Investigations of the Dynamical Response in Solids by Time-Dependent Density-Functional Theory

The present dissertation studies a joint theoretical-experimental investigation of the dynamical structure factor of wide-gap insulators, using lithium-fluoride as a prototype. Ground-state (energy bands and electron densities) was calculated using Linear Augmented Plane Wave (LAPW) method and local density approximation (LDA) of density functional theory (DFT). Ab-initio principal is applied to obtain a realistic description of the band structure, which is central to the current research in the condensed matter physics. Dynamical response function has been evaluated within time-dependent density functional theory (DFT) with an adiabatic approximation (TDLDA), for the exchange-correlation kernel. Our TDLDA spectra contain one adjustable parameter: a “scissors-operator” shift of conduction bands of LDA electronic structure. This parameter is determined in view of the line-shape of the Non-resonant Inelastic X-Ray Scattering (NIXS) cross section for q= 6Å-1 along (111) direction. All other spectra are calculated “ab-initio.” The important interplay between band structure and electron dynamics is emphasized within our results. The picture of excitations offers an alternative view to previous investigations involving an approximate solution of the Bethe-Salpeter equation coupled with a more limited range of NIXS data

Kvantti Monte Carlo -simulointi positroneille kiinteässä aineessa

Positron annihilation spectroscopy is a non-destructive method used to extract information from atomic matter. It is particularly useful in characterizing open-volume defects and their complexes, which often determine the electronic, mechanical and thermal properties of the studied material. Experimental use of positron annihilation spectroscopy requires a strong theoretical background for drawing conclusions from the measurements and making a link between the atomic structures of the defects detected and the indirect information included in the measured spectra. While the widely used density functional theory enables efficient and practical modeling and provides rather reliable theoretical predictions, a demand for more accurate quantum many-body methods remains. Therefore the theoretical study of interacting electrons in a solid-state atomistic system with an included positron remains important. In this work, an implementation of a variational Monte Carlo simulation for positrons in periodic solids is presented. To the knowledge of the author, this is the first time such a method is used to model positron states and annihilation. First an overview to the theoretical study of many-body quantum phenomena and periodic solids is presented. Then relevant computational methods are discussed. The second part of the thesis focuses on the variational Monte Carlo method and a novel implementation for positrons in solids. Finally some results for positrons in solids calculated using the variational Monte Carlo method developed in this work are presented and analysed.Positroniannihilaatiospektroskopia on kokeellinen menetelmä, jolla voidaan kohdemateriaalia vahingoittamatta tutkia sen atomirakennetta. Erityisen tehokas se on havaitsemaan puutuvia atomeja, eli vakansseja, tai niiden kasautumia kiteisissä aineissa, mitkä puolestaan usein määrittävät materiaalien elektronisia, mekaanisia ja termisiä ominaisuuksia. Positroniannihilaatiospektroskopian kokeellinen käyttö tarvitsee vahvan teoreettisen taustatuen, jotta sen tuottamia tuloksia voidaan tulkita ja tehdä johtopäätöksiä havaittujen aineen atomivirheiden sekä mitatun spektrin tarjoaman epäsuoran informaation perusteella. Laajalti käytetyn tiheysfunktionaaliteorian tuottaessa usein luotettavia teoreettisia tuloksia löytyy edelleen kysyntää tarkemmalle monen hiukkasen kvanttitilojen laskemiselle. Näin ollen realistisissa kiteissä vuorovaikuttavien elektronien sekä niiden joukkoon upotetun positronin teoreettinen tutkimus on tärkeää. Tämä työ esittelee variaatio Monte Carlo -menetelmän käyttöä positronien simuloimiseen periodisessa aineessa. Tietääksemme tämä on ensimmäinen kerta, kun tämän kaltaista menetelmää on käytetty positroniannihilaation tai -tilojen mallinnuksessa. Aluksi esitetään yleiskatsaus monen hiukkasen kvantti-ilmiöiden sekä periodisten kiteiden teoriaan. Myös tarpeellisia laskennallisia menetelmiä teoreettisessa mallinnuksessa käydään läpi. Työn loppuosa käsittelee variaatio Monte Carlo menetelmää sekä siihen perustuvaa positronin mallinnuksen menetelmää. Lopuksi näytetään tuloksia positronien simulaatiosta työssä kehitetyllä Monte Carlo menetelmällä sekä analysoidaan niitä

Gratings: Theory and Numeric Applications, Second Revisited Edition

International audienceThe second Edition of the Book contains 13 chapters, written by an international team of specialist in electromagnetic theory, numerical methods for modelling of light diffraction by periodic structures having one-, two-, or three-dimensional periodicity, and aiming numerous applications in many classical domains like optical engineering, spectroscopy, and optical telecommunications, together with newly born fields such as photonics, plasmonics, photovoltaics, metamaterials studies, cloaking, negative refraction, and super-lensing. Each chapter presents in detail a specific theoretical method aiming to a direct numerical application by university and industrial researchers and engineers.In comparison with the First Edition, we have added two more chapters (ch.12 and ch.13), and revised four other chapters (ch.6, ch.7, ch.10, and ch.11

