The existence of highest proton numbers at which the nuclear landscape cease to ex- ist, the end of the periodic table of elements and the limits of the existence of the nu- clei are some of the difficult questions to answer. To explore those questions, we in- vestigated hyperheavy nuclei (Z ≥ 126) using covariant density functional theory. We demonstrate the existence of three regions of spherical hyperheavy nuclei centered around (Z ∼ 138, N ∼ 230), (Z ∼ 156, N ∼ 310) and (Z ∼ 174, N ∼ 410). Also, we explored other properties of hyperheavy nuclei such as octupole deformation, alpha decay half lives, chemical potential, etc.

No description available.

Une première partie de ce mémoire portera sur l’analyse des états fondamentaux ma- gnétiques de deux composés isolants et magnétiquement frustrés SrDy2O4 et SrHo2O4. Une étude de la chaleur spécifique à basse température sous l’effet de champs magné- tiques de ces échantillons a été menée afin de détecter la présence de transitions de phases. L’utilisation d’un composé isotructurel non magnétique, le SrLu2O4, a permis l’isolement de la composante magnétique à la chaleur spécifique. Les comportements observés sont non conformes avec les transitions magnétiques conventionnelles. De plus, le calcul de l’entropie magnétique ne montre qu’un recouvrement partiel de l’entropie associée à un système d’ions magnétiques. En second lieu, une analyse des oscillations quantiques de Haas-van Alphen a été effectuée dans le LuCoIn5, composé apparenté au supraconducteur à fermions lourds CeCoIn5. Les résultats obtenus montrent une topologie de la surface de Fermi très différente comparativement aux CeCoIn5 et LaCoIn5, ayant un comportement beaucoup plus tridimensionnel sans les cylindres caractéristiques présents chez les autres membres de cette famille. Finalement, le montage d’un système de détection PIXE a permis l’analyse nucléaire d’échantillons afin de déterminer la concentration de chacun des éléments les constituant. L’analyse a été effectuée sur une série d’échantillons YbxCe1−xCoIn5 dont le changement de concentration a des effets importants sur les propriétés du système. / The first part of this thesis consist of the analysis the magnetic ground states of two magnetically frustrated insulator compounds SrDy2O4 and SrHo2O4. A study of the low temperature specific heat in magnetic fields has been carried on in order to detect phase transitions. The magnetic contribution to the specific heat has been determined using the isostructural but non magnetic compound SrLu2O4. The observed behaviour does not conform with conventional magnetic phase transitions. Also, the calculated magnetic entropy shows only a partial recovery of the entropy normally associated with magnetic ions in the systems. In the second study, I measured and analyzed de Haas-van Alphen quantum oscil- lations in LuCoIn5, a compound related to the heavy fermion superconductor CeCoIn5. The obtained results show a Fermi surface topology greatly differing from the CeCoIn5 and LaCoIn5, having a much more tridimensional behaviour, compared to the characteristics cylinder exhibited by the other members of this family. In the last part of my thesis, I’m am describing the set up of a PIXE detection system used for the nuclear analysis of thick samples in order to calculate the concentra- tion of each element present. The analysis has been carried on a series of samples of YbxCe1−xCoIn5, where the variation of concentration has major repercussions on the electronic and magnetic properties of the system.

Swarms of animals exhibit aggregations whose behavior is a challenge for mathematicians to understand. We analyze this behavior numerically and analytically by using the pairwise interaction model known as the Morse potential. Our goal is to prove the global stability of the candidate local minimizer in 1D found in A Primer of Swarm Equilibria. Using the calculus of variations and eigenvalues analysis, we conclude that the candidate local minimizer is a global minimum with respect to all solution smaller than its support. In addition, we manage to extend the global stability condition to any solutions whose support has a single component. We are still examining the local minimizers with multiple components to determine whether the candidate solution is the minimum-energy configuration.

