Tesi sul tema "Gases in"

Interacting Fermi gases are one of the chief paradigms of condensed matter physics. They have been studied since the beginning of the development of quantum mechanics, but continue to produce surprises today. Recent experimental developments in the field of ultracold atomic gases, as well as conventional solid state materials, have produced new and exotic forms of Fermi gases, the theoretical understanding of which is still in its infancy. This Thesis aims to provide updated tools and additional insights into some of these systems, through the application of both numerical and analytical techniques. The first Part of this Thesis is concerned with the development of improved numerical tools for the study of interacting Fermi gases. These tools take the form of accurate model potentials for the dipolar and contact interactions, as found in various ultracold atomic gas experiments, and a new form of Jastrow correlation factor that interpolates between the radial symmetry of the inter-electron Coulomb potential at short inter-particle distances, and the symmetry of the numerical simulation cell at large separation. These methods are designed primarily for use in quantum Monte Carlo numerical calculations, and provide high accuracy along with considerable acceleration of simulations. The second Part shifts focus to an analytical analysis of spin-imbalanced Fermi gases with an attractive contact interaction. The spin-imbalanced Fermi gas is shown to be unstable to the formation of multi-particle instabilities, generalisations of a Cooper pair containing more than two fermions, and then a theory of superconductivity is built from these instabilities. This multi-particle superconductivity is shown to be energetically favourable over conventional superconducting phases in spin-imbalanced Fermi gases, and its unusual experimental consequences are discussed.

This thesis discusses diverse electrochemical strategies for the determination of the concentration of the gases hydrogen sulfide, ammonia and halothane. The chemical tagging of sulfide by a variety of structurally diverse substituted benzoquinone species was studied over a wide range of pH (22S in the range 20-200 μM. More sensitive (LoD= 1 (μM) amperometric detection of sulfide was obtained at modified nickel electrodes in acidic media in which sulfide was stripped from the nickel oxide layer. This approach was exploited further by using nickel modified screen printed carbon (Ni-SPC) electrodes as economical and disposable sensors for sulfide. Next, two different strategies for determining gaseous ammonia in the ionic liquid 1-ethyl-3-methylimidazolium bis(trifluromethylsulfonyl)imide, [EMIM][N(Tf)₂], and in DMF are described. The first approach exploits the effect of ammonia as a proton acceptor species on the anodic oxidation of hydroquinone, resulting in a linear detection range from 10 to 95 ppm ammonia (LoD= 4.2 ppm). The second approach is based on the direct oxidation of ammonia in either DMF or [EMIM][N(Tf)₂]. The possibility of photochemically induced electrocatalytic processes within microdroplets containing p-chloranil (2,3,5,6-tetrachloro-1,4-benzoquinone, TCBQ) was examined as a means of detecting the anaesthetic gas halothane.

Finally, two of the more promising routes for sulfide detection were studied at elevated temperatures (up to 70 °C) with a view to developing H₂S sensors capable of meeting the demands of oilfield applications.

Orientador: Silvio Antonio Sachetto Vitiello
Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin
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Resumo: Nessa dissertação nós investigamos dois sistemas de muitos corpos. Na primeira parte nós escolhemos uma abordagem clássica para estudar a adsorção de gases nobres pesados, Ne, Ar, Kr, Xe e Rn, em substratos de grafeno. Nós apresentamos evidências de camadas adsorvidas comensuradas, as quais dependem fortemente da simetria do substrato, para duas estruturas: camadas de Ne na rede sqrt{7} X sqrt{7} e Kr na rede sqrt{3} X sqrt{3}. Para estudar o derretimento nós introduzimos um parâmetro de ordem e sua susceptibilidade. O calor específico e a susceptibilidade em função da temperatura foram calculados para os gases nobres pesados em diversas densidades. A posição e largura característica dos picos do calor específico e da susceptibilidade foram determinadas. Finalmente, nós investigamos a distância dos primeiros vizinhos e a distância entre a camada e o substrato, identificando contribuições relacionadas aos picos do calor específico e da susceptibilidade. A segunda parte da dissertação trata de uma linha de vórtice no gás unitário de Fermi. Gases fermiônicos ultrafrios são notáveis devido à possibilidade experimental de variar as interações interpartículas através de ressonâncias de Feshbach, o que possibilita a observação do crossover BCS-BEC. No meio do crossover encontra-se um estado fortemente interagente, o gás unitário de Fermi. Uma linha de vórtice corresponde a uma excitação desse sistema com unidades de circulação quantizadas. Nós construímos funções de onda, inspiradas na função BCS, para descrever o estado fundamental e também o sistema com uma linha de vórtice. Nossos resultados para o estado fundamental elucidam aspectos da geometria cilíndrica do problema. O perfil de densidade é constante no centro do cilindro e vai a zero suavemente na borda. Nós separamos a contribuição devido à parede da energia do estado fundamental e determinamos a energia por partícula do bulk, epsilon_0=(0.42 +- 0.01) E_{FG}. Nós também calculamos o gap superfluído para essa geometria, Delta=(0.76 +- 0.01) E_{FG}. Para o sistema com a linha de vórtice nós obtivemos o perfil de densidade, o qual corresponde a uma densidade não nula no centro do vórtice, e a energia de excitação por partícula, epsilon_{ex}=(0.0058 +- 0.0003) E_{FG}. Os métodos empregados nessa dissertação, Dinâmica Molecular, Monte Carlo Variacional e Monte Carlo de Difusão, nos dão uma base sólida para a investigação de sistemas relacionados, e outros sistemas, de muitos corpos no futuro
Abstract: In this dissertation we investigated two many-body systems. For the first part we chose a classical approach to study the adsorption of heavy rare-gases, Ne, Ar, Kr, Xe and Rn, on graphene substrates. We presented evidences of commensurate adlayers, which depend strongly on the symmetry of the substrate, for two structures: Ne adlayers in the sqrt{7} X sqrt{7} superlattice and Kr in the sqrt{3} X sqrt{3} lattice. In order to study the melting of the system we introduced an order parameter, and its susceptibility. The specific heat and susceptibility as a function of the temperature were calculated for the heavy noble gases at various densities. The position and characteristic width of the specific heat and susceptibility peaks of these systems were determined. Finally, we investigated the first neighbor distance and the distance between the adlayer and the substrate, identifying contributions related to specific heat and melting peaks. The second part of the dissertation deals with a vortex line in the unitary Fermi gas. Ultracold Fermi gases are remarkable due to the experimental possibility to tune interparticle interactions through Feshbach resonances, which allows the observation of the BCS-BEC crossover. Right in the middle of the crossover lies a strongly interacting state, the unitary Fermi gas. A vortex line corresponds to an excitation of this system with quantized units of circulation. We developed wavefunctions, inspired by the BCS wavefunction, to describe the ground state and also for a system with a vortex line. Our results for the ground state elucidate aspects of the cylindrical geometry of the problem. The density profile is flat in the center of the cylinder and vanishes smoothly at the wall. We were able to separate from the ground state of the system the wall contribution and we have determined the bulk energy as epsilon_0=(0.42 +- 0.01) E_{FG} per particle. We also calculated the superfluid pairing gap for this geometry, Delta=(0.76 +- 0.01) E_{FG}. For the system with a vortex line we obtained the density profile, which corresponds to a non-zero density at the core, and the excitation energy, epsilon_{ex}=(0.0058 +- 0.0003) E_{FG} per particle. The methods employed in this dissertation, Molecular Dynamics, Variational Monte Carlo and Diffusion Monte Carlo, give us a solid basis for the investigation of related and other many-body systems in the future
Mestrado
Física
Mestre em Física
2012/24195-2
FAPESP