Convergence properties of Fock-space based approaches in strongly correlated Fermi gases : a dissertation presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Physics at Massey University, Albany, New Zealand

Listed in 2019 Dean's List of Exceptional ThesesThe main objective of this thesis is the effcient numerical description of strongly correlated quantum gases. Due to the complex many-body structure of the wave function, usually, numerical methods are required for its computation. The exact diagonalization approach is considered, where the energies and the wave functions are obtained by diagonalizing the Hamiltonian in a many-body basis. The dimension of the space increases combinatorially with the number of particles and the number of single-particle basis functions, which limits the characterization of fewbody systems to intermediate interactions. One of the main components of the convergence rate originates from the particle-particle interaction itself. The bare contact interaction introduces a singularity in the wave function at the particleparticle coalescence point. This is responsible for the slow convergence in the nite basis expansion in one dimension and it even causes pathological behavior in higher dimensions. Firstly, the Gaussian interaction potential is examined as an alternative pseudopotential. After the description of the accurate calculation of the s-wave scattering length of this potential, the convergence properties are investigated. As this function is smooth, by construction the wave function is free from any singularity implying an exponentially fast convergence rate. If the resolution of the basis set is not fine enough, the finite-range pseudopotential is indistinguishable from the pathological contact potential. Through the example of few particles in a two-dimensional harmonic trap, we show that in order to reach the necessary resolution, the number of harmonic-oscillator single-particle basis functions must increase quadratically with the inverse characteristic length of the pseudopotential. This scaling property combined with the combinatorial growth of the many-body space makes the physically realistic short-range potentials computationally inaccessible. We have also applied the so-called transcorrelated approach, where the singular part of the wave function is isolated in a Jastrow-type factor. This factor can be transformed into the Hamiltonian reducing the irregularity of the eigenfunction and improving the convergence rate. We will show through the example of the homogeneous gas in one dimension that this transformation efficiently improves the convergence from M⁻¹ to M⁻³, where M is the number of the single-particle plane-wave basis functions

Deep Nuclear Resonant Tunneling Thermal Rate Constant Calculations

This thesis presents a new method to calculate thermal rate constants for arbitrary one dimensional scattering potentials in the presence of many quasi-bound states. This novel methodology can be proficiently applied to the case of multiple-barrier passages where quasi-bound states are present. After showing that thermal rate constants can be calculated from asymptotic conditions, the Schr\uf6dinger equation has been solved as an ordinary differential equation, with the energy as a fixed parameter, by choosing suitable asymptotic boundaries conditions. The method we propose is time-independent and it provides a significant advantage over any available time-dependent method, since time-dependent methods are not adequate for the calculation of rate constants in the presence of long-lived resonance states. The error respect to the exact expression was typically less than 1%, even at extremely low temperatures. Possible multidimensional implementations of the method are under way. Three main applications of our method have been considered: i) Separation of Helium isotopes by resonant tunneling in a double layer Polyphenylene system (2D-PP). Due to the presence of resonant states given by the double barrier potential, the 2D-PP filter was able to select between He3 from He4, even at relatively high temperatures. ii) Extensive studies of the effects of resonant tunneling on the thermal rate constants for double barrier potentials. We numerically observed two important phenomena: the "oscillation" of the thermal rate constant as a function of the distance between the two barriers, and the "Inverse Kinetic Isotope Effect" where the heavier isotope has a larger thermal rate constant with respect to the lighter isotope. iii) Realization of a quantum protocol for the calculation of the thermal rate constant on a quantum computer. In particular, we take advantage of our time-independent method to devise a quantum algorithm with an exponential speed-up with respect to any equivalent classical algorithm

Gratings: Theory and Numeric Applications

International audienceThe book containes 11 chapters written by an international team of specialist in electromagnetic theory, numerical methods for modelling of light diffraction by periodic structures having one-, two-, or three-dimensional periodicity, and aiming numerous applications in many classical domains like optical engineering, spectroscopy, and optical telecommunications, together with newly born fields such as photonics, plasmonics, photovoltaics, metamaterials studies, cloaking, negative refraction, and super-lensing. Each chapter presents in detail a specific theoretical method aiming to a direct numerical application by university and industrial researchers and engineers

Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018

This open access book features a selection of high-quality papers from the presentations at the International Conference on Spectral and High-Order Methods 2018, offering an overview of the depth and breadth of the activities within this important research area. The carefully reviewed papers provide a snapshot of the state of the art, while the extensive bibliography helps initiate new research directions