Neste trabalho apresentamos a produção de moléculas frias heteronucleares em uma armadilha magneto-óptica mista de 39K e 85Rb e detectadas no estado fundamental. A técnica de detecção consiste na fotoionização pulsada das moléculas que, após terem sido fotoassociadas, decaem através de emissão espontânea para estados ligados do potencial do estado molecular fundamental. A partir dos resultados da produção de moléculas frias KRb, estudamos-as com relação ao tipo de colisões que as originam, e à temperatura associada ao seu movimento translacional. Experimentos foram também realizados para comprovar que as moléculas detectadas são provenientes do estado fundamental. Finalmente, também estudamos neste trabalho, a taxa segundo a qual são formadas. Concomitantemente à produção de KRb, moléculas frias homonucleares 39K2 e 85Rb2 são também formadas, detectadas e caracterizadas. São apresentados também, os primeiros passos dados em direção à realização de espectroscopia fotoassociativa dos estados ligados das moléculas heteronucleares obtidas. / In this work, cold ground-state KRb molecules were produced by photoassociation in a two species magneto-optical trap (MOT) containing 39K and 85Rb. The KRb molecules are produced through photoassociation and detected in the ground state by multiphoton pulsed ionization. We have characterized their translational temperature and measured their formation rate constant. Homonuclear cold molecules 39K2 and 85Rb2 detected in their ground state were also formed in our trap and characterized as well. It is also reported our first efforts towards the realization of photoassociation spectroscopy of the heteronuclear molecules produced in our trap.

Since the last few decades frustrated spin systems have attracted much interest. These studies are motivated by the rich variety of their unusual magnetic properties and potential applications. In this thesis, excitation spectra of the weakly coupled dimer system Ba3Cr2O8, the spin-1/2 chain material with distorted diamond structure Cu3(CO3)2(OH)2 (natural mineral azurite), and the quasi-twodimensional antiferromagnet with triangle spin structure Cs2CuBr4 have been studied by means of high-field electron spin resonance. Two pairs of gapped modes corresponding to transitions from a spin-singlet ground state to the first excited triplet state with zero-field energy gaps, of 19.1 and 27 K were observed in Ba3Cr2O8. The observation of ground-state excitations clearly indicates the presence of a non-secular term allowing these transitions. Our findings are of crucial importance for the interpretation of the field-induced transitions in this material (with critical fields Hc1 = 12.5 T and Hc2 = 23.6 T) in terms of the magnon Bose-Einstein condensation. The natural mineral azurite, Cu3(CO3)2(OH)2, has been studied in magnetic fields up to 50 T, revealing several modes not observed previously. Based on the obtained data, all three critical fields were identified. A substantial zero-field energy gap, Δ = 9.6 K, has been observed in Cs2CuBr4 above the ordering temperature. It is argued that contrary to the case for the isostructural Cs2CuCl4, the size of the gap can not be explained solely by the uniform Dzyaloshinskii-Moriya interaction, but it is rather the result of the geometrical frustration stabilizing the spin-disordered state in Cs2CuBr4 in the close vicinity of the quantum phase transition between a spiral magnetically ordered state and a 2D quantum spin liquid.

No description available.