The present work consists of three parts. In the first part (chapters III and IV), the dynamics of Lorentz lattice gases (LLG) on graphs is analyzed. We study the fixed scatterer model on finite graphs. A tight bound is established on the size of the orbit for arbitrary graphs, and the model is shown to perform a depth-first search on trees. Rigidity models on trees are also considered, and the size of the resulting orbit is established. In the second part (chapter V), we give a complete description of dynamics for LLG on the one-dimensional integer lattice, with a particular interest in showing that these models are not capable of universal computation. Some statistical properties of these models are also analyzed. In the third part (chapter VI) we attempt to partition a pool of workers into teams that will function as independent TSS lines. Such partitioning may be aimed to make sure that all groups work at approximately the same rate. Alternatively, we may seek to maximize the rate of convergence of the corresponding dynamical systems to their fixed points with optimal production at the fastest rate. The first problem is shown to be NP-hard. For the second problem, a solution for splitting into pairs is given, and it is also shown that this solution is not valid for partitioning into teams composed of more than two workers.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2001.
Includes bibliographical references (leaves 93-96).
In this thesis, we study the effects of interparticle interactions on the optical spectrum of cold gases. We first consider homogenous gas in the weak excitation regime and find that the optical spectrum of a system of Bosons is highly sensitive to interactions. We find that optical excitations, at temperatures low enough for the thermal de Broglie wavelength to be larger than the scattering length, become collective modes. We study collective affects in the optical spectrum both above and below Bose-Einstein condensation, and show that the spectrum acquires a doublet structure when the condensate forms. We present a detailed theory of spectral shift and an estimate of some of the broadening effects. We derive a sum rule for the average frequency shift of an optical spectrum and investigate the basic conservation laws and symmetries of the system lying at the basis of this sum rule. We also compare the sum rule for the optical spectrum with the f-sum rule for the density-density correlation function. Finally we derive a transport equation for the optical modes in a dilute Bose system, which allows us to study the non-linear response to the excitation field. We map the problem onto the dynamics of two interacting anisotropic spins, and calculate the precession frequencies exactly both below and above Bose condensation. We demonstrate a relation between Rabi oscillations and internal Josephson oscillations, and find that an analogue of the internal Josephson effect exists in a non-condensed system.
(cont.) We also derive the transport equation for a dilute Fermi system and find that the dependence of the precession frequencies on interparticle interactions is very weak for fermions.
by Mehmet Özgür Oktel.
Ph.D.

