Neste trabalho à feita uma revisÃo das principais propriedades da molÃcula de poliacetileno sob o ponto de vista da teoria de campos. A seguir, estuda-se duas cadeias de poliacetileno acopladas usando o mesmo formalismo e verifica-se que esse sistema apresenta um gap em sua estrutura de bandas. Esse gap de energia à calculado em termos de uma massa efetiva quantizada que depende do acoplamento entre as cadeias de poliacetileno. Quando o acoplamento cessa o gap desaparece e recupera-se o resultado prÃvio de uma simples cadeia nÃo dimerizada. Mostra-se que entÃo hà uma quebra da simetria quiral. O comportamento do poliacetileno acoplado tambÃm à analisado quando existem sÃlitons em sua estrutura. Um formalismo à desenvolvido para mostrar que hà um fenÃmeno oscilatÃrio de natureza quÃntica anÃlogo Ãs oscilaÃÃes de Bloch. A condutividade do sistema à tambÃm calculada. / We review in this work the principal properties of single polyacetylene chain from a theoretical field formalism. Then, we study a coupled polyacetylene chain using the same formalism and verify that this system presents a gap in its electronic band structure. This energy gap is calculated in terms of a quantized effective mass that depends on the coupling between the polyacetylene chains. As the coupling decreases the gap vanishes and we restore the previous results of one single polyacetylene chain not dimerized. We show that there is a chiral broken symmetry. We study also the behavior of coupled polyacetilene in presence of solitons. A formalism is developed to show that there is an oscillatory phenomenon of quantum character analogous to Bloch oscillations. The conductivity of the system is also calculated.

Cette thèse est consacrée à l'étude des phases de Mott isolantes des systèmes unidimensionnels d'atomes froids fermioniques à plusieurs composantes. La première partie de ce travail consiste en l'étude du modèle des atomes froids de type alcalinoterreux de spin nucléaire I=1/2. Ces atomes possèdent un état excité métastable offrant à ces atomes un degré de liberté orbital supplémentaire et en fait des fermions à quatre composantes. L'étude est menée au demi-remplissage, aux forts et aux faibles couplages par des moyens analytiques (théorie conforme, bosonisation, refermionisation, groupe de renormalisation); elle conduit à un diagramme de phase très riche. Il comporte sept phases isolantes de Mott dont trois sont particulièrement intéressantes, car elles présentent un ordre caché qui s'apparente à la physique de Haldane de la chaîne antiferromagnétique de spin-1. Ces conclusions sont mises en regard avec des simulations numériques exécutées avec l'algorithme du groupe de renormalisation de la matrice densité (DMRG), pour un régime de couplages intermédiaires. La comparaison montre une continuité adiabatique entre les différents régimes de couplages. Une étude similaire d'un modèle d'atomes froids de spin-3/2 met en évidence la physique de Haldane dans le secteur de charge des degrés de liberté, avec pour modèle effectif une chaîne de (pseudo-)spin-1. L'étude nous permet également l'investigation des propriétés de température nulle de la chaîne bilinéaire et biquadratique de Heisenberg SO(5). On montre qu'elle présente deux phases gappées : l'une dimerisée et l'autre possédant une symétrie cachée (Z_2xZ_2)² et des états de bords de spin-3/2, séparées par un point critique appartenant à la classe d'universalité SO(5)_1. Enfin, une étude de systèmes d'atomes froids de spins demi-entiers (à 2N composantes) généralise les résultats obtenus pour les spins-3/2. Cela nous conduit en particulier à mettre en évidence un effet pair/impair suivant N, en tout point similaire à l'effet pair/impair des chaînes de spin, découvert par Haldane en 1983. / This thesis is devoted to the investigation of the Mott insulating phases arising in onedimensionalmulticomponent fermionic cold atoms systems. The first part of this work isthe study of a model with alkaline-earth cold atoms with nuclear spin I = 1/2. Thoseatoms enjoy an additional orbital degree of freedom, due to the presence of a metastableexcited state ; they thus have a total of four components. Our investigation is carried athalf-filling, at strong and at weak couplings by means of analytic methods (conformaltheory, bononization, refermionization, renormalisation group). We found that the zerotemperature phase diagram of the system is very rich : it contains seven Mott insulatingphases, among which three are particularly interesting, since they