Le travail présenté dans cette thèse est inspiré de précédents résultats sur les modèles de Gaudin ne contenant que des spins-1/2 (ces modèles sont intégrables) qui, par un changement de variable dans les équations de Bethe algébriques, parviennent à simplifier le traitement numérique de ces modèles. Cette optimisation numérique s'effectue par l'intermédiaire d'une construction en déterminant, ne dépendant que des variables précédemment mentionnées, pour chaque produit scalaire intervenant dans l'expression de la moyenne d'une observable à un temps donné. En montrant qu'il est possible d'utiliser la méthode du Quantum Inverse Scattering Method (QISM), même dans un cas où l'état du vide n'est pas état propre de la matrice de transfert, les résultats précédents concernant uniquement des spins-1/2 sont généralisés à des modèles contenant en plus une interaction spin-boson. De fait, cette généralisation a ouvert plusieurs voies de recherche possibles. Premièrement, il est montré qu'il est possible de continuer à généraliser l'utilisation de déterminants pour des modèles de spins décrivant l'interaction d'un spin de norme arbitraire avec des spins-1/2. La méthode permettant d'obtenir la construction des expressions explicites de ces déterminants est donnée. On peut également pousser la généralisation à d'autres modèles de Gaudin dont l'état du vide n'est pas état propre de la matrice de transfert. C'est ce que nous avons fait pour des spins-1/2 en interaction avec un champ magnétique dont l'orientation est arbitraire. Enfin, un traitement numérique de ces systèmes de spins-1/2 interagissant avec un mode bosonique est présenté. L'évolution temporelle de l'occupation bosonique et de l'aimantation locale des spins est ainsi étudiée selon deux Hamiltoniens différents, l'Hamiltonien de Tavis-Cummings et un Hamiltonien type spin central. Cette étude nous apprend que la dynamique de ces systèmes, qui relaxent d'un état initial vers un état stationnaire, conduit à un état superradiant lorsque l'état initial choisi y est favorable / The work presented in this thesis was inspired by precedent results on the Gaudin models (which are integrable) for spins-1/2 only which, by a change of variables in the algebraic Bethe equations, manage to considerably simplify the numerical treatment of such models. This numerical optimisation is carried out by the construction of determinants, only depending on the previously mentioned variables, for every scalar products appearing in the expression of the mean value of an observable of interest at a given time. By showing it is possible to use the Quantum Inverse Scattering Method (QISM), even when the vacuum state is not eigenstate of the transfer matrix, the previous results concerning spins-1/2 only are generalised to models including an additional spin-boson interaction. De facto, this generalisation opened different possible paths of research. First of all, we show that it is possible to further generalise the use of determinants for spin models describing the interaction of one spin of arbitrary norm with many spins-1/2. We give the method leading to the explicit construction of determinants’ expressions. Moreover, we can extend this work to other Gaudin models where the vacuum state is not an eigenstate of the transfer matrix. We did this work for spins-1/2 interacting with an arbitrarily oriented magnetic field. Finally, a numerical treatment of systems describing the interaction of many spins-1/2 with a single bosonic mode is presented. We study the time evolution of bosonic occupation and of local magnetisation for two different Hamiltonians, the Tavis-Cummings Hamiltonian and a central spin Hamiltonian. We learn that the dynamics of these systems, relaxing from an initial state to a stationary state, leads to a superradiant-like state for certain initial states

Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2016-02-01T08:04:44Z No. of bitstreams: 2 Dissertação - Vinícius Vaz da Cruz - 2015.pdf: 2292478 bytes, checksum: 170721177f0dc0267e59c8d54868ae20 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2016-02-01T08:06:56Z (GMT) No. of bitstreams: 2 Dissertação - Vinícius Vaz da Cruz - 2015.pdf: 2292478 bytes, checksum: 170721177f0dc0267e59c8d54868ae20 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Made available in DSpace on 2016-02-01T08:06:56Z (GMT). No. of bitstreams: 2 Dissertação - Vinícius Vaz da Cruz - 2015.pdf: 2292478 bytes, checksum: 170721177f0dc0267e59c8d54868ae20 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2015-08-28 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / This dissertation presents a wavepacket simulation study of the H + HCl collinear reaction when the HCl molecule is initially prepared by an infrared laser pulse in a coherent superposition of vibrational states. A detailed discussion of wavepacket motion, reactive flux and reaction probabilities as function of the superposition state parameters is presented. We apply the flux formalism to derive an analytical expression for the reaction probabilities, which is then used to analyse our numerical simulations. The results show a strong phase dependence of the reaction probabilities, as well as the spatial distribution of the reactant molecules. The full reaction probability surface is