Thesis (MTech (Chemical Engineering))--Peninsula Technikon, 2000.
Oxygen transport across biofilms and membranes may be a limiting factor in the operation of a membrane bio-reactor. A Gradostat fungal membrane bio-reactor is one in which fungi are immobilized within the wall of a porous polysulphone capillary membrane. In this study the mass transfer rates of gases (oxygen and carbon dioxide) were investigated in a bare membrane (without a biofilm being present). The work provides a basis for further transport study in membranes where biomass is present. The diaphragm-cell method can be employed to study mass transfer of gases in flat-sheet membranes. The diaphragm-cell method employs two well-stirred compartments separated by the desired membrane to be tested. The membrane is maintained horizontally. -The gas (solute) concentration in the lower compartment is measured versus time, while the concentration in the upper liquid-containing compartment is maintained at a value near zero by a chemical reaction. The resistances-in-series model can be used to explain the transfer rate in the system. The two compartments are well stirred; this agitation reduces the resistances in the liquid boundary layers. Therefore it can be assumed that in this work the resistance in the membrane will be dominating. The method was evaluated using oxygen as a test. The following factors were found to influence mass transfer coefficient: i) the agitation in the two compartments; ii) the concentration of the reactive solution and iii) the thickness of the membrane.

This work will introduce the Efimov effect and the resonant and scaling limits and derive the formula for the binding energies of the Efimov states. We use the hyperspherical coordinates for the stationary wave function of three particles and solve the low-energy Faddeev equation with the hyperspherical expansion and use the expansion for solving the channel eigenvalues. The channel eigenvalues are defined by a constant, which is the solution of the resulting transcendental equation. We also solve the scaling-violation parameter and finally compile all the results to derive the Efimov states. In the unitary limit we find infinitely many Efimov states, with an accumulation point at zero energy and an asymptotic discrete scaling symmetry with the discrete scaling factor of about 22.7. In this work, we will also delve into effective field theories, which can be used to numerically analyze and solve Efimov states in different cases. We will first go through the two-body problem which is used as a simpler example on how to solve the three-body problem and to solve the two-body coupling constant, which will also appear in the three-body problem. By using the diatom field trick introduced by Bedaque, Hammer and van Kolck, we derive the Skorniakov-Ter-Martirosian equation for the three-body problem. Finally this work will take a quick look at the first experimental evidences for Efimov states that were found since 2006. In the experiment, proper Efimov resonances in measurements of three-body recombination have been observed.

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Physics, 2019
Cataloged from the official PDF of thesis.
Includes bibliographical references (pages 147-151).
Quantum simulation is a very active and growing field. Various quantum systems can be used to emulate existing materials in an accurate and controllable way, as well as to generate new states of matter that have not been found in the real world but the existence of which does not contradict the fundamental laws of physics. Ultracold atoms form a perfect system to realize idealized models and study physical mechanisms that stand out clearly in them. Recent efforts have been made to simulate artificial gauge fields with ultracold atoms, including spin-dependent gauge fields, such as spin-orbit coupling. Motivated by this goal our lab explored several approaches to generate a one-dimensional spinorbit coupling interaction, which has a rich phase diagram and plays an important role for topological insulators, the quantum spin Hall effect and spintronics.
The first method we developed allowed us to detect a stripe phase by dressing Bose-Einstein condensates with an optical superlattice and Raman beams. The observed density modulation in the ground state meets the definition of the long-awaited supersolid state of matter. The second approach we took was to generate spin-orbit coupling without use of lasers. The method is based on the idea of periodic driving of the quantum system and dressing its evolution with fast micromotion, often refered to as Floquet engineering. Our experiment provided an insightful pedagogical example of what Floquet engineering is capable of. In the experiment we endowed a low energy radio-frequency photon with tunable momentum. When dressed with recoil momentum, the interaction of a radio-frequency photon with an atom occurred in a Doppler-sensitive way. We also demonstrated how to tune the momentum and flip its direction. In this thesis, I first describe the experiments done in the optical superlattice.
Then I discuss the behavior of periodically driven classical and quantum systems and provide detailed analysis of how a radio-frequency photon can be magnetically dressed with tunable momentum. The experiments we carried out demonstrated novel methods of generation for spin-dependent gauge fields and showed pedagogical examples and interpretations of evolution of periodically driven systems. The scheme of periodically driven atoms inspired a theoretical study of heating in Floquet systems.
by Boris Shteynas.
Ph. D.
Ph.D. Massachusetts Institute of Technology, Department of Physics

Transonic flow of dense gases for two-dimensional, steady state, flow over a NACA 0012 airfoil was predicted analytically. The computer code used to model the dense gas behavior was a modified version of Jameson's FLOS2 airfoil code. The modifications to the code enabled modeling the dense gas behavior near the saturated vapor curve and critical pressure region where the fundamental derivative, Γ, is negative. This negative Γ region is of interest because the nonclassical gas behavior such as formation and propagation of expansion shocks, and the disintegration of inadmissible compression shocks. The results of this study indicated that dense gases with undisturbed thermodynamic states in the negative Γ region show a significant reduction in the extent of the transonic regime as compared to that predicted by the perfect gas theory. The results of the thesis support existing theories and predictions of the nonclassical, dense gas behavior from previous investigations.
Master of Science

The goal of this work was to assess the feasibility of using corona discharge quenching by anesthetic gases as a technique for anesthetic gas concentration measurement. Two experiments were conducted to investigate corona discharge and measure changes due to anesthetic gases. Experiment One used a chamber in which a high voltage was imposed across two parallel plane electrodes, between which gases under test could flow. Halothane, ethrane, and nitrous oxide were shown to have corona discharge quenching effects proportional to their relative potency. In an attempt to improve accuracy and decrease baseline drift a second system was fabricated. This system used an improved voltage source, temperature and humidity control and a chamber in which gases flowed between two concentric cylindrical electrodes. Results from the second experiment showed that the complex physics of corona discharge quenching by anesthetic gases could not be easily used for reliable measurement of anesthetic gas concentrations.

