An integral equation based numerical solution for nanoparticles illuminated with collimated and focused light

To address the large number of parameters involved in nanooptical problems, a more efficient computational method is necessary. An integral equation based numerical solution is developed when the particles are illuminated with collimated and focused incident beams. The solution procedure uses the method of weighted residuals, in which the integral equation is reduced to a matrix equation and then solved for the unknown electric field distribution. In the solution procedure, the effects of the surrounding medium and boundaries are taken into account using a Green’s function formulation. Therefore, there is no additional error due to artificial boundary conditions unlike differential equation based techniques, such as finite difference time domain and finite element method. In this formulation, only the scattering nano-particle is discretized. Such an approach results in a lesser number of unknowns in the resulting matrix equation. The results are compared to the analytical Mie series solution for spherical particles, as well as to the finite element method for rectangular metallic particles. The Richards-Wolf vector field equations are combined with the integral equation based formulation to model the interaction of nanoparticles with linearly and radially polarized incident focused beams

Stopping power of antiprotons in H, H2, and He targets

The stopping power of antiprotons in atomic and molecular hydrogen as well as helium was calculated in an impact-energy range from 1 keV to 6.4 MeV. In the case of H2 and He the targets were described with a single-active electron model centered on the target. The collision process was treated with the close-coupling formulation of the impact-parameter method. An extensive comparison of the present results with theoretical and experimental literature data was performed in order to evaluate which of the partly disagreeing theoretical and experimental data are most reliable. Furthermore, the size of the corrections to the first-order stopping number, the average energy transferred to the target electrons, and the relative importance of the excitation and the ionization process for the energy loss of the projectile was determined. Finally, the stopping power of the H, H2, and He targets were directly compared revealing specific similarities and differences of the three targets.Comment: v1: 12 pages, 8 figures, and 1 table v2: 15 pages, 9 figures, and 2 tables; extended discussion on IPM in Method; influence of double ionization on stopping power discussed in Result

Investigating quantum many-body systems with tensor networks, machine learning and quantum computers

(English) We perform quantum simulation on classical and quantum computers and set up a machine learning framework in which we can map out phase diagrams of known and unknown quantum many-body systems in an unsupervised fashion. The classical simulations are done with state-of-the-art tensor network methods in one and two spatial dimensions. For one dimensional systems, we utilize matrix product states (MPS) that have many practical advantages and can be optimized using the efficient density matrix renormalization group (DMRG) algorithm. The data for two dimensional systems is obtained from entangled projected pair states (PEPS) optimized via imaginary time evolution. Data in form of observables, entanglement spectra, or parts of the state vectors from these simulations, is then fed into a deep learning (DL) pipeline where we perform anomaly detection to map out the phase diagram. We extend this notion to quantum computers and introduce quantum variational anomaly detection. Here, we first simulate the ground state and then process it in a quantum machine learning (QML) manner. Both simulation and QML routines are performed on the same device, which we demonstrate both in classical simulation and on a physical quantum computer hosted by IBM.(Español) En esta tesis, realizamos simulaciónes cuánticas en ordenadores clásicos y cuánticos y diseñamos un marco de aprendizaje automático en el que podemos construir diagramas de fase de sistemas cuánticos de muchas partículas de manera no supervisada. Las simulaciones clásicas se realizan con métodos de red de tensores de última generación en una y dos dimensiones espaciales. Para sistemas unidimensionales, utilizamos estados de productos de matrices (MPS) que tienen muchas ventajas prácticas y pueden optimizarse utilizando el eficiente algoritmo del grupo de renormalización de matrices de densidad (DMRG). Los datos para sistemas bidimensionales se obtienen mediante los denominados estados de pares entrelazados proyectados (PEPS) optimizados a través de la evolución en tiempo imaginario. Los datos, en forma de observables, espectros de entrelazamiento o partes de los vectores de estado de estas simulaciones, se introducen luego en un algoritmo de aprendizaje profundo (DL) donde realizamos la detección de anomalías para construir el diagrama de fase. Extendemos esta noción a los ordenadores cuánticos e introducimos la detección de anomalías cuánticas variacionales. Aquí, primero simulamos el estado fundamental y luego lo procesamos utilizando el aprendizaje automático cuántico (QML). Tanto las rutinas de simulación como el QML se realizan en el mismo dispositivo, lo que demostramos tanto en una simulación clásica como en un ordenador cuántico real de IBM.Postprint (published version

Coupled-cluster in real space: CC2 correlation and excitation energies using multiresolution analysis

In this work algorithms for the computation of electronic correlation and excitation energies with the Coupled-Cluster method on adaptive grids are developed and implemented. The corresponding functions and operators are adaptively represented with multiresolution analysis allowing a basis-set independent description with controlled numerical accuracy. Equations for the coupled-cluster model are reformulated in a generalized framework independent of virtual orbitals and global basis-sets. For this, the amplitude weighted excitations into virtuals are replaced by excitations into n-electron functions which are determined by projected equations in the n-electron position space. The resulting equations can be represented diagrammatically analogous to basis-set dependent approaches with slightly adjusted rules of interpretation. Due to the singular Coulomb potential, the working equations are regularized with an explicitly correlated ansatz. Coupled-cluster singles with approximate doubles (CC2) and similar models are implemented for closed-shell systems and in regularized form into the MADNESS library (a general library for the representation of functions and operators with multiresolution analysis). With the presented approach electronic CC2 pair-correlation energies and excitation energies can be computed with definite numerical accuracy and without dependence on global basis sets, which is verified on small molecules

Die neuen Hochschulprofessionellen in Europa: Ausdifferenzierung und Aufgaben im internationalen Vergleich

In den vergangenen zwei Jahrzehnten mussten europäische Universitäten eine Vielzahl verschiedens-ter Anforderungen und Wandlungen bewältigen. Neben der Autonomisierung der Universitäten ge-hörten dazu vor allem die fortgesetzte Expansion der Hochschulsysteme, die Implementation der Bologna-Reformen, die Internationalisierung von Lehre und Forschung sowie die Einführung neuer Mechanismen zur Steuerung und Regulierung des Hochschulsektors. Universitäten sehen sich durch diese Veränderungen einer gesteigerten Komplexität gegenüber, die ihnen nicht nur ein höheres Maß an Verantwortlichkeit für ihr eigenes Handeln auferlegt, sondern es auch notwendig macht, dass Universitäten in der Lage sind, reflektierte Entscheidungen zu treffen. Dies setzt wiederum vo-raus, dass sie über entsprechende personelle Kapazitäten verfügen bzw. solche Kapazitäten entwi-ckeln, die sie in die Lage versetzen, den gesteigerten Anforderungen gerecht zu werden