computed for two average collision energies, and the enhancement and suppression of the H+HCl!H2+Cl reaction channel is discussed in terms of the surface’s critical points. / Esta dissertação apresenta o estudo por meio de simulações de pacote de ondas das colisões colineares H + HCl quando a molécula de HCl é preparada por pulsos de laser de infravermelho em uma superposição de níveis vibracionais. É feita uma discussão detalhada do movimento do pacote de ondas, fluxo reativo e probabilidades de reação em termos dos parâmetros da superposição de estados. Nós aplicamos o formalismo de fluxo para deduzir uma expressão analítica para as probabilidades de reação, a qual é então utilizada na análise de nossas simulações numéricas. Os resultados mostram uma grande dependência das probabilidades de reação com a fase e com a distribuição espacial das moléculas reagentes. A superfície completa de probabilidade de reação é calculada para duas energias de colisão médias, e as condições de melhora e supressão da reação H+HCl!H2+Cl é discutida em termos dos pontos críticos da superfície.

Semiclassical initial value representations (SC-IVRs) are popular methods for an approximate description of the quantum dynamics of atomic and molecular systems. A very efficient special case is the propagator by Herman and Kluk, which will be the basis for the investigations in this work. It consists of a phase space integration over initial conditions of classical trajectories which are guiding Gaussian wavepackets. A complex phase factor in the integrand allows for interference between different trajectories, which leads to soft quantum effects being naturally included in the description. The underlying classical trajectories allow for an approximate description of the dynamics of large quantum systems that are inaccessible for a full quantum propagation. Moreover, they also provide an intuitive understanding of quantum phenomena in terms of classical dynamics. The main focus of this work is on further approximations to Herman-Kluk propagation whose applicability to complex dynamics is limited by the number of trajectories that are needed for numerical convergence of the phase space integration. The central idea for these approximations is the semiclassical hybrid formalism which utilizes the costly Herman-Kluk propagator only for a small number of system degrees of freedom (DOFs). The remaining environmental DOFs are treated on the level of Heller's thawed Gaussian wavepacket dynamics, a single trajectory method which is exact only for at most harmonic potentials. If the environmental DOFs are weakly coupled and therefore close to their potential minimum, this level of accuracy is sufficient to account for their effect on the system. Thus, the hybrid approximation efficiently combines accuracy and low numerical cost. As a central theoretical result, we apply this hybrid idea to a time-averaging scheme to arrive at a method for the calculation of vibrational spectra of molecules that is both accurate and efficient. This time-averaged hybrid propagation is then used to study the vibrational dynamics of an iodine-like Morse oscillator bilinearly coupled to a Caldeira-Leggett bath of harmonic oscillators. We first validate the method by comparing it to full quantum and Herman-Kluk propagation for appropriately sized environments. After having established its accuracy, we include more bath DOFs to investigate the influence of the Caldeira-Leggett counter term on the shift of the vibrational levels of the Morse oscillator. As a result, we find out that a redshift, which is observed experimentally for, e.g., iodine in a rare gas matrix, occurs only if the counter term is not included in the Hamiltonian. We then move away from the model bath and on to a realistic, experimentally relevant environment consisting of krypton atoms. We put the iodine molecule into a cluster of 17 krypton atoms and investigate the loss of coherence of the iodine vibration upon coupling to just a few normal coordinates of the bath. These modes with the same symmetry as the iodine vibration turn out to be sufficient to reproduce the expected qualitative dependence on bath temperature and initial state of the iodine molecule. With these few normal modes, a full quantum calculation yields values for coherence loss rates that are close to experimental results. Furthermore, a comparison to semiclassical calculations with more bath modes included confirms the importance of the few highly symmetric normal coordinates. Then, we apply the time-averaged hybrid formalism once more to calculate the vibrational spectrum of the iodine molecule in this now anharmonic krypton environment. Using a krypton matrix instead of a cluster geometry, we find the correct qualitative and also quite good quantitative agreement for the shift of the iodine potential. Finally, we will investigate a more fundamental question, namely, if SC-IVRs contain the spin effects due to the Pauli exclusion principle. To this end, we apply a number of SC-IVRs to the scattering of two electrons with initial states corresponding to either parallel or antiparallel spin. We compare the outcome to full quantum results and find that the difference is resolved by those methods that comprise multiple interfering trajectories.

