京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第21549号 / 理博第4456号 / 新制||理||1640(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 高橋 義朗, 教授 田中 耕一郎, 教授 前野 悦輝 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

Thermalization is ubiquitous to all physical systems and is an essential assumption for the postulates of statistical mechanics. Generally, every system evolves under its own dynamics and reaches thermal equilibrium. In the quantum realm, thermal equilibrium is described by the Eigenstate Thermalization Hypothesis (ETH); hence every system that thermalizes is expected to follow ETH. Moreover, the thermalization process is always manifested as transport of matter and quantum information across the system. Thermalizing quantum systems with local interactions are expected to show diffusive transport of global conserved quantities and ballistic information spreading. The vast majority of many-body systems show the typical behavior described above. In this thesis, we study two mechanisms that break the standard picture of quantum thermalization. On the one hand, information spreading may be faster in the presence of long-range interactions. By simulating the Lieb-Robinson bounds in a spin chain with power-law decaying interactions, we distinguish the regime where the long-range character of the interactions becomes irrelevant for information spreading. On the other hand, the interplay of disorder and interactions can slow down transport, entering a sub-diffusive regime. We study this dynamical regime in an Anderson model on random regular graphs, where the emergence of a sub-diffusive regime before the localization transition is highly debated. Looking at long-range spectral correlations, we found that the sub-diffusive regime may be extended over the whole thermal phase of the model. Moreover, when disorder is strong enough, quantum many-body systems can undergo an ergodicity breaking transition to a many-body localized (MBL) phase. These systems do not follow ETH, so they present a challenge for conventional statistical mechanics. In particular, we study how the structure of local operator eigenstate matrix elements (central assumption of ETH) change between the thermal and MBL phase. A complete characterization of matrix elements of correlation functions is achieved via strong disorder quasi-degenerate perturbation theory. Furthermore, we study the MBL transition mechanism, which is still an open question due to the limitations of the available techniques for addressing that regime. Focusing on the avalanche mechanism, we simulate MBL spin chains coupled to a finite and infinite thermal bath. We could estimate the thermalization rate, which behaves as an order parameter and provide bounds for the actual critical disorder in the thermodynamic limit. We propose the existence of an intermediate MBL ``regime' where the system is slowly de-localizing, but relevant time scales are out-of-reach for current experiments and numerical simulations.

Thermoelektrika (TE) sind Materialien die Elektrizität aus Abwärme gewinnen können. Eine wichtige Kenngröße für die Effizienz, und damit die Anwendbarkeit, von TE ist ihre Gitterwärmeleitfähigkeit. In meiner Doktorarbeit habe ich die Invarianz dieser Größe im Kontext der Linear-Response Theorie (LR) bewiesen. Dies ermöglichte es, eine Korrektur der Boltzmann-Transport Gleichung (BTE) für die Gitterwärmeleitfähigkeit in kristallinen Materialien mittels LR herzuleiten. Diese Korrektur ist wichtig um zu beurteilen, wie genau die BTE die Wärmeleitfähigkeit eines Kristalls vorhersagen kann. Um die dafür notwendigen symbolischen Umformungen durchzuführen, habe ich ein Computer-Algebra System (CAS) entwickelt. Die Anzahl an Beiträgen zum finalen Resultat stellte sich als zu groß heraus um Grenzfälle zu analysieren oder prüfbare Approximationen herzuleiten. Aus diesem Grund habe ich alle Beiträge mit so wenigen Approximationen wie möglich ausgewertet. Dafür habe ich eine Software entwickelt, um diese Terme numerisch auszuwerten. Damit habe ich meine Korrektur für altbekannte wie auch vielversprechende TE ausgewertet, nämlich PbTe, Bi2Te3 , SnSe und B4 C. Zusätzlich habe ich MgO und KF untersucht. Das Resultat lässt sich wie folgt zusammenfassen: Die Korrektur zur BTE für die Gitterwärmeleitfähigkeit hat in keinem der untersuchten Materialien und bei keiner der simulierten Temperaturen einen nennenswerten Einfluss. Meine Untersuchung legt nahe, dass die BTE für eine große Bandbreite an Materialien sicher angewandt werden kann, auch besonders stark Anharmonische. Folglich ist diese Arbeit in Übereinstimmung mit der Literatur, dass die am stärksten anharmonischen Materialien genau die mit der niedrigsten Wärmeleitfähigkeit sind. Es scheint daher sinnvoll, dass sich zukünftige