This thesis is devoted to the study of excitations in atomic and polariton Bose-Einstein condensates (BEC). These two specimens are prime examples for equilibrium and non equilibrium BEC. The corresponding condensate wave function of each system satisfies a particular partial differential equation (PDE). These PDEs are discussed in the beginning of this thesis and justified in the context of the quantum many-body problem. For high occupation numbers and when neglecting quantum fluctuations the quantum field operator simplifies to a semiclassical wave. It turns out that the interparticle interactions can be simplified to a single parameter, the scattering length, which gives rise to an effective potential and introduces a nonlinearity to the PDE. In both cases, i.e. equilibrium and non equilibrium, the main model corresponding to the semiclassical wave is the Gross-Pitaevskii equation (GPE), which includes certain mathematical adaptions depending on the physical context of the consideration and the nature of particles/quasiparticles, such as additional complex pumping and growth terms or terms due to motion. In the course of this work I apply a variety of state-of-the-art analytical and numerical tools to gain information about these semiclassical waves. The analytical tools allow e.g. to determine the position of the maximum density of the condensate wave function or to find the critical velocities at which excitations are expected to be generated within the condensate. In addition to analytical considerations I approximate the GPE numerically. This allows to gain the condensate wave function explicitly and is often a convenient tool to study the emergence of excitations in BEC. It is in particular shown that the form of the possible excitations significantly depends on the dimensionality of the considered system. The generated excitations within the BEC include quantum vortices, quantum vortex rings or solitons. In addition multicomponent systems are considered, which enable more complex dynamical scenarios. Under certain conditions imposed on the condensate one obtains dark-bright soliton trains within the condensate wave function. This is shown numerically and analytical expressions are found as well. In the end of this thesis I present results as part of an collaborative effort with a group of experimenters. Here it is shown that the wave function due to a complex GPE fits well with experiments made on polariton condensates, statically and dynamically.

Orientador: Maurice de Koning / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin / Made available in DSpace on 2018-08-18T18:05:04Z (GMT). No. of bitstreams: 1 Barrozo_AlexandreHernandes_M.pdf: 4359405 bytes, checksum: c11339c45a35270724d3ee11084432af (MD5) Previous issue date: 2011 / Resumo: Fizemos estudos de uma nova técnica proposta para amostrar o ensemble canônico [H. Dammak et al., Phys. Rev. Lett. 103,190601 (2009)], capaz de amostrar flutuações quânticas através de Dinâmica Molecular(DM) clássica. Esta técnica é baseada nos termostatos estocásticos clássicos, que se baseiam nas equações de Langevin, com a diferença de usar um ruído com correlação temporal, ao invés de ruído branco. Aplicamos esta técnica para o cálculo de grandezas termodinâmicas de sistemas cuja solução analítica (ou numérica) é conhecida. Mais especificamente, focamos o estudo no cálculo de energias livres através de integração termodinâmica fora do equilíbrio. Neste trabalho também desenvolvemos um método que nos permite alterar a temperatura do termostato ao longo da simulação. Este método é baseado no reescalonamento do ruído aleatório que constitui este termostato quântico. Mostramos aqui que, apesar de termos excelentes resultados para o caso do oscilador harmônico, esta técnica apresenta falhas no que se diz respeito a potenciais anarmônicos, amostrando distribuições fundamentalmente incorretas / Abstract: We study a new method devised to sample the canonical ensemble [H. Dammak et al., Phys. Rev. Lett. 103,190601 (2009)], which includes quantum uctuations by means of classical Molecular Dynamics. This method is based on classical stochastic thermostats, except that it uses colored noise, instead of a white one. We apply this method to compute thermodynamical properties of systems whose analytical (or numerical) solution for the Schr odinger equation is known. Specifically, we focus on free-energy calculations using non-equilibrium thermodynamics integration. In this work, we also develop a technique that allows one to change the thermostat's temperature during the simulation. This technique is based on rescaling the random noise sequence that constitutes the thermostat. We show that, although we have excelent results for the harmonic oscillator case, problems arise while studying anharmonic potentials, in which the method sample distributions that are fundamentally incorrect / Mestrado / Física Estatistica e Termodinamica / Mestre em Física