Many-body quantum dynamics is a challenging problem that has induced the development of many different computational techniques. One powerful technique is the multiconfiguration time-dependent Hartree-Fock (MCTDHF) method. This method allows proper consideration of electronic correlation with much less computational overhead compared to other similar methods. In this work, we present our implementation of the MCTDHF method on a non-uniform cylindrical grid. With the one-body limit of our code, we studied the controversial topic of tunneling delay, and showed that our results agree with one recent experiment while disagreeing with another. Using the fully correlated version of the code, we demonstrated the ability of MCTDHF to address correlation by calculating the ground state ionization energies of a few strongly correlated systems.

京都大学 / 新制・論文博士 / 博士(理学) / 乙第13434号 / 論理博第1576号 / 新制||理||1682(附属図書館) / 京都大学大学院理学研究科 / (主査)教授 谷村 吉隆, 教授 林 重彦, 教授 渡邊 一也 / 学位規則第4条第2項該当 / Doctor of Science / Kyoto University / DGAM

This thesis describes work on several research topics in which transport and spectroscopy are influenced by strong electron-nuclear or nuclear-nuclear interactions. First, I give a broad overview of the motivations and background for the main topics covered in this thesis. In the next section, I explore the applicability of perturbative quantum master equations to linear absorption and nonlinear two-dimensional and pump-probe spectroscopies. Next, I introduce a theory of charge transport in organic semiconductors that unifies two popular pictures: incoherent polaron hopping and transient localization due to dynamic disorder. In the next section, I investigate the impact of phonon anharmonicity on the charge transport dynamics of soft semiconductors. Finally, I present a new method of efficiently calculating anharmonic vibrational spectra from ab initio molecular potential energy surfaces.

In this thesis, we focus attention on the effects of disorder in closed interacting quantum systems that give rise to a many-body localization (MBL) transition between an ergodic phase and a many-body localized phase. This transition is not a conventional one, since it takes place at any finite energy density and can neither be described by thermodynamics nor conventional statistical mechanics. We explain why systems experiencing such an MBL transition can be regarded as generic in many ways, we do so by discussing many of their spectral properties and by giving a detailed account of their manifestation in the nonequilibrium dynamics and long-time behavior. Surprisingly, a wide variety of MBL systems consistently reflect strikingly similar characteristic effects in each side of the MBL transition. This is backed by myriads of numerical and experimental observations which in turn can be partially explained by theories developed in the past decade. However, some mechanisms behind the ergodic side of the MBL transition and the nature of the MBL transition itself remain elusive. These, as well as the lack of an accurate description of the nonergodic character of the steady states of such systems, have been some of the issues for active research and speculation by scholars that need to be timely addressed. In the following, we describe our modest contributions at bridging the gap of understanding of some of the issues exposed above. On the one hand, reduced density matrices are central objects for the description of the relaxation of local observables in closed quantum many-body systems, and on the other, quench protocols are experimentally relevant procedures. In the first part of this thesis we study the long-time behavior of the one-particle density matrix (OPDM) occupation spectrum after a quench. It was shown that, in the many-body localized phase (which can be understood in terms of localized quasiparticles), the