Topological order is a new field of research involving exotic physics. Among other things it has been suggested as a means for realising fault-tolerant quantum computation. Topological degeneracy, i.e. the ground state degeneracy of a topologically ordered state, is one of the quantities that have been used to characterize such states. Topological order has also been suggested as a possible quantum information storage. We study two-dimensional lattice models defined on a closed manifold, specifically on a torus, and find that these systems exhibit topological degeneracy proportional to the genus of the manifold on which they are defined. We also find that the addition of lattice dislocations increases the ground state degeneracy, a behaviour that can be interpreted as artificially increasing the genus of the manifold. We derive the fusion and braiding rules of the model, which are then used to calculate the braiding properties of the dislocations themselves. These turn out to resemble non-abelian anyons, a property that is important for the possibility to achieve universal quantum computation. One can also emulate lattice dislocations synthetically, by adding an external field. This makes them more realistic for potential experimental realisations. / Topologisk ordning är ett nytt område inom fysik som bland annat verkar lovande som verktyg för förverkligandet av kvantdatorer. En av storheterna som karakteriserar topologiska tillstånd är det totala antalet degenererade grundtillstånd, den topologiska degenerationen. Topologisk ordning har också föreslagits som ett möjligt sätt att lagra kvantdata. Vi undersöker tvådimensionella gittermodeller definierade på en sluten mångfald, specifikt en torus, och finner att dessa system påvisar topologisk degeneration som är proportionerlig mot mångfaldens topologiska genus. När dislokationer introduceras i gittret finner vi att grundtillståndets degeneration ökar, något som kan ses som en artificiell ökning av mångfaldens genus. Vi härleder sammanslagningsregler och flätningsregler för modellen och använder sedan dessa för att räkna ut flätegenskaperna hos själva dislokationerna. Dessa visar sig likna icke-abelska anyoner, en egenskap som är viktiga för möjligheten att kunna utföra universella kvantberäkningar. Det går också att emulera dislokationer i gittret genom att lägga på ett yttre fält. Detta gör dem mer realistiska för eventuella experimentella realisationer.

Une première partie de ce mémoire portera sur l’analyse des états fondamentaux ma- gnétiques de deux composés isolants et magnétiquement frustrés SrDy2O4 et SrHo2O4. Une étude de la chaleur spécifique à basse température sous l’effet de champs magné- tiques de ces échantillons a été menée afin de détecter la présence de transitions de phases. L’utilisation d’un composé isotructurel non magnétique, le SrLu2O4, a permis l’isolement de la composante magnétique à la chaleur spécifique. Les comportements observés sont non conformes avec les transitions magnétiques conventionnelles. De plus, le calcul de l’entropie magnétique ne montre qu’un recouvrement partiel de l’entropie associée à un système d’ions magnétiques. En second lieu, une analyse des oscillations quantiques de Haas-van Alphen a été effectuée dans le LuCoIn5, composé apparenté au supraconducteur à fermions lourds CeCoIn5. Les résultats obtenus montrent une topologie de la surface de Fermi très différente comparativement aux CeCoIn5 et LaCoIn5, ayant un comportement beaucoup plus tridimensionnel sans les cylindres caractéristiques présents chez les autres membres de cette famille. Finalement, le montage d’un système de détection PIXE a permis l’analyse nucléaire d’échantillons afin de déterminer la concentration de chacun des éléments les constituant. L’analyse a été effectuée sur une série d’échantillons YbxCe1−xCoIn5 dont le changement de concentration a des effets importants sur les propriétés du système. / The first part of this thesis consist of the analysis the magnetic ground states of two magnetically frustrated insulator compounds SrDy2O4 and SrHo2O4. A study of the low temperature specific heat in magnetic fields has been carried on in order to detect phase transitions. The magnetic contribution to the specific heat has been determined using the isostructural but non magnetic compound SrLu2O4. The observed behaviour does not conform with conventional magnetic phase transitions. Also, the calculated magnetic entropy shows only a partial recovery of the entropy normally associated with magnetic ions in the systems. In the second study, I measured and analyzed de Haas-van Alphen quantum oscil- lations in LuCoIn5, a compound related to the heavy fermion superconductor CeCoIn5. The obtained results show a Fermi surface topology greatly differing from the CeCoIn5 and LaCoIn5, having a much more tridimensional behaviour, compared to the characteristics cylinder exhibited by the other members of this family. In the last part of my thesis, I’m am describing the set up of a PIXE detection system used for the nuclear analysis of thick samples in order to calculate the concentra- tion of each element present. The analysis has been carried on a series of samples of YbxCe1−xCoIn5, where the variation of concentration has major repercussions on the electronic and magnetic properties of the system.

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