Forschung weniger auf die Herleitung solcher Korrekturen zur BTE als vielmehr auf die korrekte Berechnung des Phononpropagators in stark anharmonischen Materialien konzentrieren sollte. / Thermoelectrics (TE) are materials that can be used to generate electricity from waste heat. A key quantity to the efficiency, and therefore the applicability, of TE is the lattice thermal conductivity. In this work, I prove the invariance of the lattice thermal conductivity in the context of linear-response theory (LR). This invariance enables me to derive novel formulas for a correction to the widely used Boltzmann-transport equation (BTE) for lattice thermal transport in crystalline solids using LR. It turned out that these derivations cannot be performed by a human by hand, using the formalism I chose. To perform the necessary symbolic manipulations, I programmed a computer algebra system (CAS), that implements LR, starting from expectation values, over Feynman diagrams to mathematical formulas. The number of resulting terms turned out to be too large for an analysis of all limiting cases. Consequently, I aimed at evaluating all terms, with as few approximations as possible, to generate a simple, numerical result. To do so, I developed a software package to evaluate the formulas numerically without further approximation and applied it to long-serving as well as promising new TE, namely PbTe, Bi2 Te3 , SnSe, and B4C. Additionally I investigated MgO and KF. The result can be summed up as follows: The correction to the BTE for the lattice thermal conductivity has almost no influence in the investigated materials at any simulated temperature. My investigation suggests that the BTE can be used for a wide range of materials, including the most anharmonic ones. Consequently, this work is in agreement with the literature, that the most anharmonic materials are exactly those with the lowest lattice thermal conductivity. It suggests that future theoretic work on lattice thermal conductivity should focus to find the correct phonon-propagator of strongly anharmonic systems.

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付記する学位プログラム名: 京都大学卓越大学院プログラム「先端光・電子デバイス創成学」 / 京都大学 / 新制・課程博士 / 博士(理学) / 甲第23694号 / 理博第4784号 / 新制||理||1685(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 川上 則雄, 教授 柳瀬 陽一, 教授 高橋 義朗 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

We consider a gas of indistinguishable bosons, confined to a ring of radius R, and interacting via a pair-wise cosine potential. This may be thought of as the quantized Hamiltonian Mean Field (HMF) model for bosons originally introduced by Chavanis as a generalization of Antoni and Ruffo’s classical model. This thesis contains three parts: In part one, the dynamics of a Bose-condensate are considered by studying a generalized Gross-Pitaevskii equation (GGPE). Quantum effects due to the quantum pressure are found to substantially alter the system’s dynamics, and can serve to inhibit a pathological instability for repulsive interactions. The non-commutativity of the large-N , long-time, and classical limits is discussed. In part two, we consider the GGPE studied above and seek static solutions. Exact solutions are identified by solving a non-linear eigenvalue problem which is closely related to the Mathieu equation. Stationary solutions are identified as solitary waves (or solitons) due to their small spatial extent and the system’s underlying Galilean invariance. Asymptotic series are developed to give an analytic solution to the non- linear eigenvalue problem, and these are then used to study the stability of the solitary wave mentioned above. In part three, the exact solutions outlined above are used to study quantum fluctuations of gapless excitations in the HMF model’s symmetry broken phase. It is found that this phase is destroyed at zero temperature by large quantum fluctuations. This demonstrates that mean-field theory is not exact, and can in fact be qualitatively wrong, for long-range interacting quantum systems, in contrast to conventional wisdom. / Thesis / Doctor of Philosophy (PhD) / The Hamiltonian Mean Field (HMF) model was initially proposed as a simplified description of self-gravitating systems. Its simplicity shortens calculations and makes the underlying physics more transparent. This has made the HMF model a key tool in the study of systems with long-range interactions. In this thesis we study a quantum extension of the HMF model. The goal is to understand how quantum effects can modify the behaviour of a system with long-range interactions. We focus on how the model relaxes to equilibrium, the existence of special “solitary waves”, and whether quantum fluctuations can prevent a second order (quantum) phase transition from occurring at zero temperature.