Modelos numéricos envolvendo a transferência de calor por radiação em gases participantes são bastante complexos de ser resolvidos devido à dependência espectral das propriedades radiantes. Contudo, a radiação térmica não pode ser negligenciada em processos de combustão, onde as elevadas temperaturas envolvidas tornam a radiação o principal fenômeno de transferência de calor. O cálculo da transferência de calor por radiação envolve propriedades de absorção que variam de forma complexa com a temperatura e número de onda, sendo assim necessária a utilização de modelos espectrais para obtenção de resultados confiáveis com baixo tempo computacional. Neste trabalho, o método da soma-ponderada-degases- cinzas (WSGG) foi aplicado na resolução da transferência de calor radiante em um sistema unidimensional formado por duas placas finitas, paralelas e negras, para diferentes perfis de temperatura e de concentração de espécies químicas. Foram obtidas novas correlações para misturas de vapor d’água e dióxido de carbono, além de correlações para as espécies químicas individuais de vapor d’água, monóxido de carbono, dióxido de carbono e metano. A partir do banco de dados HITEMP 2010, as correlações foram geradas para três, quatro e cinco gases-cinzas. A partir das correlações obtidas para o modelo da somaponderada- de-gases-de-cinzas seus resultados são comparados com a solução benchmark obtida pela integração linha-por-linha (LBL). Para todos os casos propostos, é possível verificar uma boa concordância entre os resultados do método da soma-ponderada-de-gasescinzas com o método linha-por-linha.
Problems involving radiation heat transfer in participating media are in general very complex to be solved due to the dependence of the radiative properties with the wavenumber. However, thermal radiation cannot be neglected, especially in combustion processes due to the high temperatures that are involved, making radiation the main heat transfer mode. Calculating the heat transfer by radiation involves absorption properties which varies with the temperature and wavelength, therefore the use of spectral models are required to obtain good results with low computational time. In this dissertation, the weighted-sum-of-gray-gases (WSGG) model was applied to resolve the radiation heat transfer in a one-dimensional finite system formed by two parallel plates with black walls, for different temperature profiles and concentrations of the participating species. New WSGG correlations were obtained for mixtures of vapor water and carbon dioxide, besides correlations for the individual chemical species of vapor water, carbon monoxide, carbon dioxide and methane. From the HITEMP 2010 database correlations were generated for three, four and five gray gases. From the correlations obtained for the weighted-sum-of-gray-gases (WSGG) model, their results are compared with the benchmark solution obtained by integrating line-by-line (LBL). For all the proposed cases, in general, it is possible to observe a satisfactory agreement between the results of the weighted-sum-of-gray-gases with the line-by-line method.

Esta tesis es un trabajo teórico, en el que estudiamos la física de los átomos dipolares bosónicos ultrafríos en retículos ópticos. Éstos gases consisten de átomos o moléculas bosónicas, enfriados bajo la temperatura de degeneración cuántica, típicamente del orden de nK. En éstas condiciones, en una trampa armónica tridimensional (3D), los bosones que interaccionan débilmente condensan y forman un Condensado de Bose Einstein (BEC). Cuando se carga un BEC en un retículo óptico producido por ondas estacionarias de luz láser, se producen nuevos fenómenos físicos. Estos sistemas entonces realizan modelos de tipo Hubbard y pueden ser llevados a regimenes fuertemente correlacionados.

En 1989, M. Fisher et. al. predecían que el modelo de Bose-Hubbard homogéneo (BH) presenta la transición de fase cuántica Superfluid-Mott insulator (SF-MI). En 2002, la transición entre éstas dos fases fue observada experimentalmente por primera vez en el grupo de T. Esslinger e I. Bloch. La realización experimental de un BEC dipolar de cromo en el grupo de T. Pfau, y los progresos recientes en las técnicas de enfriamiento y atrapamiento de moléculas dipolares en los grupos de D. Jin e J. Ye, han abierto el camino hacia los gases cuánticos ultra-fríos dominados por la interacción dipolar. La evolución natural, y el reto de hoy en día por parte experimental, es de cargar BEC dipolares en retículos ópticos y estudiar los gases dipolares fuertemente correlacionados.

Antes de éste trabajo de doctorado, estudios sobre modelos de BH con interacciones extendidas a los primeros vecinos mostraron la evidencia de nuevas fases cuánticas, como el supersólido (SS) y la fase checkerboard (CB). Debido al carácter de largo alcance de la interacción dipolo-dipolo, que decae con la potencia cúbica inversa de la distancia, es necesario incluir más de un primer vecino para obtener una descripción fiel y cuantitativa de los sistemas dipolares. De hecho, al incluir más vecinos se permiten y se estabilizan aún más nuevas fases.

