The emergence of many-body physical phenomena from the quantum mechanical properties of atoms can be studied using ultracold alkali gases. The ability to manipulate both Bose-Einstein condensates (BECs) and degenerate Fermi gases (DFGs) with designer potential energy landscapes, variable interaction strengths and out-of-equilibrium initial conditions provides the opportunity to investigate collective behaviour under diverse conditions. With an appropriately chosen wavelength, optical standing waves provide a lattice potential for one target species while ignoring another spectator species. A “tune-in” scheme provides an especially strong potential for the target and works best for Li-Na, Li-K, and K-Na mixtures, while a “tune-out” scheme zeros the potential for the spectator, and is pre- ferred for Li-Cs, K-Rb, Rb-Cs, K-Cs, and 39K-40K mixtures. Species-selective lattices provide unique environments for studying many-body behaviour by allowing for a phonon-like background, providing for effective mass tuning, and presenting opportunities for increasing the phase-space density of one species. Ferromagnetism is manifest in a two-component DFG when the energetically preferred many-body configuration segregates components. Within the local density approximation (LDA), the characteristic energies and the three-body loss rate of the system all give an observable signature of the crossover to this ferromagnetic state in a trapped DFG when interactions are increased beyond kF a(0) = 1.84. Numerical simulations of an extension to the LDA that account for magnetization gradients show that a hedgehog spin texture emerges as the lowest energy configuration in the ferromagnetic regime. Explorations of strong interactions in 40K constitute the first steps towards the realization of ferromagnetism in a trapped 40K gas. The many-body dynamics of a 87Rb BEC in a double well potential are driven by spatial phase gradients and depend on the character of the junction. The amplitude and frequency characteristics of the transport across a tunable barrier show a crossover between two paradigms of superfluidity: Josephson plasma oscillations emerge for high barriers, where transport is via tunnelling, while hydrodynamic behaviour dominates for lower barriers. The phase dependence of the many-body dynamics is also evident in the observation of macroscopic quantum self trapping. Gross-Pitaevskii calculations facilitate the interpretation of system dynamics, but do not describe the observed damping.

In this thesis, we will show how certain classes of quantum many-body Hamiltonians with $\su{2}_1 \oplus \su{2}_2 \oplus \ldots \oplus \su{2}_k$ spectrum generating algebras can be approximated by multi-dimensional shifted harmonic oscillator Hamiltonians. The dimensions of the Hilbert spaces of such Hamiltonians usually depend exponentially on $k$. This can make obtaining eigenvalues by diagonalization computationally challenging. The Shifted Harmonic Approximation (SHA) developed here gives good predictions of properties such as ground state energies, excitation energies and the most probable states in the lowest eigenstates. This is achieved by solving only a system of $k$ equations and diagonalizing $k\times k$ matrices. The SHA gives accurate approximations over wide domains of parameters and in many cases even across phase transitions. The SHA is first illustrated using the Lipkin-Meshkov-Glick (LMG) model and the Canonical Josephson Hamiltonian (CJH) which have $\su{2}$ spectrum generating algebras. Next, we extend the technique to the non-compact $\su{1,1}$ algebra, using the five-dimensional quartic oscillator (5DQO) as an example. Finally, the SHA is applied to a $k$-level Bardeen-Cooper-Shrieffer (BCS) pairing Hamiltonian with fixed particle number. The BCS model has a $\su{2}_1 \oplus \su{2}_2 \oplus \ldots \oplus \su{2}_k$ spectrum generating algebra. An attractive feature of the SHA is that it also provides information to construct basis states which yield very accurate eigenvalues for low-lying states by diagonalizing Hamiltonians in small subspaces of huge Hilbert spaces. For Hamiltonians that involve a smaller number of operators, accurate eigenvalues can be obtained using another technique developed in this thesis: the generalized Rowe-Rosensteel-Kerman-Klein equations-of-motion method (RRKK). The RRKK is illustrated using the LMG and the 5DQO. In RRKK, solving unknowns in a set of $10\times 10$ matrices typically gives estimates of the lowest few eigenvalues to an accuracy of at least eight significant figures. The RRKK involves optimization routines which require initial guesses of the matrix representations of the operators. In many cases, very good initial guesses can be obtained using the SHA. The thesis concludes by exploring possible future developments of the SHA.