Analogue quantum simulators have proven to be an extremely versatile tool for the study of strongly-correlated condensed matter systems both near and far from equilibrium. An enticing prospect is the quantum simulation of non- Fermi liquids which lack a quasiparticle description and feature prominently in the study of strange metals, fast scrambling of quantum information, as well as holographic quantum matter. Yet, large-scale laboratory realisations of such systems remain outstanding. In this thesis, we present a proposal for the analogue quantum simulation of one such system, the Sachdev–Ye–Kitaev (SYK) model, using cavity quantum electrodynamics (cQED). We discuss recent experimental advances in this pursuit, and perform analysis of this and related models. Through a combination of analytic calculations and numeric simulations, we show how driving a cloud of fermionic atoms trapped in a multi- mode optical cavity, and subjecting it to a spatially disordered AC-Stark shift, can realise an effective model which retrieves the physics of the SYK model, with random all-to-all interactions and fast scrambling. Working towards the SYK model, we present results from a recent proof-of-principle cQED experiment which implemented the disordered light-shift technique to quantum simulate all- to-all interacting spin models with quenched disorder. In this context, we show analytically how disorder-driven localisation can be extracted from spectroscopic probes employed in cQED experiments, despite their lack of spatially resolved information. Further, we numerically investigate the post-quench dynamics of the SYK model, finding a universal, super-exponential equilibration in the disorder-averaged far-from-equilibrium dynamics. These are reproduced analytically through an effective master equation. Our work demonstrates the increasing capabilities of cQED quantum simulators, highlighting how these may be used to study the fascinating physics of holographic quantum matter and other disorder models in the lab.

Among the many advances and innovations in wireless technologies over the past twenty years, MIMO is perhaps among the most successful. MIMO technology has been evolving over the past two decades. Today, the number of antennas equipped at a base station (BS) or an access point (AP) is increasing, which forms what we call ``many-antenna'' MIMO systems. Many-antenna MIMO will have significant impacts on modern wireless communications, as it will allow numerous wireless applications to operate on the vastly underexplored mid-band and high-band spectrum and is able to deliver ultra-high throughput. Although there are considerable efforts on many-antenna MIMO systems, most of them came from physical (PHY) layer information-theoretic exploitation. There is a lack of investigation of many-antenna MIMO from a networking perspective. On the other hand, new knowledge and understanding begin to emerge at the PHY layer, such as the rank-deficient channel phenomenon. This calls for new theories and models for many-antenna MIMO in a networking environment. In addition, the problem space for many-antenna MIMO systems is much broader and more challenging than conventional MIMO. Reusing existing solutions designed for conventional MIMO systems may suffer from inferior performance or require excessive computation time. The goal of this dissertation is to advance many-antenna MIMO techniques for networking research. We focus on the following two critical areas in the context of many-antenna MIMO networks: (i) DoF-based modeling and (ii) real-time optimization. This dissertation consists of two parts that study these two areas. In the first part, we aim to develop new DoF models and theories under general channel rank conditions for many-antenna MIMO networks, and we explored efficient DoF allocation based on our new DoF model. The main contributions of this part are summarized as follows. New DoF models and theories under general channel rank conditions: Existing DoF-based models in networking community assume that the channel matrix is of full rank. However, this assumption no longer holds when the number of antennas becomes many and the propagation environment is not ideal. In this study, we develop a novel DoF model under general channel rank conditions. In particular, we find that for IC, shared DoF consumption at both transmit and receive nodes is most efficient for DoF allocation, which is contrary to existing unilateral IC models based on full-rank channel assumption. Further, we show that existing DoF models under the full-rank assumption are a special case of our generalized DoF model. The findings of this study pave the way for future research of many-antenna networks under general channel rank conditions. Efficient DoF utilization for MIMO networks: We observes that, in addition to the fact that channel is not full-rank, the strength of signals on different directions in the eigenspace is extremely uneven. This offers us new opportunities to efficiently utilize DoFs in a MIMO network. In this study, we introduce a novel concept called ``effective rank threshold''. Based on this threshold, DoFs are consumed only to cancel strong interferences in the eigenspace while weak interferences are treated as noise in throughput calculation. To better understand the benefits of this approach, we study a fundamental trade-off between