En esta tesis estudiamos modelos de BH con interacciones dipolares, investigando más allá del estado fundamental. Estudiamos un retículo bidimensional (2D) donde los dipolos están polarizados en dirección perpendicular al plano 2D, dando lugar a una interacción dipolar repulsiva e isotrópica. Utilizamos aproximaciones de campo-medio y un ansatz Gutzwiller, que son suficientemente correctos y adecuados para describir este sistema. Encontramos que los gases dipolares en 2D presentan una multitud de estados metaestables de tipo MI, que compiten con el estado fundamental, de modo parecido a sistemas desordenados. Estudiamos en detalle el destino de estos estados metaestables: como pueden ser preparados de manera controlada, como pueden ser detectados, cual es su tiempo de vida debido al tunnelling, y cual es su rol en los procesos de enfriamiento. Además, encontramos que el estado fundamental está caracterizado por estados MI de tipo checkerboard con coeficiente de ocupación n fraccionario (numero medio de partículas por sitio) que depende del cut-off utilizado en el radio de alcance de la interacción. Confirmamos esta predicción estudiando el mismo sistema con métodos Quantum Monte Carlo (worm algorithm). En este caso no utilizamos ningún cut-off en el radio de alcance de la interacción, y encontramos pruebas de una "Devil's staircase" en el estado fundamental, i.e. donde las fases MI aparecen en todos los n racionales del retículo subyacente. Encontramos además, regiones de los parámetros donde el estado fundamental es supersólido, obtenido drogando los sólidos con partículas o con agujeros.

En este trabajo, investigamos también como cambia la estructura precedente en 3D. Nos focalizamos en el retículo 3D más sencillo compuesto de dos planos 2D, en el cual los dipolos están polarizados perpendicularmente a los planos; la interacción dipolar es entonces repulsiva por partículas del mismo plano, mientras es atractiva por partículas en el mismo sitio de dos planos diferentes. En cambio suprimimos el tunnelling entre los planos, lo cual hace el sistema equivalente a una mezcla bosónica en un retículo 2D. Nuestros cálculos muestran que las partículas se juntan en parejas, y demostramos la existencia de la nueva fase cuántica Pair Super Solid (PSS).

Actualmente estamos estudiando un retículo 2D donde los dipolos están libres de apuntar en ambas direcciones perpendicularmente al plano, lo cual resulta en una interacción a primeros vecinos repulsiva (atractiva) por dipolos alineados (anti-alineados). Encontramos regiones de parámetros donde el estado fundamental es ferromagnético u anti-ferromagnético, y encontramos pruebas de la existencia de la fase cuántica Counterflow Super Solid (CSS).
Las nuestras predicciones tienen directas consecuencias experimentales, y esperamos que vengan pronto controladas en experimentos con gases dipolares atómicos y moleculares ultra-fríos.
This thesis is a theoretical work, in which we study the physics of ultra-cold dipolar bosonic gases in optical lattices. Such gases consist of bosonic atoms or molecules, cooled below the quantum degeneracy temperature, typically in the nK range. In such conditions, in a three-dimensional (3D) harmonic trap, weakly interacting bosons condense and form a Bose-Einstein Condensate (BEC). When a BEC is loaded into an optical lattice produced by standing waves of laser light, new kinds of physical phenomena occur.

These systems realize then Hubbard-type models and can be brought to a strongly correlated regime. In 1989, M. Fisher et. al. predicted that the homogeneous Bose-Hubbard model (BH) exhibits the Superfluid-Mott insulator (SF-MI) quantum phase transition. In 2002 the transition between these two phases were observed experimentally for the first time in the group of T. Esslinger and I. Bloch. The experimental realisation of a dipolar BEC of Chromium by the group of T. Pfau, and the recent progresses in trapping and cooling of dipolar molecules by the groups of D. Jin and J. Ye, have opened the path towards ultra-cold quantum gases with dominant dipole interactions. A natural evolution and present challenge, on the experimental side is then to load dipolar BECs into optical lattices and study strongly correlated ultracold dipolar lattice gases.

Before this PhD work, studies of BH models with interactions extended to nearest neighbours had pointed out that novel quantum phases, like supersolid (SS) and checkerboard phases (CB) are expected. Due to the long-range character of the dipole-dipole interaction, which decays as the inverse cubic power of the distance, it is necessary to include more than one nearest neighbour to have a faithful quantitative description of dipolar systems. In fact, longer-range interactions tend to allow for and stabilize more novel phases.

In this thesis we study BH models with dipolar interactions, going beyond the ground state search. We consider a two-dimensional (2D) lattice where the dipoles are polarized perpendicularly to the 2D plane, resulting in an isotropic repulsive interaction. We use the mean-field approximations and a Gutzwiller ansatz which are quite accurate and suitable to describe this system. We find that dipolar bosonic gas in 2D exhibits a multitude of insulating metastable states, often competing with the ground state, similarly as in a disordered system. We study in detail the fate of these metastable states: how can they be prepared on demand, how they can be detected, what is their lifetime due to tunnelling, and what is their role in various cooling schemes. Moreover, we find that the ground state is characterized by insulating checkerboard-like states with fractional filling factors v(average number of particles per site) that depend on the cut-off used for the interaction range. We confirm this prediction by studying the same system with Quantum Monte Carlo methods (the worm algorithm). In this case no cut-off is used, and we find evidence for a Devil's staircase in the ground state, i.e. where insulating phases appear at all rational of the underlying lattice. We also find regions of parameters where the ground state is a supersolid, obtained by doping the solids either with particles or vacancies.

