. The experiment with H atoms captured in H2 matrix at temperatures below 1 K originated from our work with H gas. We found out that samples of H in H2 were formed during recombination of gas phase H, enabling sample preparation at temperatures below 0.5 K. Alternatively, we created the samples by electron impact dissociation of H₂ molecules in situ in the solid. By the latter method we reached highest densities of H atoms reported so far, 3.5(5)x10¹⁹ cm^-3. The H atoms were found to be stable for weeks at temperatures below 0.5 K. The observation of dipolar interaction effects provides a verification for the density measurement. Our results point to two different sites for H atoms in H2 lattice. The steady-state nuclear polarizations of the atoms were found to be non-thermal. The possibility for further increase of the impurity H density is considered. At higher densities and lower temperatures it might be possible to observe phenomena related to quantum degeneracy in solid.

Isolation of DNA sequences with homology to a degenerate FaRP oligonucleotide from the crayfish Procambarus clarkii

The neuropeptide Th1RFamide with the sequence Phe-Met-Arg-Phe-amide was originally isolated in the clam Macrocallista nimbosa (price and Greenberg, 1977). Since its discovery, a large family ofFl\1RFamide-related peptides termed FaRPs have been found to be present in all major animal phyla with functions ranging from modulation of neuronal activity to alteration of muscular contractions. However, little is known about the genetics encoding these peptides, especially in invertebrates. As FaRP-encoding genes have yet to be investigated in the invertebrate Malacostracean subphylum, the isolation and characterization ofFaRP-encoding DNA and mRNA was pursued in this project. The immediate aims of this thesis were: (1) to amplify mRNA sequences of Procambarus clarkii using a degenerate oligonucleotide primer deduced from the common amino acid sequence ofisolated Procambarus FaRPS, (2) to determine if these amplification products encode FaRP gene sequences, and (3) to create a selective cDNA library of sequences recognized by the degenerate oligonucleotide primer. The polymerase chain reaction - rapid amplification of cDNA ends (PCR-RACE) is a procedure in which a single gene-specific primer is used in conjunction with a generalized 3' or 5' primer to amplify copies ofthe region between a single point in the transcript and the 3' or 5' end of cDNA of interest (Frohman et aI., 1988). PCRRACE reactions were optimized with respect to primers used, buffer composition, cycle number, nature ofgenetic substrate to be amplified, annealing, extension and denaturation temperatures and times, and use of reamplification procedures. Amplification products were cloned into plasmid vectors and recombinant products were isolated, as were the recombinant plaques formed in the selective cDNA library. Labeled amplification products were hybridized to recombinant bacteriophage to determine ligated amplification product presence. When sequenced, the five isolated PCR-RACE amplification products were determined not to possess FaRP-encoding sequences. The 200bp, 450bp, and 1500bp sequences showed homology to the Caenorhabditis elegans cosmid K09A11, which encodes for cytochrome P450; transfer-RNA; transposase; and tRNA-Tyr, while the 500bp and 750bp sequences showed homology with the complete genome of the Vaccinia virus. Under the employed amplification conditions the degenerate oligonucleotide primer was observed to bind to and to amplify sequences with either 9 or 10bp of 17bp identity. The selective cDNA library was obselVed to be of extremely low titre. When library titre was increased, white. plaques were isolated. Amplification analysis of eight isolated Agt11 sequences from these plaques indicated an absence of an insertion sequence. The degenerate 17 base oligonucleotide primer synthesized from the common amino acid sequence ofisolated Procambarus FaRPs was thus determined to be non-specific in its binding under the conditions required for its use, and to be insufficient for the isolation and identification ofFaRP-encoding sequences. A more specific primer oflonger sequence, lower degeneracy, and higher melting temperature (TJ is recommended for further investigation into the FaRP-encoding genes of Procambarlls clarkii.

Histoire, Révolution et esthétique : le temps et ses représentations dans le Tableau de Paris et le Nouveau Paris de Louis Sébastien Mercier

Thèse réalisée en cotutelle avec l'Université Paris-Sorbonne (Paris IV), sous la direction de M. Michel Delon.