abstract: Autonomic closure is a recently-proposed subgrid closure methodology for large eddy simulation (LES) that replaces the prescribed subgrid models used in traditional LES closure with highly generalized representations of subgrid terms and solution of a local system identification problem that allows the simulation itself to determine the local relation between each subgrid term and the resolved variables at every point and time. The present study demonstrates, for the first time, practical LES based on fully dynamic implementation of autonomic closure for the subgrid stress and the subgrid scalar flux. It leverages the inherent computational efficiency of tensorally-correct generalized representations in terms of parametric quantities, and uses the fundamental representation theory of Smith (1971) to develop complete and minimal tensorally-correct representations for the subgrid stress and scalar flux. It then assesses the accuracy of these representations via a priori tests, and compares with the corresponding accuracy from nonparametric representations and from traditional prescribed subgrid models. It then assesses the computational stability of autonomic closure with these tensorally-correct parametric representations, via forward simulations with a high-order pseudo-spectral code, including the extent to which any added stabilization is needed to ensure computational stability, and compares with the added stabilization needed in traditional closure with prescribed subgrid models. Further, it conducts a posteriori tests based on forward simulations of turbulent conserved scalar mixing with the same pseudo-spectral code, in which velocity and scalar statistics from autonomic closure with these representations are compared with corresponding statistics from traditional closure using prescribed models, and with corresponding statistics of filtered fields from direct numerical simulation (DNS). These comparisons show substantially greater accuracy from autonomic closure than from traditional closure. This study demonstrates that fully dynamic autonomic closure is a practical approach for LES that requires accuracy even at the smallest resolved scales. / Dissertation/Thesis / Doctoral Dissertation Aerospace Engineering 2020

abstract: The quest to find efficient algorithms to numerically solve differential equations isubiquitous in all branches of computational science. A natural approach to address this problem is to try all possible algorithms to solve the differential equation and choose the one that is satisfactory to one's needs. However, the vast variety of algorithms in place makes this an extremely time consuming task. Additionally, even after choosing the algorithm to be used, the style of programming is not guaranteed to result in the most efficient algorithm. This thesis attempts to address the same problem but pertinent to the field of computational nanoelectronics, by using PETSc linear solver and SLEPc eigenvalue solver packages to efficiently solve Schrödinger and Poisson equations self-consistently. In this work, quasi 1D nanowire fabricated in the GaN material system is considered as a prototypical example. Special attention is placed on the proper description of the heterostructure device, the polarization charges and accurate treatment of the free surfaces. Simulation results are presented for the conduction band profiles, the electron density and the energy eigenvalues/eigenvectors of the occupied sub-bands for this quasi 1D nanowire. The simulation results suggest that the solver is very efficient and can be successfully used for the analysis of any device with two dimensional confinement. The tool is ported on www.nanoHUB.org and as such is freely available. / Dissertation/Thesis / Masters Thesis Electrical Engineering 2020

No description available.

