Relativistic Real-Time Methods

Recent advances in laser technology enable to follow electronic motion at its natural time-scale with ultrafast pulses, leading the way towards atto- and femtosecond spectroscopic experiments of unprecedented resolution. Understanding of these laser-driven processes, which almost inevitably involve non-linear light-matter interactions and non-equilibrium electron dynamics, is challenging and requires a common effort of theory and experiment. Real-time electronic structure methods provide the most straightforward way to simulate experiments and to gain insights into non-equilibrium electronic processes. In this Chapter, we summarize the fundamental theory underlying the relativistic particle-field interaction Hamiltonian as well as equation-of-motion for exact-state wave function in terms of the one- and two-electron reduced density matrix. Further, we discuss the relativistic real-time electron dynamics mean-field methods with an emphasis on Density-Functional Theory and Gaussian basis, starting from the four-component (Dirac) picture and continue to the two-component (Pauli) picture, where we introduce various flavours of modern exact two-component (X2C) Hamiltonians for real-time electron dynamics. We also overview several numerical techniques for real-time propagation and signal processing in quantum electron dynamics. We close this Chapter by listing selected applications of real-time electron dynamics to frequency-resolved and time-resolved spectroscopies

Advanced capabilities for materials modelling with Quantum ESPRESSO

Quantum ESPRESSO is an integrated suite of open-source computer codes for quantum simulations of materials using state-of-the art electronic-structure techniques, based on density-functional theory, density-functional perturbation theory, and many-body perturbation theory, within the plane-wave pseudo-potential and projector-augmented-wave approaches. Quantum ESPRESSO owes its popularity to the wide variety of properties and processes it allows to simulate, to its performance on an increasingly broad array of hardware architectures, and to a community of researchers that rely on its capabilities as a core open-source development platform to implement theirs ideas. In this paper we describe recent extensions and improvements, covering new methodologies and property calculators, improved parallelization, code modularization, and extended interoperability both within the distribution and with external software

Spatio-temporal integral equation methods with applications

Electromagnetic interactions are vital in many applications including physics, chemistry, material sciences and so on. Thus, a central problem in physical modeling is the electromagnetic analysis of materials. Here, we consider the numerical solution of the Maxwell equation for the evolution of the electromagnetic field given the charges, and the Newton or Schr\\"odinger equation for the evolution of particles. By combining integral equation techniques with new spectral deferred correction algorithms in time and hierarchical methods in space, we develop fast solvers for the calculation of electromagnetism with relaxations of the model in different scenarios. The dissertation consists of two parts, aiming to resolve the challenges in the temporal and spatial direction, respectively. In the first part, we study a new class of time stepping methods for time-dependent differential equations. The core algorithm uses the pseudo-spectral collocation formulation to discretize the Picard type integral equation reformulation, producing a highly accurate and stable representation, which is then solved via the deferred correction technique. By exploiting the mathematical properties of the formulation and the convergence procedure, we develop some new preconditioning techniques from different perspectives that are accurate, robust, and can be much more efficient than existing methods. As is typical of spectral methods, the solution to the discretization is spectral accurate and the time step-size is optimal, though the cost of solving the system can be high. Thus, the solver is particularly suited to problems where very accurate solutions are sought or large time-step is required, e.g., chaotic systems or long-time simulation. In the second part, we study the hierarchical methods with emphasis on the spatial integral equations. In the first application, we implement a parallel version of the adaptive recursive solver for two-point boundary value problem by Cilk multithreaded runtime system based on the integral equation formulation. In the second application, we apply the hierarchical method to two-layered media Helmholtz equations in the acoustic and electromagnetic scattering problems. With the method of images and integral representations, the spatially heterogeneous translation operators are derived with rigorous error analysis, and the information is then compressed and spread in a fashion similar to fast multipole methods. The preliminary results suggest that our approach can be faster than existing algorithms with several orders of magnitude. We demonstrate our solver on a number of examples and discuss various useful extensions. Preliminary results are favorable and show the viability of our techniques for integral equations. Such integral equation methods could well have a broad impact on many areas of computational science and engineering. We describe further applications in biology, chemistry, and physics, and outline some directions for future work.Doctor of Philosoph

Atomic structures and properties of oxide interfaces

This thesis uses computational approaches, mainly first-principles methods, to study interfaces in oxide thin films. One of the difficulties in interface studies is the lack of definitive atomistic models, yet they are essential input for any calculations. Here, this problem is tackled by ab initio random structure searching (AIRSS), or more broadly speaking, random structure searching (RSS). The initial work studies the interfaces in vertically aligned nanocomposites (VANs) that consist of CeO₂ pillars embedded in a SrTiO₃ matrix. Enhanced ionic conductivity has been found in these VANs in prior studies, but the role of vertical interfaces is not explained. The initial interface searches are performed with interatomic potentials due to the large size of the interface, followed by refinement first-principles calculations. Based on the obtained structures, it is shown that the majority interfaces are unlikely to directly enhance ionic conductivity. However, a parallel solid-state O¹⁷ NMR study by our collaborators later obtained interface signals that suggest fast ionic conduction. First-principles NMR calculations show the observed signals are not consistent with the majority interface initially studied; instead, they can be assigned to the minority interfaces that are in different orientations. The following work studies the planar interfaces between epitaxial films of CeO₂ and STO substrates. A significant amount of research has been devoted to fluorite-perovskite interfaces since the controversial report of colossal ionic conductivity enhancement in YSZ/STO heterostructures. However, the exact atomic structures of these interfaces are not well understood. AIRSS is used for finding stable CeO₂/STO planar interfaces taking account of different terminations and local stoichiometries. When the STO terminates with a TiO₂ layer, a rock salt structured CeO layer emerges at the interface. On the other hand, with SrO termination, the stable structure contains a partially occupied anion lattice, which gives rise to lateral diffusion of oxygen anions in molecular dynamics simulations. In both cases, the interfaces are found to attract oxygen vacancies, which hinders ionic transport in the perpendicular direction. The subsequent work starts with addressing the perovskite-perovskite interfaces between La₀.₉Ba₀.₁MnO₃ (LBMO) and STO. LBMO is a ferromagnetic insulator with a relatively high ferromagnetic transition temperature, which makes it an ideal material for spintronics applications. However, thin films of LBMO are conductive except when the thickness is less than eight unit cells. This has been attributed to the octahedral proximity effects, as electron microscopy reveals that octahedral tilting in LBMO is suppressed near the interfaces. Whist some experimental observations are successfully accounted for by the first-principles calculations, the predicted tilt angle suppression is much weaker than that observed. By studying the response of octahedral networks to corner perturbations, it is shown that a competing LBMO phase with an alternative tilt configuration is stable as a result of interface coupling.Cambridge Commonwealth, European and International Trust China Scholarship Counci

Molecular Dynamics Simulation

Condensed matter systems, ranging from simple fluids and solids to complex multicomponent materials and even biological matter, are governed by well understood laws of physics, within the formal theoretical framework of quantum theory and statistical mechanics. On the relevant scales of length and time, the appropriate ‘first-principles’ description needs only the Schroedinger equation together with Gibbs averaging over the relevant statistical ensemble. However, this program cannot be carried out straightforwardly—dealing with electron correlations is still a challenge for the methods of quantum chemistry. Similarly, standard statistical mechanics makes precise explicit statements only on the properties of systems for which the many-body problem can be effectively reduced to one of independent particles or quasi-particles. [...