Dans ce manuscrit, nous présentons une étude expérimentale d'un gaz de Bose de spin 1 avec des interactions antiferromagnétiques avec des atomes de sodium ultra-froids dans l'état hyperfin F=1. Les trois composantes Zeeman sont piégées simultanément dans des pièges dipolaires optiques. Nous obtenons un condensat de Bose-Einstein spineur par refroidissement évaporatif et nous étudions ses propriétés magnétiques. Il y a deux types d’interactions dans le système: des interactions de contact qui ne changent pas les populations des composantes Zeeman et des interactions d'échange de spin qui les modifient. Une compétition entre l'énergie Zeeman et l'énergie d'échange impose l'ordre magnétique dans le système.Nous étudions dans un premier temps les phases magnétiques de condensats de Bose-Einstein spineurs a température quasi nulle. L'état fondamental comporte deux phases qui sont observées en variant le champ magnétique (donc l'énergie Zeeman quadratique) et la magnétisation de l'échantillon. Dans la phase antiferromagnétique, le spin de l'échantillon est simplement selon l'axe du champ magnétique. Dans la phase polaire, une composante transverse apparait pour minimiser l'énergie Zeeman. Pour une magnétisation nulle, le condensat spineur forme un nématique de spin. Cet état, nommé par analogie avec la phase nématique dans les cristaux liquides, est caractérisée par des fluctuations de spin orthogonales à un axe particulier, mais sans préférer une des deux direction sur cet axe. Dans chacune des deux phases, l'ordre nématique se manifeste par un minimisation de la longueur du spin transverse en imposant une valeur particulière ($pi$) de la phase relative des composantes Zeeman ${theta = phi_{+1} + phi_{-1} - 2 phi_{0}}$. Nous mesurons la longueur du spin transverse en analysant le bruit de spin après une rotation.Dans un second temps, nous étudions la thermodynamique d'un gaz de Bose de spin 1 près de la température critique pour la condensation de Bose-Einstein. Nous mesurons plusieurs scénarios de condensation séquentiels en fonction de la magnétisation et du champ magnétique. La température critique mesurée révèle que les interactions ont un effet important quand la condensation d'une composante se fait en présence d'un condensat dans une autre composante. Nous utilisons une théorie d'Hartree-Fock simplifiée, en négligeant les interactions d’échange de spin. Nous constatons que les résultats expérimentaux sont en bon accord. Cependant, pour de bas champs magnétiques, le diagramme de phase thermodynamique est largement modifié par les interactions d'échange de spin, ce qui pose de nouvelles questions sur leur rôle a température finie. / In this manuscript, we present an experimental study of a Spin 1 Bose gas with antiferromagnetic interactions with ultracold sodium atoms in the F=1 manifold. The three Zeeman components are trapped simultaneously in optical dipole traps. By performing evaporative cooling, we obtain quasi-pure spinor Bose-Einstein condensates of which we study the magnetic properties. There are two types of interactions between the constituents of the system: Contact interactions that do not change the Zeeman populations and spin-exchange contact interactions that do. A competition between Zeeman energy and the spin-exchange energy sets the magnetic ordering in the system.We first study the magnetic phases of spinor Bose-Einstein condensates near zero temperature. The ground state present two phases that are observed by varying the magnetic field (hence the quadratic Zeeman energy) and the magnetization of the sample. In the antiferromagnetic phase, the spin of the sample is purely along the direction of the magnetic field. In the broken-axisymmetry phase, a transverse component appears in order to minimize the Zeeman energy. For zero magnetization, the spinor condensate forms a spin nematic. This state, named in analogy with the liquid crystal nematic phase, is characterized by spin fluctuations orthogonal to a particular axis, with no preferred direction along that axis. In both phases, spin nematic order manifests as a minimization of the transverse spin length that is realized by enforcing a particular value ($pi$) of the relative phase of the Zeeman components $theta = phi_{+1} + phi_{-1} - 2 phi_0$. We measure the transverse spin length by analyzing spin noise after a spin rotation.Second, we study the thermodynamics of an antiferromagnetic spin 1 Bose gas next to the critical temperature for Bose-Einstein condensation. We measure several sequential condensation scenarii depending on the magnetization and the magnetic field. The measured critical temperatures reveal a large effect of interactions when one of the Zeeman component condenses in presence of a condensate in another component. We use a simplified Hartree-Fock theory, neglecting the spin exchange interactions and note a good agreement with our data. However, for low magnetic fields, the thermodynamic phase diagram is strongly modified which raises new open questions about the role of spin exchange interactions at finite temperatures.

No description available.