network throughput and effective rank threshold for an MU-MIMO network. Our simulation results show that network throughput under optimal rank threshold is significantly higher than that under existing DoF IC models. In the second part, we offered real-time designs and implementations to solve many-antenna MIMO problems for 5G cellular systems. In addition to maximizing a specific optimization objective, we aim at offering a solution that can be implemented in sub-ms to meet requirements in 5G standards. The main contributions of this part are summarized as follows. Turbo-HB---A novel design and implementation for ultra-fast hybrid beamforming: We investigate the beamforming problem under hybrid beamforming (HB) architecture. A major practical challenge for HB is to obtain a solution in 500 $mu$s, which is an extremely stringent but necessary time requirement for its deployment in the field. To address this challenge, we present Turbo-HB---a novel beamforming design under the HB architecture that can obtain the beamforming matrices in about 500 $mu$s. The key ideas of Turbo-HB are two-fold. First, we develop low-complexity SVD by exploiting randomized SVD technique and leveraging channel sparsity at mmWave frequencies. Second, we accelerate the overall computation time through large-scale parallel computation on a commercial off-the-shelf (COTS) GPU platform, with special engineering efforts for matrix operations and minimized memory access. Experimental results show that Turbo-HB is able to obtain the beamforming matrices in 500 $mu$s for an MU-MIMO cellular system while achieving similar or better throughput performance by those state-of-the-art algorithms. mCore+---A sub-millisecond scheduler for 5G MU-MIMO systems: We study a scheduling problem in a 5G NR environment. In 5G NR, an MU-MIMO scheduler needs to allocate RBs and assign MCS for each user at each TTI. In particular, multiple users may be co-scheduled on the same RB under MU-MIMO. In addition, the real-time requirement for determining a scheduling solution is at most 1 ms. In this study, we present a novel scheduler mCore+ that can meet the sub-ms real-time requirement. mCore+ is designed through a multi-phase optimization, leveraging large-scale parallelism. In each phase, mCore+ either decomposes the optimization problem into a large number of independent sub-problems, or reduces the search space into a smaller but more promising subspace, or both. We implement mCore+ on a COTS GPU platform. Experimental results show that mCore+ can obtain a scheduling solution in $sim$500 $mu$s. Moreover, mCore+ can achieve better throughput performance than state-of-the-art algorithms. M3---A sub-millisecond scheduler for multi-cell MIMO networks under C-RAN architecture: We investigate a scheduling problem for a multi-cell environment. Under Cloud Radio Access Network (C-RAN) architecture, the signal processing can be performed cooperatively for multiple cells at a centralized baseband unit (BBU) pool. However, a new resource scheduler is needed to jointly determine RB allocation, MCS assignment, and beamforming matrices for all users under multiple cells. In addition, we aim at finding a scheduling solution within each TTI (i.e., at most 1 ms) to conform to the frame structure defined by 5G NR. To do this, we propose M3---a GPU-based real-time scheduler for a multi-cell MIMO system. M3 is developed through a novel multi-pipeline design that exploits large-scale parallelism. Under this design, one pipeline performs a sequence of operations for cell-edge users to explore joint transmission, and in parallel, the other pipeline is for cell-center users to explore MU-MIMO transmission. For validation, we implement M3 on a COTS GPU. We showed that M3 can find a scheduling solution within 1 ms for all tested cases, while it can significantly increase user throughput by leveraging joint transmission among neighboring cells. / Doctor of Philosophy / MIMO is widely considered to be a major breakthrough in modern wireless communications. MIMO comes in different forms. For conventional MIMO, the number of antennas at a base station (BS) or access point (AP) is typically small (< 8). Today, the number of antennas at a BS/AP is typically ranging from 8 to 64 when the carrier frequency is below 24 GHz. When the carrier frequency is above 24 GHz (e.g., mmWave), the number of antennas can be even larger (> 64). We call today's MIMO systems (typically with $ge$ 8 antennas at some nodes) as ``many-antenna'' MIMO systems, and this will be the focus of this dissertation. Although there exists a considerable amount of works on many-antenna MIMO techniques, most efforts focus on physical (PHY) layer for information-theoretic exploitation. There is a lack of investigation on how to efficiently and effectively utilize many-antenna MIMO from a networking perspective. The goal of this dissertation is to advance many-antenna MIMO techniques for networking research. We focus on the following two critical areas in the context of many-antenna MIMO networks: (i) degree-of-freedom (DoF)--based modeling and (ii) real-time optimization. In the first part, we investigate a novel DoF model under general channel rank conditions for many-antenna MIMO networks. The main contributions of this part are summarized as follows. New DoF models and theories under general channel rank conditions: In this