Études de l’effet tunnel des spins quantiques macroscopiques

Dans cette thèse, nous présentons quelques analyses théoriques récentes ainsi que des observations expérimentales de l’effet tunnel quantique macroscopique et des tran- sitions de phase classique-quantique dans le taux d’échappement des systèmes de spins élevés. Nous considérons les systèmes de spin biaxial et ferromagnétiques. Grâce à l’approche de l’intégral de chemin utilisant les états cohérents de spin exprimés dans le système de coordonnées, nous calculons l’interférence des phases quantiques et leur distribution énergétique. Nous présentons une exposition claire de l’effet tunnel dans les systèmes antiferromagnétiques en présence d’un couplage d’échange dimère et d’une anisotropie le long de l’axe de magnétisation aisé. Nous obtenons l’énergie et la fonc- tion d’onde de l’état fondamentale ainsi que le premier état excité pour les systèmes de spins entiers et demi-entiers impairs. Nos résultats sont confirmés par un calcul utilisant la théorie des perturbations à grand ordre et avec la méthode de l’intégral de chemin qui est indépendant du système de coordonnées. Nous présentons aussi une explica- tion claire de la méthode du potentiel effectif, qui nous laisse faire une application d’un système de spin quantique vers un problème de mécanique quantique d’une particule. Nous utilisons cette méthode pour analyser nos modèles, mais avec la contrainte d’un champ magnétique externe ajouté. La méthode nous permet de considérer les transitions classiques-quantique dans le taux d’échappement dans ces systèmes. Nous obtenons le diagramme de phases ainsi que les températures critiques du passage entre les deux régimes. Nous étendons notre analyse à une chaine de spins d’Heisenberg antiferro- magnétique avec une anisotropie le long d’un axe pour N sites, prenant des conditions frontière périodiques. Pour N paire, nous montrons que l’état fondamental est non- dégénéré et donné par la superposition des deux états de Néel. Pour N impair, l’état de Néel contient un soliton, et, car la position du soliton est indéterminée, l’état fondamen- tal est N fois dégénéré. Dans la limite perturbative pour l’interaction d’Heisenberg, les fluctuations quantiques lèvent la dégénérescence et les N états se réorganisent dans une bande. Nous montrons qu’à l’ordre 2s, où s est la valeur de chaque spin dans la théorie des perturbations dégénérées, la bande est formée. L’état fondamental est dégénéré pour s entier, mais deux fois dégénéré pour s un demi-entier impair, comme prévu par le théorème de Kramer

Growth and Characterisation of Radio Frequency Magnetron Sputttered Indium Tin Oxide Thin Films

The increasing interest in the interaction of light with electricity and electronically active materials made the materials and techniques for producing semitransparent electrically conducting films particularly attractive. Transparent conductors have found major applications in a number of electronic and optoelectronic devices including resistors, transparent heating elements, antistatic and electromagnetic shield coatings, transparent electrode for solar cells, antireflection coatings, heat reflecting mirrors in glass windows and many other. Tin doped indium oxide (indium tin oxide or ITO) is one of the most commonly used transparent conducting oxides. At present and likely well into the future this material offers best available performance in terms of conductivity and transmittivity combined with excellent environmental stability, reproducibility and good surface morphology. Although partial transparency, with a reduction in conductivity, can be obtained for very thin metallic films, high transparency and simultaneously high conductivity cannot be attained in intrinsic stoichiometric materials. The only way this can be achieved is by creating electron degeneracy in a wide bandgap (Eg > 3eV or more for visible radiation) material by controllably introducing non-stoichiometry and/or appropriate dopants. These conditions can be conveniently met for ITO as well as a number of other materials like Zinc oxide, Cadmium oxide etc. ITO shows interesting and technologically important combination of properties viz high luminous transmittance, high IR reflectance, good electrical conductivity, excellent substrate adherence and chemical inertness. ITO is a key part of solar cells, window coatings, energy efficient buildings, and flat panel displays. In solar cells, ITO can be the transparent, conducting top layer that lets light into the cell to shine the junction and lets electricity flow out. Improving the ITO layer can help improve the solar cell efficiency. A transparent ii conducting oxide is a material with high transparency in a derived part of the spectrum and high electrical conductivity. Beyond these key properties of transparent conducting oxides (TCOs), ITO has a number of other key characteristics. The structure of ITO can be amorphous, crystalline, or mixed, depending on the deposition temperature and atmosphere. The electro-optical properties are a function of the crystallinity of the material. In general, ITO deposited at room temperature is amorphous, and ITO deposited at higher temperatures is crystalline. Depositing at high temperatures is more expensive than at room temperature, and this method may not be compatible with the underlying devices. The main objective of this thesis work is to optimise the growth conditions of Indium tin oxide thin films at low processing temperatures. The films are prepared by radio frequency magnetron sputtering under various deposition conditions. The films are also deposited on to flexible substrates by employing bias sputtering technique. The films thus grown were characterised using different tools. A powder x-ray diffractometer was used to analyse the crystalline nature of the films. The energy dispersive x-ray analysis (EDX) and scanning electron microscopy (SEM) were used for evaluating the composition and morphology of the films. Optical properties were investigated using the UVVIS- NIR spectrophotometer by recording the transmission/absorption spectra. The electrical properties were studied using vander Pauw four probe technique. The plasma generated during the sputtering of the ITO target was analysed using Langmuir probe and optical emission spectral studies.