The emergence of many-body physical phenomena from the quantum mechanical properties of atoms can be studied using ultracold alkali gases. The ability to manipulate both Bose-Einstein condensates (BECs) and degenerate Fermi gases (DFGs) with designer potential energy landscapes, variable interaction strengths and out-of-equilibrium initial conditions provides the opportunity to investigate collective behaviour under diverse conditions. With an appropriately chosen wavelength, optical standing waves provide a lattice potential for one target species while ignoring another spectator species. A “tune-in” scheme provides an especially strong potential for the target and works best for Li-Na, Li-K, and K-Na mixtures, while a “tune-out” scheme zeros the potential for the spectator, and is pre- ferred for Li-Cs, K-Rb, Rb-Cs, K-Cs, and 39K-40K mixtures. Species-selective lattices provide unique environments for studying many-body behaviour by allowing for a phonon-like background, providing for effective mass tuning, and presenting opportunities for increasing the phase-space density of one species. Ferromagnetism is manifest in a two-component DFG when the energetically preferred many-body configuration segregates components. Within the local density approximation (LDA), the characteristic energies and the three-body loss rate of the system all give an observable signature of the crossover to this ferromagnetic state in a trapped DFG when interactions are increased beyond kF a(0) = 1.84. Numerical simulations of an extension to the LDA that account for magnetization gradients show that a hedgehog spin texture emerges as the lowest energy configuration in the ferromagnetic regime. Explorations of strong interactions in 40K constitute the first steps towards the realization of ferromagnetism in a trapped 40K gas. The many-body dynamics of a 87Rb BEC in a double well potential are driven by spatial phase gradients and depend on the character of the junction. The amplitude and frequency characteristics of the transport across a tunable barrier show a crossover between two paradigms of superfluidity: Josephson plasma oscillations emerge for high barriers, where transport is via tunnelling, while hydrodynamic behaviour dominates for lower barriers. The phase dependence of the many-body dynamics is also evident in the observation of macroscopic quantum self trapping. Gross-Pitaevskii calculations facilitate the interpretation of system dynamics, but do not describe the observed damping.

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.

<p>Many-core processors offer new levels of on-chip performance by capitalizing on the increasing rate of device integration. Harnessing the full performance potential of these processors requires that hardware designers not only exploit the advantages, but also consider the problems introduced by the new architectures. Such challenges arise from both the processor's increased structural complexity and the reliability issues of the silicon substrate. In this thesis, we address these challenges in a framework that targets correct execution and performance on three coordinates: 1) tolerating permanent faults, 2) facilitating static and dynamic verification through precise specifications, and 3) designing scalable coherence protocols.</p> <p>First, we propose CCA, a new design paradigm for increasing the processor's lifetime performance in the presence of permanent faults in cores. CCA chips rely on a reconfiguration mechanism that allows cores to replace faulty components with fault-free structures borrowed from neighboring cores. In contrast with existing solutions for handling hard faults that simply shut down cores, CCA aims to maximize the utilization of defect-free resources and increase the availability of on-chip cores. We implement three-core and four-core CCA chips and demonstrate that they offer a cumulative lifetime performance improvement of up to 65% for industry-representative utilization periods. In addition, we show that CCA benefits systems that employ modular redundancy to guarantee correct execution by increasing their availability.</p> <p>Second, we target the correctness of the address translation system. Current processors often exhibit design bugs in their translation systems, and we believe one cause for these faults is a lack of precise specifications describing the interactions between address translation and the rest of the memory system, especially memory consistency. We address this aspect by introducing a framework for specifying translation-aware consistency models. As part of this framework, we identify the critical role played by address translation in supporting correct memory consistency implementations. Consequently, we propose a set of invariants that characterizes address translation. Based on these invariants, we develop DVAT, a dynamic verification mechanism for address translation. We demonstrate that DVAT is efficient in detecting translation-related faults, including several that mimic design bugs reported in processor errata. By checking the correctness of the address translation system, DVAT supports dynamic verification of translation-aware memory consistency.</p> <p>Finally, we address the scalability of translation coherence protocols. Current software-based solutions for maintaining translation coherence adversely impact performance and do not scale. We propose UNITD, a hardware coherence protocol that supports scalable performance and architectural decoupling. UNITD integrates translation coherence within the regular cache coherence protocol, such that TLBs participate in the cache coherence protocol similar to instruction or data caches. We evaluate snooping and directory UNITD coherence protocols on processors with up to 16 cores and demonstrate that UNITD reduces the performance penalty of translation coherence to almost zero.</p> / Dissertation

Shrinking transistor sizes have introduced new challenges and opportunities for system-on-chip (SoC) design and reliability. Smaller transistors are more susceptible to early lifetime failure and electronic wear-out, greatly reducing their reliable lifetimes. However, smaller transistors will also allow SoC to contain hundreds of processing cores and other infrastructure components with the potential for increased reliability through massive structural redundancy. Concurrent online testing (COLT) can provide sufficient reliability and availability to systems with this redundancy. COLT manages the process of testing a subset of processing cores while the rest of the system remains operational. This can be considered a temporary, graceful degradation of system performance that increases reliability while maintaining availability. In this dissertation, techniques to assist COLT are proposed and analyzed. The techniques described in this dissertation focus on two major aspects of COLT feasibility: recovery time and test delivery costs. To reduce the time between failure and recovery, and thereby increase system availability, an anomaly-based test triggering unit (ATTU) is proposed to initiate COLT when anomalous network behavior is detected. Previous COLT techniques have relied on initiating tests periodically. However, determining the testing period is based on a device's mean time between failures (MTBF), and calculating MTBF is exceedingly difficult and imprecise. To address the test delivery costs associated with COLT, a distributed test vector storage (DTVS) technique is proposed to eliminate the dependency of test delivery costs on core location. Previous COLT techniques have relied on a single location to store test vectors, and it has been demonstrated that centralized storage of tests scales poorly as the number of cores per SoC grows. Assuming that the SoC organizes its processing cores with a regular topology, DTVS uses an interleaving technique to optimally distribute the test vectors across the entire chip. DTVS is analyzed both empirically and analytically, and a testing protocol using DTVS is described. COLT is only feasible if the applications running concurrently are largely unaffected. The effect of COLT on application execution time is also measured in this dissertation, and an application-aware COLT protocol is proposed and analyzed. Application interference is greatly reduced through this technique.