study, we develop a novel DoF model under general channel rank conditions. We show that existing works claiming that unilateral DoF consumption is optimal no longer hold when channel rank is deficient (not full-rank). We find that for IC, shared DoF consumption at both Tx and Rx nodes is the most efficient scheme for DoF allocation. Efficient DoF utilization for MIMO networks: In this study, we proposed a new approach to efficiently utilize DoFs in a MIMO network. The DoFs used to cancel interference are conserved by exploiting the interference signal strength in the eigenspace. Our simulation results show that network throughput under our approach is significantly higher than that under existing DoF IC models. In the second part, we offer real-time designs and implementations to solve many-antenna MIMO problems for 5G cellular systems. The timing performance of these designs is tested in actual wall-clock time. A novel design and implementation for ultra-fast hybrid beamforming: We investigate a beamforming problem under the hybrid beamforming (HB) architecture. We propose Turbo-HB---a novel beamforming design under the HB architecture that can obtain the beamforming matrices in about 500 $mu$s. At the same time, Turbo-HB can achieve similar or better throughput performance by those state-of-the-art algorithms. A sub-millisecond scheduler for 5G multi-user (MU)-MIMO systems: We study a resource scheduling problem in 5G NR. We present a novel scheduler called mCore+ that can schedule time-frequency resources to MU-MIMO users and meet the 500 $mu$s real-time requirement in 5G NR. A sub-millisecond scheduler for multi-cell MIMO networks under C-RAN architecture: We investigate the scheduling problem for a multi-cell environment under a centralized architecture. We present M3---a GPU-based real-time scheduler that jointly determines a scheduling solution among multiple cells. M3 can find the scheduling solution within 1 ms.

To follow up on the unexpectedly-good performance of coupled-cluster models with approx- imate inclusion of 3-body clusters [J. Chem. Phys. 151, 064102 (2019)] we performed a more complete assessment of the 3CC method [J. Chem. Phys. 125, 204105 (2006)] for accurate computational thermochemistry in the standard HEAT framework. New spin- integrated implementation of the 3CC method applicable to closed- and open-shell systems utilizes a new automated toolchain for derivation, optimization, and evaluation of operator algebra in many-body electronic structure. We found that with a double-zeta basis set the 3CC correlation energies and their atomization energy contributions are almost always more accurate (with respect to the CCSDTQ reference) than the CCSDT model as well as the standard CCSD(T) model. The mean errors in { 3CC, CCSDT, and CCSD(T) } electronic (per valence electron) and atomization energies were {23, 69, 125} μEh/e and {0.39, 1.92, 2.57} kJ/mol, respectively. The significant and systematic reduction of the error by the 3CC method and its lower cost than CCSDT suggests it as a viable candidate for post-CCSD(T) thermochemistry application. / Doctor of Philosophy / Stepping into the information age, the computing power has rapidly grown over the last half century. Solving chemical problems on computers has improved lives by reducing the cost and time of researching critical technologies. Scientific research is evolving and experimental finding are now supported with a computational model. Doing chemistry on computers requires quantum simulations, which is essentially solving the Schr ̈odinger equation on a computer that simulates a wave function for all the electrons in a system. Different models are built based on how these inter electronic interactions are treated. To predict results with accuracy on par with the experimental findings requires using higher-order wave functions methods.These are computationally expensive and often not practical. The lower-order methods that are easy to implement can be found in all quantum chemistry software packages. On the other hand, the higher-order methods are laborious and error prone to implement manually due to the sheer complexity of theory. Debugging such implementations often requires a lot of effort with the uncertainty in returns. To solve this problem, we implemented a second-quantization toolkit (SeQuant version 2.0) that derives many-body methods, specifically the general-order coupled cluster (CC) model. The CC model is systematically improvable and accurate. One such CC model, the CCSD(T), has been called the gold standard in quantum chemistry. For compactness, these equations are usually derived in their spin-orbital form. The evaluation and storage cost of these methods is reduced up to four-fold by transforming the spin-orbital expressions to a spin-traced form. In this work, the spin-tracing algorithms are described in detail. The general-order coupled cluster approach is used to derive the internally corrected approximate coupled cluster methods. These methods improve the accuracy of a model at a reduced cost. For small molecules, it was observed that the spin-traced evaluation was over three times faster than spin-orbital coupled cluster. To further reduce the cost of calculations, we added explicit correlation to our CC models. These methods improved the quality of our results with a modest increase in the computational cost.