In this thesis, we have tried to explain the regular and irregular(chaotic) dynamics of worm like micellar solutions on applying shear, through a detailed study of the equation of motion of a nematic order parameter tensor coupled to a hydrodynamic velocity field. We have assumed spatial variations only along one direction i.e. the gradient direction(1D model). The resulting phase diagram shows various interesting steady states or phases such as spatiotemporal chaos, temporal and spatiotemporal periodicities, and alignment of the director axis along the imposed flow field. The coupling of the orientational degrees of freedom of the order parameter with the hydrodynamic flow field holds the key to the appearance of dynamic shear bands in the system. We have solved numerically a set of coupled nonlinear equations to obtain the order parameter stress developed in the system; the magnitude of the order parameter tensor, the biaxiality parameter and the orientation of the director axis of the nemato gens under shear have also been studied in detail. To study the phase diagram obtained by time integration of the equation of motion mathematically, a stability analysis of the fixed point of motion for various parameter values has been performed so that the location of the chaotic-to-aligned phase boundary is verified. Also in the periodic region of the phase diagram, the stability of limit cycles is tested by analysing the fixed point of the corresponding Poincare map. Stability analysis of the periodic orbits leads to the observation that in the parameter space, there are regions of phase coexistence where chaotic or spatiotemporally intermittent behaviour coexists with periodic behaviour. When corrections in the imposed velocity field due to the order parameter stress were taken into account and the order parameter response was looked into at several points in the parameter space, the modified equations of motion were found to reproduce the earlier behaviour in all the different regimes if the value of a dimensionless viscosity parameter is taken to be such that the bare viscous stress overrides the order parameter stress. The phase boundaries are however different from the ones seen in the earlier model. However, for a choice of the viscosity parameter such that the order parameter stress and the bare viscous stress are comparable, we see two distinctly different attractors: a banded, periodic one that is common to both α1equalto 0, and not equal to 0 and a banded chaotic one for α1not equal to 0. Here, α1is a parameter that governs the nonlinearity in the stretching of the order parameter tensor along the direction of the applied shear. Quantitative analysis of the various chaotic attractors throws up not only positive Lyapunov exponents but also that the banded chaos is a “flip-flop” kind of chaos where the switching between two long-lived states of high and lows hear stress is chaotic, where as the behaviour in either of the two states is periodic, with either a single, isolated frequency or a bunch of harmonics. Also, the spatial correlation of the shear stress in the chaotic attractors is of much larger range than the temporal correlation, the latter being almost delta-function-like. On increasing the temperature of the system till it is above the isotropic–nematic transition temperature in the absence of shear, we find that under shear, similar attractors as those in the nematic case are observed, both for passive advection and for the full 1D hydrodynamics. This is an encouraging result since actual experiments are performed at a temperature for which the system is in the isotropic phase in the absence of shear. Thus for the 1D system, the parameter space has been explored quite extensively. Considering spatial variations only along the gradient axis of the system under shear is not enough since experiments have observed interesting behaviour in the vorticity plane in which Taylor velocity rolls were noted. Hence taking the system to 2D was necessary. Our numerical study of the 2D system under shear is incomplete because we came across computational difficulties. However, on shorter time scales we have seen a two-banded state with an oscillating interface and Taylor velocity rolls as well. The methodology used for the 2D study can also be used to reproduce the 1D results by the simple step of taking initial condition with no variation in the vorticity direction. This automatically ensures that no variation in the vorticity direction ever builds up because the equations of motion ensure that these variations in the system do not grow by themselves unless fed in at the start. Using this method, we were able to reproduce all the attractors found in the 1D calculation. Thus the 1D attractors have been observed using two different methods of calculation. Further work on the full 2D numerics needs to be done because we believe that spatiotemporally complex steady-state attractor s exist in the 2D system also for appropriate values of the parameters.