In this work, we also investigate how the previous scenario changes in 3D. We focus on the simplest 3D lattice composed of two 2D layers in which the dipoles are polarized perpendicularly to the planes; the dipolar interaction is then repulsive for particles laying on the same plane, while it is attractive for particles at the same lattice site on different layers. Instead we consider inter-layer tunnelling to be suppressed, which makes the system analogous to a bosonic mixture in a 2D lattice. Our calculations show that particles pair into composites, and demonstrate the existence of the novel Pair Super Solid (PSS) quantum phase.
Currently we are studying a 2D lattice where the dipoles are free to point in both directions perpendicularly to the plane, which results in a nearest neighbour repulsive (attractive) interaction for aligned (antialigned) dipoles. We find regions of parameters where the ground state is ferromagnetic or antiferromagnetic, and find evidences for the existence of a Counterflow Super Solid (CSS) quantum phase.
Our predictions have direct experimental consequences, and we hope that they will be soon checked in experiments with ultracold dipolar atomic and molecular gases.

Topological phenomena arise in a wide range of systems, with fascinating physical consequences. There is great interest in finding new ways to measure such consequences in ultracold atomic gas experiments. These experiments have significant advantages over the solid-state as ultracold atoms are controllable, tuneable and clean. They can also be used to investigate properties which are inaccessible in other quantum systems. We explore some of the novel features of topological energy bands and topological solitons in ultracold gases. Topological energy bands have important geometrical properties described by the Berry curvature. Bands with nonzero Berry curvature arise in key areas of current research, such as optical lattices with more than one band; strong artificial magnetic fields and 2D spin-orbit coupling. Topological solitons are also relevant to cutting-edge experiments as they can be created and studied with high temporal and spatial resolution. In this thesis, we investigate the consequences of Berry curvature for the semiclassical dynamics of a wavepacket and the collective modes of an ultracold gas. We also study theoretically the dynamics of skyrmion-antiskyrmion pairs in a Bose Einstein condensate. Firstly, we propose a general method by which experiments can map the Berry curvature across the Brillouin zone, and thereby determine the topological properties of the energy bands of optical lattices. The Berry curvature modifies the semiclassical dynamics and hence the trajectory of a wavepacket undergoing Bloch oscillations. Our general protocol allows a clean measurement from the semiclassical dynamics of the Berry curvature over the Brillouin zone. We discuss how this protocol may be implemented and explore the semiclassical dynamics for three relevant systems. We discuss general experimental considerations for observing Berry curvature effects before reviewing some of the progress in the field since the publication of our work. Secondly, we show that the Berry curvature changes the hydrodynamic equations of motion for a trapped Bose-Einstein condensate, and causes significant modifications to the collective mode frequencies. We illustrate our results for the case of two-dimensional Rashba spin-orbit coupling in a Zeeman field, where we also apply both a sum rule and an operator approach to the dipole mode. Extending the operator method, we derive the effects of Berry curvature on the dipole mode in very general settings. We show that the sizes of these effects can be large and readily detected in experiment. Collective modes therefore provide a sensitive way to measure geometrical properties of topological energy bands. Lastly, we study theoretically the dynamics of two-component Bose-Einstein condensates in two dimensions, which admit topological excitations related to the skyrmions of nuclear physics. We explore a branch of uniformly propagating solitary waves, which, at high momentum, can be viewed as skyrmion-antiskyrmion pairs. We study these solitary waves for a range of interaction regimes and show that, for experimentally relevant cases, there is a transition to spatially extended spin-wave states at low momentum. We explain how this can be understood by analogy to the two-dimensional ferromagnet and discuss how such solitary waves can be generated and studied in experiment.

Orientador: Gilberto Medeiros Kremer
Dissertação(mestrado) - Universidade Federal do Parana
Resumo: Desenvolve-se uma teoria baseada na termodinâmica estendida para uma mistura binária constituída de íons e elétrons, sujeitos à ação de um campo magnético externo B, caracterizando um gás completamente ionizado. Os campos básicos desta teoria são as densidades de massa parcial, velocidade parcial, tensor pressão parcial e fluxo de calor parcial, perfazendo um total de vinte e seis campos escalares, cujas equações de balanço são obtidas a partir da equação cinética de Boltzmann. Do princípio da indiferença ao referencial e princípio da entropia, restringese a generalidade das equações constitutivas, conduzindo-nos a um conjunto de equações de campo. Deste conjunto de vinte e seis equações, seis delas serão utilizadas na determinação das densidades de massa dos íons e dos elétrons, da velocidade da mistura e de sua temperatura. Considerando os constituintes da mistura a uma mesma temperatura T, restam dezenove equações que fornecerão os deviantes do tensor pressão dos íons e dos elétrons da mistura, os fluxos de calor dos íons é dos elétrons além do vetor corrente elétrica, a partir da inversão de tensores de segunda e quarta ordem. As leis fenomenológicas de Ohm, Fourier e Navier - Stokes são obtidas, identificando- se os coeficientes de transporte da mistura: os tensores de viscosidade de cisalhamento, condutividade térmica e condutividade elétrica e os tensores dos efeitos cruzados, associados à difusão-termo e termo-difusão, verificando-se as relações de reciprocidade de Onsager para estes coeficientes de transporte. Através de uma escolha adequada de forças e fluxos termodinâmicos, os efeitos termoelétricos, termomagnéticos e galvanomagnéticos são também obtidos e analisados.
Abstract: A theory based on extended thermodynamics is developed for a binary mixture in the presence of magnetic field B , which characterizes a. completely ionized gas. The basic fields of this theory are the twenty-six scalars fields of partial mass densities, partial velocities, partial pressure tensors and partial heat fluxes. The balance equations are obtained from the Boltzmann kinetic equation. From the material frame indifference principle and the entropy principle, the generality of the constitutive equations is restricted, leading to a system of field equations. From this system of twenty-six equations, six of them are used to the determination of mass density of the ions, the mass densitiy of the electrons, the velocity of the mixture and its temperature. We have considered the constituints of the mixture at the same temperature T so that the remaining equations will provide the pressure deviators of the ions and of the electrons of the mixture, the heat fluxes of the ions, the heat fluxes of the electrons and finally the electric current vector, through inversions of secondorder and fourth-order tensors. The phenomenological equations of Ohm, Fourier and Navier-Stokes are obtained, and we have identified the transport coefficients of the mixture: the shear viscosity tensor, the thermal conductivity tensor, the electric conductivity tensor and the tensors of cross effects, wich are associated with diffusion-thermo and thermo-diffusion. We have verified the Onsager reciprocity relations for these coefficients. With an appropriate choice of thermodynamic forces and fluxes the thermoeletric, thermomagnetic and galvanomagnetic effects are also obtained and analised.