This thesis describes the efficient design of a future many-core processor that can provide higher performance under the limited chip power budget. To achieve such a goal, this thesis first develops an analytical framework within which computer architects can estimate achievable performance improvement of different many-core architectures given the same power budget. From this study, this thesis found that a future many-core processor needs (1) energy-efficient parallel cores and (2) a high-performance sequential core. Based on these observations, this thesis proposes an energy-efficient broad-purpose acceleration layer that can be snapped on top of a conventional general-purpose processor. In addition to such an energy-efficient parallel cores, this thesis also proposes different architectural techniques to further boost the performance of sequential computation while those parallel cores are idle. In particular, this thesis develops low-cost architectural techniques to enhance the memory performance of a host core by utilizing those idle parallel cores. This idea is evaluated in two different system architectures: one with the aforementioned acceleration layer and the other with an emerging integrated CPU and GPU chip.

Thesis (Ph. D.)--University of Washington, 2003. / Vita. Includes bibliographical references (p. 86-89).

Computational chemistry offers one the ability to develop a better understanding of the complex physical and chemical interactions that are fundamental to macro- and mesoscopic processes that are seen in laboratory experiments, industrial processes, and ordinary, everyday life. For many systems, the physics of interest occur at the molecular or atomistic levels, and in these cases, computational modeling and two well refined simulation techniques become invaluable: Monte Carlo (MC) and molecular dynamics (MD). In this work, two well established problems were tackled. First, models and potentials for various gas molecules were produced and refined from first principles. These models, although based on work done previously by Belof et al., are novel due to the inclusion of many-body van der Waals interactions, advanced r-12 repulsion combining rules for treating unlike intra- and intermolecular interactions, and highly-efficient treatment of induction interactions. Second, a multitude of models were developed and countless MD simulations were performed in order to describe and understand the giant frictional anisotropy of d-AlCoNi, first observed by Park et al. in 2005.

As semiconductor technology continues to scale lower in the nanometer era, the communication between processor and main memory has been particularly challenged. The well-studied frequency, memory and power ``walls'' have redirect architects towards utilizing Chip Multiprocessors (CMP) as an attractive architecture for leveraging technology scaling. In order to achieve high efficiency and throughput, CMPs rely heavily on sharing resources among multiple cores, especially in the case of the memory hierarchy. Unfortunately, such sharing introduces resource contention and interference between the multiple executing threads. The ever-increasing access latency difference between processor and memory, the gradually increasing memory bandwidth demands to main memory, and the decreasing cache capacity size available to each core due to multiple core integration, has made the need for an efficient memory subsystem resource management more critical than ever before. This dissertation focuses on managing the sharing of the Last-level Cache (LLC) capacity and the main memory bandwidth, as the two most important resources that significantly affect system performance and energy consumption. The presented schemes include efficient solutions to all of the three basic requirements for implementing a resource management schemes, that is: a) profiling mechanisms to capture applications' resource requirements, b) microarchitecture mechanisms to enforce a resource allocation scheme, and c) resource allocations algorithms/policies to manage the available memory resources throughput the whole memory hierarchy of a CMP system. To achieve these targets the dissertation first describes a set of low overhead, non-invasive profiling mechanisms that are able to project applications’ memory resource requirements and memory sharing behavior. Two memory resource partitioning schemes are presented. The first one, the Bank-aware dynamic partitioning scheme provides a low overhead solution for partitioning cache resources of large CMP architectures that are based on a Dynamic Non-Uniform Cache Architecture (DNUCA) last-level cache design, consistent with the current industry trends. In addition, the second scheme, the Bandwidth-aware dynamic scheme presents a system-wide optimization of memory-subsystem resource allocation and job scheduling for large, multi-chip CMP systems. The scheme is seeking for optimizations both within and outside single CMP chips, aiming at overall system throughput and efficiency improvements. As cache partitioning schemes with isolated partitions impose a set of restrictions in the use of the last-level cache, which can severely affect the performance of large CMP designs, this dissertation presents a Quasi-partitioning scheme that breaks such restrictions while providing most of the benefits of cache partitioning schemes. The presented solution is able to efficiently scale to a significant larger number of cores than what previously described schemes that are based on isolated partition can achieve. Finally, as the memory controller is one of the fundamental components of the memory-subsystem, a well-designed memory-subsystem resource management needs to carefully utilize the memory controller resources and coordinate its functionality with the operation of the main memory and the last-level cache. To improve execution fairness and system throughput, this dissertation presents a criticality-based, memory controller requests priority scheme. The scheme ranks demand read and prefetch operations based on their latency sensitivity, while it coordinates its operation with the DRAM page-mode policy and the memory data prefetcher. / text