<p>Quantum dynamics is the study of time-dependent phenomena in fundamental processes of atomic and molecular systems. This thesis focuses on systems where nature reveals its quantum aspect; e.g. in vibrational resonance structures, in wave packet revivals and in matter wave interferometry. Grid based numerical methods for solving the time-dependent Schrödinger equation are implemented for simulating time resolved molecular vibrations and to compute photo-electron spectra, without the necessity of diagonalizing a large matrix to find eigenvalues and eigenvectors.</p><p>Pump-probe femtosecond laser spectroscopy on the sodium potassium molecule, showing a vibrational period of 450 fs, is theoretically simulated. We find agreement with experiment by inclusion of the finite length laser pulse and finite temperature effects.</p><p>Complicated resonance structures observed experimentally in photo-electron spectra of hydrogen- and deuterium chloride is analyzed by a numerical computation of the spectra. The dramatic difference in the two spectra arises from non-adiabatic interactions, i.e. the interplay between nuclear and electron dynamics. We suggest new potential curves for the 3²Σ⁺ and 4²Σ⁺ states in HCI⁺.</p><p>It is possible to guide slow atoms along magnetic potentials like light is guided in optical fibers. Quantum mechanics dictates that matter can show wave properties. A proposal for a multi mode matter wave interferometer on an atom chip is studied by solving the time-dependent Schrödinger equation in two dimensions. The results verifies a possible route for an experimental realization.</p><p>An improved representation for wave functions using a discrete set of coherent states is presented. We develop a practical method for computing the expansion coefficients in this non-orthogonal set. It is built on the concept of frames, and introduces an iterative method for computing a representation of the identity operator. The phase-space localization property of the coherent states gives adaptability and better sampling efficiency.</p>

Quantum dynamics is the study of time-dependent phenomena in fundamental processes of atomic and molecular systems. This thesis focuses on systems where nature reveals its quantum aspect; e.g. in vibrational resonance structures, in wave packet revivals and in matter wave interferometry. Grid based numerical methods for solving the time-dependent Schrödinger equation are implemented for simulating time resolved molecular vibrations and to compute photo-electron spectra, without the necessity of diagonalizing a large matrix to find eigenvalues and eigenvectors. Pump-probe femtosecond laser spectroscopy on the sodium potassium molecule, showing a vibrational period of 450 fs, is theoretically simulated. We find agreement with experiment by inclusion of the finite length laser pulse and finite temperature effects. Complicated resonance structures observed experimentally in photo-electron spectra of hydrogen- and deuterium chloride is analyzed by a numerical computation of the spectra. The dramatic difference in the two spectra arises from non-adiabatic interactions, i.e. the interplay between nuclear and electron dynamics. We suggest new potential curves for the 32Σ+ and 42Σ+ states in HCI+. It is possible to guide slow atoms along magnetic potentials like light is guided in optical fibers. Quantum mechanics dictates that matter can show wave properties. A proposal for a multi mode matter wave interferometer on an atom chip is studied by solving the time-dependent Schrödinger equation in two dimensions. The results verifies a possible route for an experimental realization. An improved representation for wave functions using a discrete set of coherent states is presented. We develop a practical method for computing the expansion coefficients in this non-orthogonal set. It is built on the concept of frames, and introduces an iterative method for computing a representation of the identity operator. The phase-space localization property of the coherent states gives adaptability and better sampling efficiency.

Artificial Intelligence Planning is about acting in order to achieve a desired goal. Under incomplete information, the task of finding the actions needed to achieve the goal can be modelled as a search problem in the belief space. This task is costly, as belief space is exponential in the number of states, which is exponential in the number of variables. Good belief representations and heuristics are thus critical for scaling up in this setting. The translation-based approach to automated planning with incomplete information deals with both issues by casting the problem of search in belief space to a search problem in state space, where each node of the search space represents a belief state. We develop plan synthesis tools that use translated versions of planning problems under uncertainty, with partial or null sensing available. We show formally under which conditions the introduced translations are polynomial, and capture all and only the plans of the original problems. We study empirically the value of these translations. / La Planificación es la disciplina de Inteligencia Artificial que estudia los procesos de razonamiento necesarios para conseguir las acciones que logren un objetivo dado. En presencia de información incompleta, el problema de planificación puede ser modelado como una búsqueda en el espacio de estados de creencia, cada uno de ellos representando un conjunto de estados posibles. Este problema es costoso ya que el numero de estados de creencia puede ser exponencial en el número de estados, lo cual es exponencial en el número de variables del problema. El uso de buenas representaciónes de los estados y de heurísticas informadas resultan cruciales para escalar en este espacio de búsqueda. En esta tesis se presentan traducciones para planificación con información incompleta, que transforman el problema de búsqueda en el espacio de estados de creencia, en búsqueda en espacio de estados, donde cada nodo representa un estado de creencia. Hemos desarrollado herramientas para la generación de planes para el problema traducido, ya sea con percepción parcial o nula. A su vez, demostramos formalmente bajo qué circunstancias las traducciones son polinómicas, completas y correctas. La evaluación empírica remarca el valor de dichas traducciones

Cette étude est consacrée au problème inverse d’estimation de l’intensité et de la position d’une source de polluant. Nous inversons tout d’abord des mesures de concentration à l’intérieur d’une chambre à sable(extension des égouts souterrain) en utilisant la méthode d’identification modale pour estimer l’intensité d’émission du gaz H2S. Une approche originale est ensuite proposée pour estimer la position d’une source en utilisant la notion de transmittance entre deux capteurs. Des outils de régularisation sont utilisés afin d’estimer chaque transmittance, dont le produit de convolution avec la concentration d’un capteur choisi comme référence correspond à la réponse d’un capteur quelconque. Les transmittances estimées à partir des signaux de concentration simulés dans une configuration d’un écoulement tunnel avec source ponctuelle sont ensuite comparées à la sortie d’un modèle analytique 1D de l’équation de transport.L’utilisation d’un algorithme de minimisation non linéaire a permis d’estimer d’abord la vitesse et le coefficient de diffusion de l’écoulement et ensuite la position de la source, sous certaines hypothèses / This numerical study deals with the inverse problem of estimating the intensity and the positionof a pollutant source. The estimation of time-varying emission rates of pollutant sources of H2S in asewer chamber is first implemented through inversion of concentration measurements using the modal identification method. A specific method based on transmittance functions between sensors output isused to estimate the source position. Regularization tools are applied to estimate each transmittance,whose convolution product with the concentration of a reference sensor models the response of any sensor.Transmittances estimated from simulated concentration signals in a tunnel flow with a point source arethen compared to the output of 1D analytical model for the transport equation. A nonlinear minimizationalgorithm is used to estimate the velocity and the diffusion coefficient first and the source position next,under some assumption