OPDM occupation spectrum in eigenstates shows a zero-temperature Fermi liquid-like discontinuity at any finite energy density. In this thesis we show that in the steady state reached at long times after a global quench from a perfect density-wave state, the discontinuity in the OPDM occupation spectrum is absent, reminiscent of a Fermi liquid at a finite temperature, while the full occupation function remains strongly nonthermal. We discuss how one can understand this as a consequence of the local structure of the density-wave state and the resulting partial occupation of quasiparticles. We further show how these partial occupations can be controlled by tuning the structure of initial state and described by an effective temperature. Another part of this thesis was devoted to the study of dynamics on the ergodic side of the transition in periodically driven systems in the absence of global conservation laws. Most numerical studies in this context were done in models with conserved quantities (e.g., energy and/or particle number) which could account for the reduction of the overall complexity of the problem, while in this thesis, we use a numerical technique based on the fast Walsh-Hadamard transform that allows us to perform an exact time evolution for large systems and long times. As in models with conserved quantities, we observe a slowing down of the dynamics as the transition into the many-body localized phase is approached. This is reflected in anomalous behavior of the energy absorption of the system, as well as consistent with a subballistic spread of entanglement and a stretched-exponential decay of an autocorrelation function, with their associated exponents reflecting slow dynamics near the transition for a fixed system size. However, with access to larger system sizes, we observe a clear flow of the exponents towards faster dynamics and cannot rule out that the slow dynamics is a finite-size effect. Furthermore, we observe examples of nonmonotonic dependence of the exponents with time, with the dynamics initially slowing down but accelerating again at larger times, which could be consistent with the slow dynamics being a crossover phenomenon with a localized critical point. In addition, we observe no difference between the typical and average value of the autocorrelation function and therefore our results are inconsistent with the phenomenological explanation of the anomalous behavior based on Griffiths effects. In the last part of this thesis, we study dynamics in the ergodic phase relating to two main quantum information measures: One is the entanglement entropy, which is an intrinsic property of the wave function and generated by the time evolution operator, while the other is the operator entanglement entropy of the time evolution operator, which quantifies the complexity of the latter. It is known that generic quantum many-body systems typically show a linear growth of the entanglement entropy growth after a quench from a product state. In this thesis we show that there is a robust correspondence between the operator entanglement entropy of the time evolution operator and the entanglement entropy growth of typical product states, whereas special product states, e.g., $\sigma_z$ basis states, may exhibit faster entanglement production. We base our analysis on numerical simulations of a static and a periodically driven quantum spin chain in the presence of a disordered magnetic field, showing that both the wave function and operator entanglement entropies exhibit a power-law growth with the same disorder-dependent exponent. With this, we clarify the discrepancy between the exponents observed in previous results. Our results provide further evidence for slow information spreading on the ergodic side of the many-body localization transition in the absence of conservation laws. / In