display a hiddenorder, related to the Haldane physics of the antiferromagnetic spin-1 Heisenberg chain.Our conclusions are checked against numerical simulations, that were carried out with thedensity matrix renormalization group (DMRG) algorithm for intermediate couplings. Thecomparison shows an adiabatic continuity between the different regimes. A similar studyfor a model of cold atoms with hyperfine spin-3/2 highlights the Haldane physics in thecharge sector of the degrees of freedom, with an effective model given by an antiferromagneticpseudo-spin-1 chain. This analysis provides us an opportunity to investigate thezero temperature properties of the SO(5) bilinear-biquadratic Heisenberg chain. We showthe presence of two gapped phases : one is dimerized, the other has a hidden symmetry(Z2 × Z2)2 and spin-3/2 edge states, and they are separated by a critical point that belongsto the SO(5)1 universality class. Finally, we investigate half-integer hyperfine spincold atoms systems with 2N components which generalized the results obtained for thehyperfine spin-3/2 model. This leads us to find an even/odd effect according to the parityof N, very similar to the even/odd effect of spin chains, discovered by Haldane in 1983.

Dans cette thèse nous présentons une description théorique et numérique détaillée des instabilités et des dynamiques observées dans des systèmes quasi-unidimensionnels de particules en interaction répulsive soumises à un bain thermique. Lorsque le confinement transverse décroît, ces systèmes présentent une transition structurelle les faisant passer d'une configuration en ligne à une configuration en zigzag, homogène ou inhomogène. Nous avons mis en évidence et expliqué le changement de caractère de cette bifurcation qui passe de sur-critique à sous-critique. La description quantitative de configurations d'équilibre stables, appelées " bulles ", a été réalisée, celles-ci correspondent à une coexistence de domaines en ligne et en zigzag.La dynamique des " bulles " a été ensuite étudiée à l'aide d'un modèle de particule effective diffusant dans un potentiel périodique induit par le caractère discret du système. Lorsque plusieurs " bulles " coexistent, elles interagissent et se réorganisent pour former une configuration stable à une seule " bulle " selon des mécanismes de coalescence ou de collapse. Nous avons montré que la topologie de la configuration peut induire des effets de frustration conduisant à une interaction attractive ou répulsive selon les cas.Enfin, nous avons montré que les fluctuations transverses des particules divergent à l'approche des seuils de transition et expliqué ces comportements par l'apparition de modes mous dans le spectre de vibration. Cette description en modes propres nous a permis par ailleurs de comprendre l'augmentation observée de la diffusion d'une chaîne de particules dans un potentiel périodique asymétrique par rapport à une chaîne libre. / In this thesis, we provide a detailed theoretical and numerical study of instabilities and dynamics in quasi-one-dimensional systems of repulsively interacting particles in a thermal bath.When the transverse confinement decreases, theses systems display a structural transition from a line to an homogeneous or inhomogeneous staggered row configuration. We have exhibited and explained the supercritical or subcritical character of the bifurcation according to the particles interaction and to the system geometry. The quantitative description of stable equilibrium configurations called "bubbles" has been done, their shapes consist in coexistence of line and zigzag phases.The "bubble" dynamics has been modelized by considering an effective particle that diffuses in a periodic potential induced by the discrete character of the system. When several "bubbles" coexist, they interact and evolve towards a single stable "bubble" through coalescence and collapse mechanisms. We have shown that the configuration topology has to be taken into account and exhibited frustration effects leading to either an attractive or repulsive interaction between "bubbles". Then we have shown the divergence of the mean squared transverse displacements of the particles near the transition thresholds and analytically explained these critical behaviors by the existence of a soft mode in the configuration vibrational spectrum. With this eigenmodes description, we have also interpreted a diffusion enhancement of a particle file moving on an asymmetrical periodic potential with respect to the free file diffusion.