Growth of metal and semiconductor nanostructures for nonlinear optical applications

Nonlinear optics has been a rapidly growing field in recent decades since the invention of lasers. The systematic progress in the laser technology increases our efficiency in the generation and control of coherent optical radiations. Nonlinear optics is based on the study ofeffects and phenomena related to the interaction of intense coherent light radiation with matter. Compared to other light sources laser radiation can provide high directionality, high monochromaticiry, high brightness and high photon degeneracy. At such a very intense incident beam, the matter responds in a nonlinear manner to the incident radiation fields, which endows the media :1 characteristic to change the refractive index or absorption coe fflcient of the media or the wavelength, or the frequency of the incident electromagnetic waves. This thesis encompasses the fabrication of nonlinear optical devices based on semiconductor and metal nanostructures. The presented work focus on the experimental and theoretical discussions on nonlinear optical effects especially nonlinear absorption and refraction exhibitted by metal and semiconductor nanostructures

Raman and FTIR spectra of [Cu(H2O)6](BrO3)2 and [Al(H2O)6](BrO3)3 · 3H2O

Raman and FTIR spectra of [Cu(H2O)6](BrO3)2 and [Al(H2O)6](BrO3)3 · 3H2O are recorded and analyzed. The observed bands are assigned on the basis of BrO3 − and H2O vibrations. Additional bands obtained in the region of 3 and 1 modes in [Cu(H2O)6](BrO3)2 are due to the lifting of degeneracy of 3 modes, since the BrO3 − ion occupies a site of lower symmetry. The appearance 1 mode of BrO3 − anion at a lower wavenumber (771 cm−1) is attributed to the attachment of hydrogen to the BrO3 − anion. The presence of three inequivalent bromate groups in the [Al(H2O)6](BrO3)3 · 3H2O structure is confirmed. The lifting of degeneracy of 4 mode indicates that the symmetry of BrO3 − anion is lowered in the above crystal from C3v to C1. The appearance of additional bands in the stretching and bonding mode regions of water indicates the presence of hydrogen bonds of different strengths in both the crystals. Temperature dependent Raman spectra of single crystal [Cu(H2O)6](BrO3)2 are recorded in the range 77–523 K for various temperatures. A small structural rearrangement takes place in BrO3 − ion in the crystal at 391 K. Hydrogen bounds in the crystal are rearranging themselves leading to the loss of one water molecule at 485 K. This is preceded by the reorientation of BrO3 − ions causing a phase transition at 447 K. Changes in intensities and wavenumbers of the bands and the narrowing down of the bands at 77 K are attributed to the settling down of protons into ordered positions in the crystal

Vibrational spectroscopic studies of FeClMoO4, Na2MoO4 and Na2MoO4·2H2O:D2O

FTIR and Raman spectra of FeClMoO4 single crystal and polycrystalline Na2MoO4, Na2MoO4·2H2O and Na2MoO4·2D2O are recorded and analysed. The band positions for different modes suggest that MoO4 tetrahedron is more distorted in FeClMoO4. The larger splitting observed for the bending modes and partial retention of degeneracy of the asymmetric stretching mode indicate that angular distortion is greater than liner distortion in MoO4 2 ion in FeClMoO4 confirming x-ray data. The non-appearance of the n1 and n2 modes in the IR and partial retention of the degeneracies of various modes show that MoO4 2 ion retains Td symmetry in Na2MoO4. Wavenumber values of the n1 mode indicate that the distortion of MoO4 tetrahedra in the four crystals are in the order FeClMoO4\ Na2MoO4·2H2O\Na2MoO4·2D2O\Na2MoO4. The water bands suggest the presence of two crystallographically distinct water molecules in Na2MoO4·2H2O. They form strong hydrogen bonds

Behavioral Measures and their Correlation with IPM Iteration Counts on Semi-Definite Programming Problems

We study four measures of problem instance behavior that might account for the observed differences in interior-point method (IPM) iterations when these methods are used to solve semidefinite programming (SDP) problem instances: (i) an aggregate geometry measure related to the primal and dual feasible regions (aspect ratios) and norms of the optimal solutions, (ii) the (Renegar-) condition measure C(d) of the data instance, (iii) a measure of the near-absence of strict complementarity of the optimal solution, and (iv) the level of degeneracy of the optimal solution. We compute these measures for the SDPLIB suite problem instances and measure the correlation between these measures and IPM iteration counts (solved using the software SDPT3) when the measures have finite values. Our conclusions are roughly as follows: the aggregate geometry measure is highly correlated with IPM iterations (CORR = 0.896), and is a very good predictor of IPM iterations, particularly for problem instances with solutions of small norm and aspect ratio. The condition measure C(d) is also correlated with IPM iterations, but less so than the aggregate geometry measure (CORR = 0.630). The near-absence of strict complementarity is weakly correlated with IPM iterations (CORR = 0.423). The level of degeneracy of the optimal solution is essentially uncorrelated with IPM iterations.