In dieser Arbeit werden Messungen der elektrischen und thermischen Transportkoeffizienten an einem antiferromagnetisch ordnenden Iridat und FeAs-basierten Hochtemperatursupraleitern vorgestellt und analysiert. Iridate sind Materialien mit starker Spin-Bahn-Kopplung. In dem zweidimensionalen Vertreter Sr_2IrO_4 führt diese Kopplung zu isolierendem Mott-Verhalten mit gleichzeitiger antiferromagnetischer Ordnung der gekoppelten Spin-Bahn-Momente. Somit stellt Sr2IrO4 ein Modellsystem für die Untersuchung magnetischer Anregungen dieser Momente in Iridaten dar. Die Analyse der Wärmeleitfähigkeit von Sr_2IrO_4 liefert erstmals klare Hinweise auf magnetische Wärmeleitung in den Iridaten. Die extrahierte magnetische freie Weglänge gibt Aufschluss über die Streuprozesse der zum Wärmetransport beitragenden Magnonen und lässt Schlüsse über die Anregungen des gekoppelten Spin-Bahnsystems zu. Die FeAs-Hochtemperatursupraleiter haben aufgrund ihrer geschichteten Kristallstruktur einen hauptsächlich zweidimensionalen Ladungstransport. Die Phasendiagramme dieser Materialien setzen sich aus Ordnungsphänomenen zusammen, die Magnetismus, Supraleitung und eine Strukturverzerrung umfassen. Das Hauptaugenmerk richtet sich auf die Reaktion der Transportkoeffizienten mit den sich ausbildenden Phasen in Vertretern der 111- und 122-Familien unter chemischer Dotierung innerhalb und außerhalb der Schichtstruktur. Mithilfe von Widerstand und magnetischer Suszeptibilität lassen sich Phasendiagramme der verschiedenen Supraleiterfamilien konstruieren. In ausgewählten Fällen werden der Hall-Koeffizient und elektrothermische Transporteffekte genutzt, um das Phasendiagramm näher zu erforschen. Der Großteil der Untersuchungen zeigt omnipräsente elektrische Ordnungsphänomene, die als nematische Phase bezeichnet werden. Die Messdaten zeigen, dass die Wärmeleitfähigkeit und der Nernst-Koeffizient dominant von Fluktuationen, die der nematischen Phase vorausgehen, beeinflusst werden. Aus den Ergebnissen der Nernst-Daten an dotiertem BaFe_2As_2 werden Schlüsse über die der nematischen Phase zugrunde liegenden Mechanismen des korrelierten Elektronensystems gezogen.

No description available.

No description available.

No description available.

No description available.