Made available in DSpace on 2015-05-14T12:14:21Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 1279127 bytes, checksum: 1105a6754e6a3c23ca4d9086f96248a1 (MD5) Previous issue date: 2011-02-25 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / We study two problems involving granular media, the heat transport in viscous granular gases and the mechanical pulse propagation in a granular chains of toroidal ring. To study the heat transport in granular gases, we consider two mechanisms of viscous dissipation during collisions between grains. In the first mechanism, the dissipative force is proportional to the speed of the grain and dissipates not only energy but also momentum. On the other hand, the dissipative force is proportional to the relative velocity of grains and therefore conserves momentum when it dissipates energy. This allows us to explore the role of the conservation of momentum in the heat transport properties of one-dimensional nonlinear systems. We found a thermal conductivity not divergent with or without conservation of momentum. For the system where there is conservation of momentum we obtain the heat flux decreases faster than the energy loss by inelastic dissipation due to shocks, unlike what happens with the momentum conserving system, indicating that the conservation of momentum has a role relevant. We also implemented an approximation of binary collisions to study the propagation of pulses in a onedimensional chain of O-rings. In particular, we get the analytical results from which the pulse velocity is obtained by simple quadrature. The pulse velocity thus calculated is compared with the velocity obtained by numerical integration of the equations of motion. We study chains with and without precompression, chains precompressed by a constant force at both ends (constant precompression), chains precompressed by gravity (variable precompression). The application of binary collisions approximation for precompressed chains gives us an important generalization of a theory, which until then had been developed for chains without precompression, in other words sonic vacuum state. The velocities calculated using the approximation of binary collisions showed a good agreement with the results obtained from numerical simulations, with relative errors lesser than 8%. / Estudamos dois problemas envolvendo meios granulares, o transporte de calor em gases granulares viscosos e a propagação de pulsos mecânicos em cadeias granulares de anéis toróidais. Para estudar o transporte de calor em gases granulares, consideramos dois mecanismos de dissipação viscosa durante as colisões entre grãos. No primeiro mecanismo, a força dissipativa é proporcional á velocidade do grão e dissipa não apenas energia mas também momentum. No outro, a força dissipativa é proporcional a velocidade relativa dos grãos e portanto conserva momento mesmo quando dissipa energia. Isso nos permite explorar o papel da conservação do momento nas propriedades de transporte de calor desse sistema não linear unidimensional. Encontramos uma condutividade térmica não divergente com ou sem conservação de momento. Para o sistema onde não há conservação do momento obtemos que o fluxo de calor decresce mais rapidamente do que a perda de energia por dissipação devido aos choques inelásticos, diferente do que ocorre no sistema com momento conservado, indicando que a conservação de momento apresenta um papel relevante. Também implementamos uma aproximação de colisões binárias para estudar a propagação de pulsos em uma cadeia de unidimensional de anéis toroidais (O-rings). Em particular, chegamos a resultados analíticos a partir dos quais a velocidade do pulso é obtida por quadratura simples. A velocidade do pulso assim calculada é comparada com a velocidade obtida por integraçãoo numérica das equações de movimento. Estudamos cadeias com e sem precompressão, cadeias precomprimidas por uma força constante nas duas extremidades, (precompressão constante) e cadeias precomprimidas pela gravidade (precompressão variável). A aplicação da aproximação de colisões binárias para cadeias precomprimidas nos dá uma importante generalização de uma teoria que até então só havia sido desenvolvida para cadeias sem precompressão, ou seja, para cadeias em vácuo sônico. As velocidades calculadas usando a aproximação de colisões binárias apresentaram uma boa concordância com os resultados obtidos a partir das simulações numéricas, com erros relativos inferiores a 8%.