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The filtration of gases is an important industrial operation with the primary aim of removing unwanted solid particles contained in a gas. The filtration of gases at high pressures is an operation widely used in natural gas industry with the aim of separating impurities called black powder, from rust inside pipelines along the transportation. These residues can cause wear on equipment such as, for example, rotor pump, obstruction of gauges and pressure decrease in product quality. Despite being an operation widely used, few studies exist in the area to study what the best type of filter. Therefore this study is very useful to improve the steps of transportation, measurement and purity of the final product. To simulate this process, we used the dry compressed air, injecting a phosphate rock as particulate matter. The filters were tested RAD cellulose and acrylic. The surface speed of filtration was kept constant at 0.05 m / s, throughout the filtering operation. The flow of compressed air used were 14 l / min to the total pressure 1 bar, 42 l / min at a total pressure of 3 bar and 86 l / min at a total pressure of 6 bar. Total load losses were 5, 10, 20 and 30 mbar. The results showed that, initially, the curves of head loss versus deposited mass showed the same growth trend. However, when forming a layer of cake from about 0.03 kg/m2, the filtrations higher pressures had lower pressure loss. This is because the larger pressure forming pies more porous and less resistant to air flow. At the end of the study it was also observed that the acrylic filter performed better compared to the cellulose RAD, due to its greater mass of accumulated dust and low pressure drop.
A filtração de gases é uma importante operação industrial com o principal intuito de remover as partículas sólidas indesejadas contidas em um determinado gás. A filtração de gases a altas pressões é uma operação muito utilizada na indústria de gás natural com o objetivo de separar as impurezas denominadas pó preto, provenientes da oxidação no interior de gasodutos ao longo do seu transporte. Estes resíduos podem causar desgaste de equipamentos como, por exemplo, rotor de bombas, obstrução de aparelhos de medição de pressão e diminuição da qualidade do produto. Apesar de ser uma operação muito utilizada, poucas pesquisas existem na área a fim de estudar qual o melhor tipo de filtro. Por isso este estudo é muito útil no sentido de melhorar as etapas de transporte, medição e pureza do produto final. Para simular este processo, foi utilizado o ar comprimido seco, injetando-se a rocha fosfática como material particulado. Os filtros testados foram de celulose RAD+ e acrílico. A velocidade superficial de filtração foi mantida constante em 0,05 m/s, durante toda a operação de filtração. As vazões do ar comprimido utilizadas foram de 14 l/min para a pressão total de 1 bar, 42 l/min para a pressão total de 3 bar e 86 l/min para a pressão total de 6 bar. As perdas de carga totais foram de 5, 10, 20 e 30 mbar. Os principais resultados mostraram que, inicialmente, as curvas de perda de carga versus massa depositada apresentaram igual tendência de crescimento. Porém, no momento que forma uma camada de torta a partir de aproximadamente 0,03 kg/m2, as filtrações de maiores pressões apresentaram menor perda de carga. Isso porque as maiores pressões formam tortas mais porosas e menos resistentes ao escoamento de ar. Ao final do estudo observou-se também que o filtro de acrílico obteve melhor desempenho comparado com o de celulose RAD+, por apresentar maior massa de pó acumulada e menor perda de carga.

In this thesis we investigate strongly-correlated states of ultracold bosonic atoms in rotating ring lattices and arrays of double-well potentials. In the first part of the thesis, we study the tunneling dynamics of ultracold bosons in double-well potentials. In the non-interacting limit single-particle transitions dominate, while in the interaction-dominated regime correlated tunneling of all particles prevails. At intermediate times of the many-particle flopping process correlated states occur, but the timescales of these processes increase dramatically with the number of particles. Using an array of double-well potentials, a large number of such few-particle superposition states can be produced in parallel. In the second part of the thesis, we study the effects of rotation on ultracold bosons confined to one-dimensional ring lattices. We find that at commensurate filling there exists a critical rotation frequency, at which the ground state of the weakly-interacting gas is fragmented into a macroscopic superposition of different quasi-momentum states. We demonstrate that the generation of such superposition states using slightly non-uniform ring lattices has several practical advantages. Moreover, we show that different quasi-momentum states can be distinguished in time-of-flight absorption imaging and propose to probe correlations via the many-body oscillations induced by a sudden change in the rotation frequency. Finally, we compare these macroscopic superposition states to those occurring in superconducting quantum interference devices. In the third part of the thesis, we demonstrate the creation of entangled states with ultracold bosonic atoms by dynamical manipulation of the shape of the lattice potential. To this end, we consider an optical superlattice that allows both the splitting of each site into a double-well potential and the variation of the height of the potential barrier between the sites. We show how to use this array of double-well potentials to perform entangling operations between neighboring qubits encoded on the Zeeman levels of the atoms. As one possible application, we present a method of realizing a resource state for measurement-based quantum computation via Bell-pair measurements. In the final part of the thesis, we study ultracold bosons on a two-dimensional square lattice in the presence of an effective magnetic field and point out a couple of features this system has in common with ultracold bosons in one-dimensional rotating ring lattices.