dieser Dissertation setzen wir uns mit dem Effekt von Unordnung auf geschlossene wechselwirkende Quantensysteme auseinander. Unordnung kann einen Übergang von einer ergodischen in eine lokalisierte Phase induzieren, eine sogenannte Vielteilchenlokalisierung oder Many body localization (MBL). Dieser Phasenübergang ist alles andere als konventionell: Er kann weder durch Thermodynamik noch durch klassische statistische Mechanik beschrieben werden. Wir erklären, warum Systeme, die solch einen MBL Übergang aufweisen, in vielerlei Hinsicht als generisch angesehen werden können. Dazu diskutieren wir die spektralen Eigenschaften, die Nichtgleichgewichtsdynamik und das Langzeitverhalten. Erstaunlicherweise weist eine große Vielfalt verschiedener MBL Systeme auf beiden Seiten des MBL Übergangs mit großer Konsistenz ähnliche Charakteristiken auf. Dies wird durch unzählige numerische und experimentelle Beobachtungen unterstützt, die wiederum zumindest teilweise durch theoretische Arbeiten aus dem letzten Jahrzehnt erklärt werden können. Trotzdem bleiben manche Mechanismen auf der ergodischen Seite des MBL Übergangs und die Art des MBL Übergangs weiterhin im Verborgenen. Zusammen mit der fehlenden akkuraten Beschreibung des nicht-ergodischen Charakters der stationären Zustände dieser Systeme sind diese Probleme im derzeitigen Fokus der Forschung, wobei es eine Vielzahl fundierter Vermutungen gibt, die diese Phänomene erklären. Im Folgenden beschreiben wir unseren Beitrag wie diese oben gelisteten Probleme überwunden werden können. Reduzierte Dichteoperatoren sind zentrale Objekte, um die Relaxation von lokalen Observablen in geschlossenen Quantenvielkörpersystemen zu beschreiben und sogenannte Quenches, also die plötzliche Änderung einiger systemrelevanter Parameter, ähnlich wie beim Abschrecken mit Wasser oder Luft, sind experimentell relevante Vorgänge. Im ersten Teil dieser Arbeit untersuchen wir das Langzeitverhalten des Besetzungsspektrums des Einteilchendichteoperators (one-particle density matrix, OPDM) nach solch einem Quench. Wie zuvor gezeigt wurde, weist das OPDM Besetzungsspektrum in der MBL Phase (die im Sinne von lokalisierten Quasiteilchen verstanden werden kann) für alle endlichen Energiedichten eine Diskontinuität auf, ähnlich wie in Fermi-Flüssigkeiten. In dieser Arbeit zeigen wir, dass diese Diskontinuität in stationären Zuständen, die von perfekten Dichtewellen ausgehend nach langer Zeit nach einem globalen Quench erreicht werden, abwesend ist, ähnlich wie in einer Fermi-Flüssigkeit bei einer endlichen Temperatur, während die gesamte Besetzungsfunktion stark nicht-thermal bleibt. Wir diskutieren, wie man dies als Konsequenz der lokalen Struktur des Dichtewellenzustands und der daraus folgenden teilweisen Besetzung der Quasiteilchen verstehen kann. Wir zeigen außerdem, wie die teilweise Besetzung durch Änderung der Struktur des Ausgangszustands kontrolliert und durch eine effektive Temperatur beschrieben werden kann. Im nächsten Teil dieser Arbeit untersuchen wir die Dynamik der ergodischen Seite des MBL Übergangs in periodisch getriebenen Systemen ohne globale Erhaltungsgrößen. Die meisten bisherigen in diesem Zusammenhang vorgenommenen numerischen Untersuchungen wurden in Modellen mit Erhaltungsgrößen (wie Energie und/oder Teilchenzahl) durchgeführt, was an der Reduzierung der Komplexität des Problems liegen mag. In dieser Arbeit nutzen wir hingegen eine numerische Methode, die auf einer schnellen Walsh-Hadamard Transformation beruht, was uns ermöglicht, eine exakte Zeitentwicklung für lange Zeiten und große Systeme vorzunehmen. Wie in Modellen mit Erhaltungsgrößen beobachten wir eine Verlangsamung der Dynamik, wenn wir uns dem Übergangspunkt zu der MBL Phase nähern. Dies macht sich in einem ungewöhnlichen Verhalten der Energieabsorption des Systems bemerkbar, was mit einer unterballistischen