This thesis, which contains fourteen chapters in two parts, presents theoretical and computer simulation studies of dynamics in supercooled liquids and thermotropic liquid crystals. These two apparently diverse physical systems are unified by a startling similarity in their complex slow dynamics. Part I consists of six chapters on supercooled liquids while Part II comprises seven chapters on thermotropic liquid crystals. The fourteenth chapter provides a concluding note. Part I starts with an introduction to supercooled liquids given in chapter 1. This chapter discusses basic features of supercooled liquids and the glass transition and portrays some of the theoretical frameworks and formalisms that are widely recognized to have contributed to our present understanding. Chapter 2 introduces a new model of binary mixture in order to study dynamics across the supercooled regime. The system consists of an equimolar mixture of the Lennard-Jones spheres and the Gay-Berne ellipsoids of revolution, and thus one of its components has orientational degrees of freedom (ODOF). A decoupling between trans-lational diffusion and rotational diffusion is found to occur below a temperature where the second rank orientational correlation time starts showing a steady deviation from the Arrhenius temperature behavior. At low temperatures, the optical Kerr effect (OKE) signal derived from the system shows a short-to-intermediate time power law decay with a very weak dependence on temperature, if at all, of the power law exponent as has been observed experimentally. At the lowest temperature investigated, jump motion is found to occur in both the translational and orientational degrees of freedom. Chapter 3 studies how the binary mixture, introduced in the previous chapter, explores its underlying potential energy landscape. The study reveals correlations between the decoupling phenomena, observed almost universally in supercooled molecular liquids, and the manner of exploration of the energy landscape of the system. A significant deviation from the Debye model of rotational diffusion in the dynamics of ODOF is found to begin at a temperature at which the average inherent structure energy of the system starts falling as the temperature decreases. Further, the coupling between rotational diffusion and translational diffusion breaks down at a still lower temperature, where a change occurs in the temperature dependence of the average inherent structure energy. Chapters 4-6 describe analytical and numerical approaches to solve kinetic models of glassy dynamics for various observables. The β process is modeled as a thermally activated event in a two-level system and the a process is described as a β relaxation mediated cooperative transition in a double-well. The model resembles a landscape picture, conceived by Stillinger [Science 267, 1935 (1995)], where the a process is assumed to involve a concerted series of the β processes, the latter being identified as elementary relaxations involving transitions between contiguous basins. For suitable choice of parameter values, the model could reproduce many of the experimentally observed features of anomalous heat capacity behavior during a temperature cycle through the glass transition as described in chapter 4. The overshoot of the heat capacity during the heating scan that marks the glass transition is found to be caused by a delayed energy relaxation. Chapter 5 shows that the model can also predict a frequency dependent heat capacity that reflects the two-step relaxation behavior. The high-frequency peak in the heat capacity spectra appears with considerably larger amplitude than the low-frequency peak, the latter being due to the a relaxation. The model, when simplified with a modified description of the a process that involves an irreversible escape from a metabasin, can be solved analytically for the relaxation time. This version of the model captures salient features of the structural relaxation in glassy systems as described in chapter 6. In Part II, thermotropic liquid crystals are studied in molecular dynamics simulations using primarily the family of the Gay-Berne model systems. To start with, chapter 7 provides a brief introduction to thermotropic liquid crystals, especially from the perspective of the issues discussed in the following chapters. This chapter ends up with a detail description of the family of the Gay-Berne models. Chapter 8 demonstrates that a model system for calamitic liquid crystal (comprising rod-like molecules) could capture the short-to-intermediate time power law decay in the OKE signal near the isotropic-nematic (I-N) phase transition as observed experimentally. The single-particle second rank orientational time correlation function (OTCF) for the model liquid crystalline system is also found to sustain a power law decay regime in the isotropic phase near the I-N transition. On transit across the I-N phase boundary, two power law decay regimes, separated by a plateau, emerge giving rise to a step-like feature in the single-particle second rank OTCF. When the time evolution of the rotational non-Gaussian parameter is monitored as a diagnostic of spatially heterogeneous dynamics, a dominant peak is found to appear following a shoulder at short times, signaling the growth of pseudonematic domains. These observations are compared with those relevant ones obtained for the supercooled binary mixture, as discussed in chapter 2, in the spirit of the analogy suggested recently by Fayer and coworkers [J. Chem. Phys. 118, 9303 (2003)]. In chapter 9, orientational dynamics across the I-N transition are investigated in a variety of model systems of thermotropic liquid crystals. A model discotic system that consists of disc-like molecules as well as a lattice system have been considered in the quest of a universal short-to-intermediate time power law decay in orientational relaxation, if any. A surprisingly general power law decay at short to intermediate times in orientational relaxation is observed in all these systems. While the power law decay of the OKE signal has been recently observed experimentally in calamitic systems near the I-N phase boundary and in the nematic phase by Fayer and coworkers [J. Chem. Phys. 116, 6339 (2002), J. Phys. Chem. B 109, 6514 (2005)], the prediction for the discotic system can be tested in experiments. Chapter 10 presents the energy landscape view of phase transitions and slow dynamics in thermotropic liquid crystals by determining the inherent structures of a family of one-component Gay-Berne model systems. This study throws light on the interplay between the orientational order and the translational order in the mesophases the systems exhibit. The onset of the growth of the orientational order in the parent phase is found to induce a translational order, resulting in a smectic-like layer in the underlying inherent structures. The inherent structures, surprisingly, never seem to sustain orientational order alone if the parent nematic phase is sandwiched between the high-temperature isotropic phase and the low-temperature smectic phase. The Arrhenius temperature dependence of the orientational relaxation time breaks down near the I-N transition and this breakdown is found to occur at a temperature below which the system explores increasingly deeper potential energy minima. There exists a remarkable similarity in the manner of exploration of the potential energy landscape between the Gay-Berne systems studied here and the well known Kob-Andersen binary mixture reported previously [Nature, 393, 554 (1998)]. In search of a dynamical signature of the coupling between orientational order and translational order, anisotropic translational diffusion in the nematic phase has been investigated in the Gay-Berne model systems as described in chapter 11. The translational diffusion coefficient parallel to the director D// is found to first increase and then decrease as the temperature drops through the nematic phase. This reversal occurs where the smectic order parameter of the underlying inherent structures becomes significant for the first time. The non-monotonic temperature behavior of D// can thus be viewed from an energy landscape analysis as a dynamical signature of the coupling between orientational and translational order at the microscopic level. Such a view is likely to form the foundation of a theoretical framework to explain the anisotropic translation diffusion. Chapter 12 investigates the validity of the Debye model of rotational diffusion near the I-N phase boundary with a molecular dynamics simulation study of a Gay-Berne model system for calamitic liquid crystals. The Debye model is found to break down near the I-N phase transition. The breakdown, unlike the one observed in supercooled molecular liquids where a jump diffusion model is often invoked, is attributed to the growth of orientational pair correlation. A mode-coupling theory analysis is provided in support of the explanation. Chapter 13 presents a molecular dynamics study of a binary mixture of prolate ellipsoids of revolution with different aspect ratios interacting with each other through a generalized Gay-Berne potential. Such a study allows to investigate directly the aspect ratio dependence of the dynamical behavior. In the concluding note, chapter 14 starts with a brief summary of the outcome of the thesis and ends up with suggestion of a few relevant problems that may prove worthwhile to be addressed in future.

No description available.