Systems of ultracold atoms in optical potentials have taken a place at the forefront of research into many-body atomic systems because of the clean experimental environment they exist in and the tunability of the system parameters. In this thesis we study how light scattered from these ultracold atomic gases reveals information about the state of the atomic gas and also leads to changes in that state. We begin by investigating the angular dependence of light scattered from atoms in optical lattices at finite temperature. We demonstrate how correlations in the superfluid and Mott insulator states affect the scattering pattern, and we show that temperature affects the number of photons scattered. This effect could be used to measure the temperature of the gas, however, we show that when the lattice band structure is taken into account the efficiency of this temperature measurement is reduced. We then investigate light scattering from small optical lattices where the Bose-Hubbard Hamiltonian can be solved exactly. For small lattices, scattering a photon from the atomic system significantly perturbs the atomic system. We develop a model of the evolution of the many-body state that results from the consecutive scattering and detection of photons. This model shows that light scattering pushes the system towards eigenstates of the light scattering measurement process, in some cases leading to a superposition of atomic states. In the second half of this thesis we study light scattering that depends on the internal hyperfine spin state of the atoms, in which case the scattered light can form images of the spatial atomic spin distribution. We demonstrate how scattering spatially correlated light from the atoms can result in spin state images with enhanced spatial resolution. We also show how using spatially correlated light can lead to direct measurement of the spatial correlations of the atomic spin distribution. We then apply this theory of spin-dependent light scattering to the detection of different spin states of ultracold gases in synthetic magnetic fields. We show that it is possible to distinguish between ground states in the quantum Hall regime using light scattering. Moreover, we show how noise correlation analysis of the spin state images can be used to identify the correlations between atoms and how a variant on phase-contrast imaging can reveal the relationship between the atomic spins.

Entanglement in many-body systems of identical particles often resides between modes of the field occupied by particles rather than between the particles themselves, or their internal degrees of freedom. Spatial field modes are an important choice of modes and investigating entanglement between them for a non-interacting Bose gas is the concern of this thesis. A particularly interesting phase of a Bose gas is a Bose-Einstein condensate (BEC). Long-range correlations between all points in space exist in a BEC, which are detected by the single-particle reduced density matrix.

Inelastic collisions between dipolar molecules, assumed to be trapped in a static electric field at cold (> 10−3K) temperatures, are investigated and compared with elastic collisions. For molecules with a Λ-doublet energy-level structure, a dipole moment arises because of the existence of two nearly degenerate states of opposite parity, and the collision of two such dipoles can be solved entirely analytically in the energy range of interest. Cross sections and rate constants are found to satisfy simple, universal formulas. In contrast, for molecules in a Σ electronic ground state, the static electric field induces a dipole moment in one of three rotational sublevels. Collisions between two rotor dipoles are calculated numerically; the results scale simply with molecule mass, rotational constant, dipole moment, and field strength. It might be expected that any particles interacting only under the influence of the dipole-dipole interaction would show similar behavior; however, the most important and general result of this research is that at cold temperatures inelastic rate constants and cross sections for dipoles depend strongly upon the internal structure of the molecules. The most prominent difference between the Λ-doublet and rotor molecules is variation of the inelastic cross section with applied field strength. For Λ-doublet dipoles, cross sections decrease with increasing field strength. For rotor dipoles, cross sections increase proportionally with the square of field strength. Furthermore, the rate constants of the two types of molecules depend very differently on the angular orientations of the dipoles in the electric field.

Recent work by a number of researchers has highlighted areas in which conservative numerical methods give poor solutions. One such situation is in the modelling of material interfaces. A number of methods for overcoming this shortfall of conservative numerical methods are developed. The flow situations that are considered include multicomponent gases and systems of gases and liquids. It is shown that the errors associated with conservative methods when applied to model gas-liquid interfaces are considerably larger than those for gas-gas interfaces. The first approach used for overcoming the errors in conservative methods is a hybrid primitive-conservative method. This method is used in conjunction with a number of new Riemann solvers for a liquid ambient to provide accurate solutions to a number of challenging one and two dimensional test problems. These test problems include the interaction of a shock wave with a bubble in a gas and an underwater explo.; ion. The application of these hybrid methods to the problem of the interaction of a shock wave with a gas bubble in aa liquid demonstrate that they are unable to provide an accurate solution. Two one dimensional methods are described that are able to provide solutions to such test problems. These methods are the moving grid-Chimera approach and a cut cell approach. The cut cell approach is extended into two dimensions and is shown to be able to provide solutions to the problem of the interaction of a shock wave with a gas bubble in a liquid. This method is also shown to be able to provide more accurate solutions to multicomponent gas problems than those on a standard Cartesian grid.