Ausbreitung der Verschränkung und einem gedehnt-exponentiellen Abklingen der Autokorrelationsfunktion im Einklang steht, wobei die zugehörigen Exponenten die verlangsamte Dynamik für fixe Systemgrößen widerspiegeln. Durch den Zugang zu größeren Systemen können wir jedoch einen deutlichen Fluss der Exponenten Richtung schnellerer Dynamik feststellen und daher nicht ausschließen, dass die verlangsamte Dynamik durch die endlichen Systemgrößen hervorgerufen wird (ein sogenannter finite size effect). Des weiteren finden wir Beispiele für eine nicht-monotone Zeitabhängigkeit der Exponenten, wobei die Dynamik sich zunächst verlangsamt, bevor sie zu späteren Zeiten wieder beschleunigt. Dies könnte mit der Betrachtung der verlangsamten Dynamik als Crossover-Phänomen mit einem lokalisierten kritischen Punkt vereinbar sein. Außerdem können wir keinen Unterschied zwischen dem geometrischen und arithmetischen Mittel der Autokorrelationsfunktion feststellen, sodass unsere Ergebnisse der phänomenologischen Erklärung des ungewöhnlichen Verhaltens, die auf Griffiths-Effekten beruht, widersprechen. Im letzten Teil der Dissertation widmen wir der Dynamik in der ergodischen Phase und verknüpfen zwei zentrale Größen der Quanteninformation: die Verschränkungsentropie, eine der Wellenfunktion intrinsische Größe, die aus dem Zeitentwicklungsoperator generiert werden kann, und der Operatorverschränkungsentropie des Zeitentwicklungsoperators, die die Komplexität des Operators quantifiziert. In generischen Quantenvielkörpersystemen wächst die Verschränkungsentropie nach einem Quench aus einem Produktzustand typischerweise linear. In dieser Arbeit zeigen wir, dass es eine belastbaren Übereinstimmung zwischen der Operatorverschränkungsentropie des Zeitentwicklungsoperators und der Verschränkungsentropie typischer Produktzustände gibt, wobei bestimmte Produktzustände, z.B. $\sigma_z$-Basiszustände, eine schnellere Verschränkungsproduktion aufweisen können. Unsere Analyse basiert auf numerischen Simulationen von statischen und periodisch getriebenen Quanten-Spinketten in einem ungeordneten Magnetfeld. Sowohl die Verschränkungsentropie der Wellenfunktion als auch die Operatorverschränkungsentropie wächst einem Potenzgesetz folgend mit den selben unordnungsabhängigen Exponenten. Damit schaffen wir Klarheit bezüglich der Unstimmigkeiten der Exponenten in den vorherigen Ergebnissen. Unsere Resultate geben außerdem Hinweise auf eine verlangsamte Informationsausbreitung auf der ergodischen Seite des MBL Übergangs ohne Erhaltungsgrößen.

This thesis deals with the process of molecular ions formation in interstellar space, which played an important role in the early Universe. A large part of the work focuses on the theoretical study of quantum dynamics of the process of radiative association pre- dominantly induced by dipole transitions. The effect of quadrupole transitions on the radiative association have also been taken into account, which has been studied for the first time. Furthermore, spectroscopic characteristics of rovibronic transitions of selected di- atomic ions for the study of cosmological variability of fundamental constants were determined. The main outcomes of the thesis include the characterization of depopulation of metastable levels He (23S) and He (21S) due to radiative collisions with hydrogen, helium and lithium ions, i. e. He + A+ → HeA+ + hν. Within the study quantum dynamics calculations were carried out using a fully quan- tal approach. Studied spontaneous and stimulated processes on a specific spin manifold were characterized by energy-dependent cross sections and temperature-dependent rate coefficients. Compared to previous published works by other authors highly excited electronic states are considered. The results showed that a) the spontaneous radiative association contributes significantly to the...