abstract: I describe the first continuous space nuclear path integral quantum Monte Carlo method, and calculate the ground state properties of light nuclei including Deuteron, Triton, Helium-3 and Helium-4, using both local chiral interaction up to next-to-next-to-leading-order and the Argonne $v_6'$ interaction. Compared with diffusion based quantum Monte Carlo methods such as Green's function Monte Carlo and auxiliary field diffusion Monte Carlo, path integral quantum Monte Carlo has the advantage that it can directly calculate the expectation value of operators without tradeoff, whether they commute with the Hamiltonian or not. For operators that commute with the Hamiltonian, e.g., the Hamiltonian itself, the path integral quantum Monte Carlo light-nuclei results agree with Green's function Monte Carlo and auxiliary field diffusion Monte Carlo results. For other operator expectations which are important to understand nuclear measurements but do not commute with the Hamiltonian and therefore cannot be accurately calculated by diffusion based quantum Monte Carlo methods without tradeoff, the path integral quantum Monte Carlo method gives reliable results. I show root-mean-square radii, one-particle number density distributions, and Euclidean response functions for single-nucleon couplings. I also systematically describe all the sampling algorithms used in this work, the strategies to make the computation efficient, the error estimations, and the details of the implementation of the code to perform calculations. This work can serve as a benchmark test for future calculations of larger nuclei or finite temperature nuclear matter using path integral quantum Monte Carlo. / Dissertation/Thesis / Doctoral Dissertation Physics 2020

In soil, where trees and crops grow, heavy vehicles shear and compact the soil, leading to reduced plant growth and diminished nutrient recycling. Computer simulations offer the possibility to improve the understanding of these undesired phenomena. In this thesis, soils were modelled as large collections of contacting spherical particles using the Discrete Element Method (DEM) and the physics engine AGX Dynamics, and these entities were analyzed. In the first part of the thesis, soils, which were considered to be continua, were subjected to various controlled deformations and fields for quantities such as stress and strain were visualized using coarse graining (CG). These fields were then compared against analytical solutions. The main goal of the thesis was to evaluate the usefulness, accuracy, and precision of this plotting technique when applied to DEM-soils. The general behaviour of most fields agreed well with analytical or expected behaviour. Moreover, the fields presented valuable information about phenomena in the soils. Relative errors varied from 1.2 to 27 %. The errors were believed to arise chiefly from non-uniform displacement (due to the inherent granularity in the technique), and unintended uneven particle distribution. The most prominent drawback with the technique was found to be the unreliability of the plots near the boundaries. This is significant, since the behaviour of a soil at the surface where it is in contact with e.g. a vehicle tyre is of interest. In the second part of the thesis, a vehicle traversed a soil and fields were visualized using the same technique. Following a limited analysis, it was found that the stress in the soil can be crudely approximated as the stress in a linear elastic solid.

Strongly correlated low-dimensional quantum spin models provide a well-established frame- work to study magnetic properties of insulators, and are of great theoretical interest and experimental relevance in condensed-matter physics. In this thesis, I use quantum Monte Carlo methods to numerically study quantum critical behavior in low-dimensional quantum spin models and wavefunctions. First, I study spinons &ndash emergent spin-1/2 bosonic excitations &ndash at certain one- and two-dimensional quantum phase transitions (QPTs) in spin models, by characterizing their size and confinement length quantitatively. In particular, I focus on the QPT from an antiferromagnetic (AFM) phase into a valence-bond solid (VBS) phase, which is an example of a violation of the standard Landau-Ginzburg-Wilson paradigm for phase transitions. This transition in two dimensions (2D) is instead likely described by a novel theory called "deconfined quantum criticality" (DQC). According to the theory, spinons should be deconfined. The degree of deconfinement is quantified in my calculations. Second, I present a comprehensive study of so-called short-bond resonating-valence-bond (RVB) spin liquids in 2D, which have been suggested as a good starting point for understanding the spin physics of high-temperature cuprates. I find that these RVB states can also be classified as quantum-critical VBS states, which indicates that RVB is less disordered than expected. This work suggests a possible mapping from the quantum RVB states to classical dimer models via a classical continuum field theory--the height model. This map explicitly bridges well-established classical results to future quantum studies. Third, I consider 1D amplitude product (AP) states, which are generalized versions of RVB states, with different wavefunction weightings of bonds according to their lengths. AP states constitute a good ansatz for certain Hamiltonians and are of broad interest in quantum magnetism. I study phase transitions from AFM-VBS phases in AP states by tuning their amplitudes, and obtain continuously varying critical exponents. In addition, I classify the 1D AP states through entanglement entropy calculations of the central charge in (1+1)D conformal field theory. This new classification could serve as guide for AP states as trial wavefunctions to search for ground states of corresponding quantum spin models.

