Transport through nanostructures is studied at the many-body level using exact diagonalization and nonequilibrium Green's functions. Organic molecular junctions are a particular focus because of their technological promise. Work is presented regarding: (1) A π-electron model of organic molecular junctions developed using effective field theory; (2) series transmission and transmission node structure in interacting systems; (3) the effect of interactions on quantum interference and thermoelectricity in polycyclic junctions; and (4) nanoscale transport calculations using self-consistent statistical ensembles.

I present a detailed study of many-body effects associated with the interband 1s transition and intraband 1s-2p transition in two- and three-dimensional photo-excited semiconductors. I employ a previously developed excitonic model to treat effects of exchange and phase space filling. I extend the scope of the model to include static free-carrier screening. I also develop a factorization scheme to obtain a consistent set of excitonic dynamical equations. The exciton transition energies are renormalized by many-body interactions, and the excitonic dynamical equations provide simple expressions for the individual contributions of screening, phase space filling and exchange. The effects of exchange and phase space filling are quantified by a set of excitonic coefficients. I first calculate these coefficients analytically by omitting screening effects. In contrast, the screened coefficients involve multi-dimensional integrals which must be evaluated numerically. I present a detailed discussion of the numerical methods used to evaluate these integrals, which include a novel algorithm for segmenting multi-dimensional integration regions. The excitonic model correctly predicts the blue shift and bleaching of the 1s exciton resonance due to exchange and phase space filling. Free-carrier screening is found to enhance these effects by lowering the exciton binding energy. In contrast, the effects of free-carrier screening on the 1s-2p transition energy are more subtle. In the absence of free-carrier screening, exchange and phase space filling lead to a blue shift of the transition energy. However, screening decreases the 1s binding energy faster than the 2p binding energy, which in turn decreases the transition energy. Thus, screening effects oppose exchange and phase space filling, and the overall magnitude and sign of the 1s-2p transition energy shift depends on the free-carrier density. Specifically, for low-moderate excitation densities exchange and phase space filling can be dominated by screening, leading to a net red shift of the transition energy. The results for two- and three-dimensional systems are qualitatively similar, although the magnitudes of the shifts are much smaller in three dimensions. / Thesis (Master, Physics, Engineering Physics and Astronomy) -- Queen's University, 2011-05-31 15:58:27.222

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.

Understanding the collective behavior of a quantum many-body system, a system composed of a large number of interacting microscopic degrees of freedom, is a key aspect in many areas of contemporary physics. However, as a direct consequence of the difficultly of the so-called many-body problem, many exotic quantum phenomena involving extended systems, such as high temperature superconductivity, remain not well understood on a theoretical level. Entanglement renormalization is a recently proposed numerical method for the simulation of many-body systems which draws together ideas from the renormalization group and from the field of quantum information. By taking due care of the quantum entanglement of a system, entanglement renormalization has the potential to go beyond the limitations of previous numerical methods and to provide new insight to quantum collective phenomena. This thesis comprises a significant portion of the research development of ER following its initial proposal. This includes exploratory studies with ER in simple systems of free particles, the development of the optimisation algorithms associated to ER, and the early applications of ER in the study of quantum critical phenomena and frustrated spin systems.

Thesis (Ph. D.)--University of Washington, 1998. / Vita. Includes bibliographical references (leaves [120]-124).

Thesis (Ph. D.)--Florida State University, 2004. / Advisor: Dr. Jorge Piekarewicz, Florida State University, College of Arts and Sciences, Dept. of Physics. Title and description from dissertation home page (Jan. 19, 2005). Includes bibliographical references.

Thesis (Ph. D.)--Rutgers University, 2008. / "Graduate Program in Physics and Astronomy." Includes bibliographical references (p. 142-151).

Thesis (MPh)--University of Melbourne, Dept. of Physics, 2010. / Typescript. Includes bibliographical references (p. 77-83)

This dissertation investigates the theory of quantum stochastic processes and its applications in quantum many-body physics. The main goal is to analyse complexity-theoretic aspects of both static and dynamic properties of physical systems modelled by quantum stochastic processes. The thesis consists of two parts: the first one addresses the computational complexity of certain quantum and classical divisibility questions, whereas the second one addresses the topic of Hamiltonian complexity theory. In the divisibility part, we discuss the question whether one can efficiently sub-divide a map describing the evolution of a system in a noisy environment, i.e. a CPTP- or stochastic map for quantum and classical processes, respectively, and we prove that taking the nth root of a CPTP or stochastic map is an NP-complete problem. Furthermore, we show that answering the question whether one can divide up a random variable $X$ into a sum of $n$ iid random variables $Y_i$, i.e. $X=\sum_{i=1}^n Y_i$, is poly-time computable; relaxing the iid condition renders the problem NP-hard. In the local Hamiltonian part, we study computation embedded into the ground state of a many-body quantum system, going beyond "history state" constructions with a linear clock. We first develop a series of mathematical techniques which allow us to study the energy spectrum of the resulting Hamiltonian, and extend classical string rewriting to the quantum setting. This allows us to construct the most physically-realistic QMAEXP-complete instances for the LOCAL HAMILTONIAN problem (i.e. the question of estimating the ground state energy of a quantum many-body system) known to date, both in one- and three dimensions. Furthermore, we study weighted versions of linear history state constructions, allowing us to obtain tight lower and upper bounds on the promise gap of the LOCAL HAMILTONIAN problem in various cases. We finally study a classical embedding of a Busy Beaver Turing Machine into a low-dimensional lattice spin model, which allows us to dictate a transition from a purely classical phase to a Toric Code phase at arbitrarily large and potentially even uncomputable system sizes.