Semiclassical initial value representations (SC-IVRs) are popular methods for an approximate description of the quantum dynamics of atomic and molecular systems. A very efficient special case is the propagator by Herman and Kluk, which will be the basis for the investigations in this work. It consists of a phase space integration over initial conditions of classical trajectories which are guiding Gaussian wavepackets. A complex phase factor in the integrand allows for interference between different trajectories, which leads to soft quantum effects being naturally included in the description. The underlying classical trajectories allow for an approximate description of the dynamics of large quantum systems that are inaccessible for a full quantum propagation. Moreover, they also provide an intuitive understanding of quantum phenomena in terms of classical dynamics. The main focus of this work is on further approximations to Herman-Kluk propagation whose applicability to complex dynamics is limited by the number of trajectories that are needed for numerical convergence of the phase space integration. The central idea for these approximations is the semiclassical hybrid formalism which utilizes the costly Herman-Kluk propagator only for a small number of system degrees of freedom (DOFs). The remaining environmental DOFs are treated on the level of Heller's thawed Gaussian wavepacket dynamics, a single trajectory method which is exact only for at most harmonic potentials. If the environmental DOFs are weakly coupled and therefore close to their potential minimum, this level of accuracy is sufficient to account for their effect on the system. Thus, the hybrid approximation efficiently combines accuracy and low numerical cost. As a central theoretical result, we apply this hybrid idea to a time-averaging scheme to arrive at a method for the calculation of vibrational spectra of molecules that is both accurate and efficient. This time-averaged hybrid propagation is then used to study the vibrational dynamics of an iodine-like Morse oscillator bilinearly coupled to a Caldeira-Leggett bath of harmonic oscillators. We first validate the method by comparing it to full quantum and Herman-Kluk propagation for appropriately sized environments. After having established its accuracy, we include more bath DOFs to investigate the influence of the Caldeira-Leggett counter term on the shift of the vibrational levels of the Morse oscillator. As a result, we find out that a redshift, which is observed experimentally for, e.g., iodine in a rare gas matrix, occurs only if the counter term is not included in the Hamiltonian. We then move away from the model bath and on to a realistic, experimentally relevant environment consisting of krypton atoms. We put the iodine molecule into a cluster of 17 krypton atoms and investigate the loss of coherence of the iodine vibration upon coupling to just a few normal coordinates of the bath. These modes with the same symmetry as the iodine vibration turn out to be sufficient to reproduce the expected qualitative dependence on bath temperature and initial state of the iodine molecule. With these few normal modes, a full quantum calculation yields values for coherence loss rates that are close to experimental results. Furthermore, a comparison to semiclassical calculations with more bath modes included confirms the importance of the few highly symmetric normal coordinates. Then, we apply the time-averaged hybrid formalism once more to calculate the vibrational spectrum of the iodine molecule in this now anharmonic krypton environment. Using a krypton matrix instead of a cluster geometry, we find the correct qualitative and also quite good quantitative agreement for the shift of the iodine potential. Finally, we will investigate a more fundamental question, namely, if SC-IVRs contain the spin effects due to the Pauli exclusion principle. To this end, we apply a number of SC-IVRs to the scattering of two electrons with initial states corresponding to either parallel or antiparallel spin. We compare the outcome to full quantum results and find that the difference is resolved by those methods that comprise multiple interfering trajectories.

This thesis examines the quantum dynamics of electrons in periodic semiconductor superlattices in the presence of electric fields, especially uniform static fields. Chapter 1 is an introduction to this vast and active field of research, with an analysis and suggested solutions to the fundamental theoretical difficulties. Chapter 2 is a detailed historical review of relevant theories, and Chapter 3 is a historical review of experiments. Chapter 4 is devoted to the time-independent quantum mechanical study of the electric-field-induced changes in the transmission properties of ballistic electrons, using the transfer matrix method. In Chapter 5, a new time-dependent quantum mechanical model free from the fundamental theoretical difficulties is introduced, with its validity tested at various limiting cases. A simplified method for calculating field-free bands of various potential models is designed. In Chapter 6, the general features of "Shifting Periodicity", a distinctive feature of this new model, is discussed, and a "Bloch-Floquet Theorem" is rigorously proven. Numerical evidences for the existence of Wannier-Stark-Ladders are presented, and the conditions for its experimental observability is also discussed. In Chapter 7, an analytical solution is found for Bloch Oscillations and Wannier-Stark-Ladders at low electric fields. In Chapter 8, a new quantum mechanical interpretation for Bloch Oscillations and Wannier-Stark-Ladders is derived from the analytical result. The extension of this work to the cases of time-dependent electric fields is also discussed.