This dissertation addresses issues that arise in the classic linear instrumental variables (IV) model when some of the underlying assumptions are violated. / Economics

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.

The adiabatic approximation is a natural approach for the description of phenomena induced by low frequency laser radiation because the ratio of the laser frequency to the characteristic frequency of an atom or a molecule is a small parameter. Since the main aim of this work is the study of ionization phenomena, the version of the adiabatic approximation that can account for the transition from a bound state to the continuum must be employed. Despite much work in this topic, a universally accepted adiabatic approach of bound-free transitions is lacking. Hence, based on Savichev's modified adiabatic approximation [Sov. Phys. JETP 73, 803 (1991)], we first of all derive the most convenient form of the adiabatic approximation for the problems at hand. Connections of the obtained result with the quasiclassical approximation and other previous investigations are discussed. Then, such an adiabatic approximation is applied to single-electron ionization and non-sequential double ionization of atoms in a strong low frequency laser field. The momentum distribution of photoelectrons induced by single-electron ionization is obtained analytically without any assumptions on the momentum of the electrons. Previous known results are derived as special cases of this general momentum distribution. The correlated momentum distribution of two-electrons due to non-sequential double ionization of atoms is calculated semi-analytically. We focus on the deeply quantum regime -- the below intensity threshold regime, where the energy of the active electron driven by the laser field is insufficient to collisionally ionize the parent ion, and the assistance of the laser field is required to create a doubly charged ion. A special attention is paid to the role of Coulomb interactions in the process. The signatures of electron-electron repulsion, electron-core attraction, and electron-laser interaction are identified. The results are compared with available experimental data. Two-electron correlated spectra of non-sequential double ionization below intensity threshold are known to exhibit back-to-back scattering of the electrons, viz., the anticorrelation of the electrons. Currently, the widely accepted interpretation of the anticorrelation is recollision-induced excitation of the ion plus subsequent field ionization of the second electron. We argue that there exists another mechanism, namely simultaneous electron emission, when the time of return of the rescattered electron is equal to the time of liberation of the bounded electron (the ion has no time for excitation), that can also explain the anticorrelation of the electrons in the deep below intensity threshold regime. Finally, we study single-electron molecular ionization. Based on the geometrical approach to tunnelling by P. D. Hislop and I. M. Sigal [Memoir. AMS 78, No. 399 (1989)], we introduce the concept of a leading tunnelling trajectory. It is then proven that leading tunnelling trajectories for single active electron models of molecular tunnelling ionization (i.e., theories where a molecular potential is modelled by a single-electron multi-centre potential) are linear in the case of short range interactions and ``almost'' linear in the case of long range interactions. The results are presented on both the formal and physically intuitive levels. Physical implications of the proven statements are discussed.

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

Session ID: TH-E1-4 / SCIS & ISIS 2010, Joint 5th International Conference on Soft Computing and Intelligent Systems and 11th International Symposium on Advanced Intelligent Systems. December 8-12, 2010, Okayama Convention Center, Okayama, Japan

Stochastic fluctuations can have profound impacts on engineered systems. Nonetheless, we can achieve significant benefits such as cost reduction based upon expanding our fundamental knowledge of stochastic systems. The primary goal of this thesis is to contribute to our understanding by developing and analyzing stochastic models for specific types of engineered systems. The knowledge gained can help management to optimize decision making under uncertainty. This thesis has three parts. In Part I, we study many-server queues that model large-scale service systems such as call centers. We focus on the positive recurrence of piecewise Ornstein-Uhlenbeck (OU) processes and the validity of using these processes to predict the steady-state performance of the corresponding many-server queues. In Part II, we investigate diffusion processes constrained to the positive orthant under infinitesimal changes in the drift. This sensitivity analysis on the drift helps us understand how changes in service capacities at individual stations in a stochastic network would affect the steady-state queue-length distributions. In Part III, we study the trading mechanism known as limit order book. We are motivated by a desire to better understand the interplay among order flow rates, liquidity fluctuation, and optimal executions. The goal is to characterize the temporal evolution of order book shape on the “macroscopic” time scale.

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.

To abstract physical into virtual computing infrastructures is a longstanding goal. Efforts in the computing industry started with early work on virtual machines in IBM's VM370 operating system and architecture, continued with extensive developments in distributed systems in the context of grid computing, and now involve investments by key hardware and software vendors to efficiently virtualize common hardware platforms. Recent efforts in virtualization technology are driven by two facts: (i) technology push -- new hardware support for virtualization in multi- and many-core hardware platforms and in the interconnects and networks used to connect them, and (ii) technology pull -- the need to efficiently manage large-scale data-centers used for utility computing and extending from there, to also manage more loosely coupled virtual execution environments like those used in cloud computing. Concerning (i), platform virtualization is proving to be an effective way to partition and then efficiently use the ever-increasing number of cores in many-core chips. Further, I/O Virtualization enables I/O device sharing with increased device throughput, providing required I/O functionality to the many virtual machines (VMs) sharing a single platform. Concerning (ii), through server consolidation and VM migration, for instance, virtualization increases the flexibility of modern enterprise systems and creates opportunities for improvements in operational efficiency, power consumption, and the ability to meet time-varying application needs. This thesis contributes (i) new technologies that further increase system flexibility, by addressing some key problems of existing virtualization infrastructures, and (ii) it then directly addresses the issue of how to exploit the resulting increased levels of flexibility to improve data-center operations, e.g., power management, by providing lightweight, efficient management technologies and techniques that operate across the range of individual many-core platforms to data-center systems. Concerning (i), the thesis contributes, for large many-core systems, insights into how to better structure virtual machine monitors (VMMs) to provide more efficient utilization of cores, by implementing and evaluating the novel Sidecore approach that permits VMMs to exploit the computational power of parallel cores to improve overall VMM and I/O performance. Further, I/O virtualization still lacks the ability to provide complete transparency between virtual and physical devices, thereby limiting VM mobility and flexibility in accessing devices. In response, this thesis defines and implements the novel Netchannel abstraction that provides complete location transparency between virtual and physical I/O devices, thereby decoupling device access from device location and enabling live VM migration and device hot-swapping. Concerning (ii), the vManage set of abstractions, mechanisms, and methods developed in this work are shown to substantially improve system manageability, by providing a lightweight, system-level architecture for implementing and running the management applications required in data-center and cloud computing environments. vManage simplifies management by making it possible and easier to coordinate the management actions taken by the many management applications and subsystems present in data-center and cloud computing systems. Experimental evaluations of the Sidecore approach to VMM structure, Netchannel, and of vManage are conducted on representative platforms and server systems, with consequent improvements in flexibility, in I/O performance, and in management efficiency, including power management.

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.

The “one-many” problem is ontological rather than logical. The thesis is a dialogue between thinkers who never met, investigating the question of what reality fundamentally is in the context of change. Textual studies distinguishing Ge Hong’s relational ontology from Platonic causational ontology lead to the conclusion that Daoist cosmogony, moving “from nothing into being” offers an evolutionary solution to Plato’s problem of change “from being to becoming”.