Comprendre l'interaction lumière-matière est toujours un sujet d'actualité malgré des décennies de recherche intense. Grâce au large couplage lumière-matière présent dans les circuits quantiques supraconducteurs, il est maintenant possible d'effectuer des expériences où la dynamique d'environnements contenant beaucoup de degrés de liberté, devient pertinente. Ainsi, relier la physique à N-corps, généralement réservée à la matières condensée, et l’optique quantique est à portée de main.Dans ce travail, nous présentons un système totalement accordable in-situ pour étudier l'interaction lumière-matière à N-corps (N grand) dans différents régimes de couplage. Le circuit est constitué d'un bit quantique de type transmon (“la matière”) couplé capacitivement à une chaîne de 4700 jonctions Josephson en géométrie squid. Cette chaîne supporte de nombreux modes électromagnétiques ou modes plasma (“la lumière”). Grâce à la grande inductance cinétique des jonctions Josephson, la chaîne présente une impédance caractéristique élevée ce qui augmente significativement le couplage qubit-modes. Les squids dans le transmon et dans la chaîne nous permettent de modifier la force de ce couplage en appliquant un flux magnétique.Avec ce sytème, nous avons les trois ingrédients requis pour explorer la physique à N-corps: un environnement avec une grande densité de modes électromagnétiques, un couplage lumière-matière ultra-fort, et une non linéarité comparable aux autres échelles d'énergie pertinentes. De plus, nous présentons un traitement de l'effet des fluctuations du vide de ce large nombre de degrées de liberté. Ce qui nous permet d'obtenir un modèle quantitatif et sans paramètre libre de ce système complexe. Finalement, à partir du décalage de phase induit par le transmon sur les modes de la chaîne, le transmon phase shift, nous quantifions l’hybridation du qubit transmon avec plusieurs modes de la chaîne (jusqu'à 10 modes) et obtenons la fréquence de résonance du transmon, ainsi que sa largeur, confirmant que nous sommes dans le régime de couplage ultra-fort.Ce travail démontre que les circuits quantiques sont un outil puissant pour explorer l'optique quantique à N-corps de manière totalement contrôlée. Combiner des métamatériaux supraconducteurs et des qubits devrait permettre de mettre en évidence des effets à N-corps qualitatifs, comme le décalage de Lamb géant, d’observer des états non-classiques de la lumière ou la production de particules ou encore de simuler des problèmes d’impuretés quantiques (par exemple le modèle de Kondo ou celui de Sine-Gordon) et des transitions de phase quantiques dissipatives. / Understanding the way light and matter interact remains a central topic in modern physics despite decades of intensive research. Owing to the large light-matter interaction in superconducting circuits, it is now realistic to think about experiments where the dynamics of environments containing many degrees of freedom becomes relevant. It suggests that bridging many-body physics, usually devoted to condensed matter, and quantum optics is within reach.In this work we present a fully tunable system for studying light-matter interaction with many bodies at different coupling regimes. The circuit consists of a transmon qubit (“the matter”) capacitively coupled to an array of 4700 Josephson junctions in a squid geometry, sustaining many electromagnetic or plasma modes (“the light”). Thanks to the large kinetic inductance of Josephson junctions, the array shows a high characteristic impedance that enhances the qubit-modes coupling. The squids in the transmon and in the array allow us to tune the strength of this coupling via an external magnetic flux.We observe the three required ingredients to explore many-body physics: an environment with a high density of electromagnetic modes, the ultra-strong light-matter coupling regime and a non-linearity comparable to the other relevant energy scales. Moreover, we present a method to treat the effect of the vacuum fluctuations of all these degrees of freedom. Thus we provide a quantitative and parameter-free model of this large quantum system. Finally, from the phase shift induced by the transmon on the modes of the array, the transmon phase shift, we quantify the hybridization of the transmon qubit with several modes in the array (up to 10) and obtain the transmon resonance frequency and its width, demonstrating that we are in the ultra-strong coupling regime.This work demonstrates that quantum circuits are a very powerful platform to explore many-body quantum optics in a fully controlled way. Combining superconducting metamaterials and qubits could allow us to observe qualitative many-body effects such as giant lambshift, non-classical states of light and particle productions or to simulate quantum impurity problems (such as the Kondo model or the sine-Gordon model) and dissipative quantum phase transitions.