abstract: Silicon photonic technology continues to dominate the solar industry driven by steady improvement in device and module efficiencies. Currently, the world record conversion efficiency (~26.6%) for single junction silicon solar cell technologies is held by silicon heterojunction (SHJ) solar cells based on hydrogenated amorphous silicon (a-Si:H) and crystalline silicon (c-Si). These solar cells utilize the concept of carrier selective contacts to improve device efficiencies. A carrier selective contact is designed to optimize the collection of majority carriers while blocking the collection of minority carriers. In the case of SHJ cells, a thin intrinsic a-Si:H layer provides crucial passivation between doped a-Si:H and the c-Si absorber that is required to create a high efficiency cell. There has been much debate regarding the role of the intrinsic a-Si:H passivation layer on the transport of photogenerated carriers, and its role in optimizing device performance. In this work, a multiscale model is presented which utilizes different simulation methodologies to study interfacial transport across the intrinsic a-Si:H/c-Si heterointerface and through the a-Si:H passivation layer. In particular, an ensemble Monte Carlo simulator was developed to study high field behavior of photogenerated carriers at the intrinsic a-Si:H/c-Si heterointerface, a kinetic Monte Carlo program was used to study transport of photogenerated carriers across the intrinsic a-Si:H passivation layer, and a drift-diffusion model was developed to model the behavior in the quasi-neutral regions of the solar cell. This work reports de-coupled and self-consistent simulations to fully understand the role and effect of transport across the a-Si:H passivation layer in silicon heterojunction solar cells, and relates this to overall solar cell device performance. / Dissertation/Thesis / Doctoral Dissertation Electrical Engineering 2019

Kohn-Sham density functional theory (KS-DFT) is one of the most widely used electronic structure methods. It is used to find the various properties of atoms, molecules, clusters, and solids. In principle, results for these properties can be found by solving self-consistent one-electron Schrödinger-like equations based on density functionals for the energy. In practice, the density functional for the exchange-correlation contribution to the energy must be approximated. The accuracy of practical DFT depends on the choice of density functional approximation (DFA) and also on the electron density produced by the DFA. The SCAN(strongly constrained and appropriately normed) functional developed by Sun, Ruzsinszky, and Perdew is the first meta-GGA (meta-generalized gradient approximation) functional that is constrained to obey all 17 known exact constraints that a meta-GGA can. SCAN has been found to outperform most other functionals when it is applied to aqueous systems. However, density-driven errors (energy errors occurring from an inexact density produced by a DFA) hinder SCAN from achieving chemical accuracy in some systems, including water. Density-corrected DFT (DC-DFT) can alleviate this shortcoming by adopting a more accurate electron density which, in most applications, is the electron density obtained at the Hartree-Fock level of theory, due to its relatively low computational cost. In the second chapter, calculations to determine the accuracy of the HF-SCAN functional for water clusters are performed. The interaction and binding energies of water clusters in the BEGDB and WATER27 data sets are computed, and then the spurious charge transfer in deprotonated, protonated, and neutral water dimer is interpreted. The density-corrected SCAN (DC-SCAN) functional elevates the accuracy of SCAN toward the CCSD(T) limit, not only for the neutral water clusters but also for all considered hydrated ion systems (to a lesser extent). In the third chapter, the barrier heights of the BH76 test set are analyzed. Three fully non-local proxy functionals (LC-ωPBE, SCAN50%, and SCAN-FLOSIC) and their selfconsistent proxy densities are used. These functionals share two important points of similarity to the exact functional. They produce reasonably accurate self-consistent barrier heights and their self-consistent total energies are nearly piecewise linear in fractional electron number. Somewhat-reliable cancellation of density - and functional-driven errors for the energy has been established. / Physics