Auditory group theory with applications to statistical basis methods for structured audio

Thesis (Ph. D.)--Massachusetts Institute of Technology, Program in Media Arts & Sciences, 1998.Includes bibliographical references (p. 161-172).Michael Anthony Casey.Ph.D

Enhanced charge density wave coherence in a light-quenched, high-temperature superconductor

Superconductivity and charge density waves (CDWs) are competitive, yet coexisting, orders in cuprate superconductors. To understand their microscopic interdependence, a probe capable of discerning their interaction on its natural length and time scale is necessary. We use ultrafast resonant soft x-ray scattering to track the transient evolution of CDW correlations in YBa2Cu3O6+x after the quench of superconductivity by an infrared laser pulse. We observe a nonthermal response of the CDW order characterized by a near doubling of the correlation length within ≈1 picosecond of the superconducting quench. Our results are consistent with a model in which the interaction between superconductivity and CDWs manifests inhomogeneously through disruption of spatial coherence, with superconductivity playing the dominant role in stabilizing CDW topological defects, such as discommensurations

Dimensional hyper-reduction of nonlinear finite element models via empirical cubature

We present a general framework for the dimensional reduction, in terms of number of degrees of freedom as well as number of integration points (“hyper-reduction”), of nonlinear parameterized finite element (FE) models. The reduction process is divided into two sequential stages. The first stage consists in a common Galerkin projection onto a reduced-order space, as well as in the condensation of boundary conditions and external forces. For the second stage (reduction in number of integration points), we present a novel cubature scheme that efficiently determines optimal points and associated positive weights so that the error in integrating reduced internal forces is minimized. The distinguishing features of the proposed method are: (1) The minimization problem is posed in terms of orthogonal basis vector (obtained via a partitioned Singular Value Decomposition) rather that in terms of snapshots of the integrand. (2) The volume of the domain is exactly integrated. (3) The selection algorithm need not solve in all iterations a nonnegative least-squares problem to force the positiveness of the weights. Furthermore, we show that the proposed method converges to the absolute minimum (zero integration error) when the number of selected points is equal to the number of internal force modes included in the objective function. We illustrate this model reduction methodology by two nonlinear, structural examples (quasi-static bending and resonant vibration of elastoplastic composite plates). In both examples, the number of integration points is reduced three order of magnitudes (with respect to FE analyses) without significantly sacrificing accurac

Principles, fundamentals, and applications of programmable integrated photonics

[EN] Programmable integrated photonics is an emerging new paradigm that aims at designing common integrated optical hardware resource configurations, capable of implementing an unconstrained variety of functionalities by suitable programming, following a parallel but not identical path to that of integrated electronics in the past two decades of the last century. Programmable integrated photonics is raising considerable interest, as it is driven by the surge of a considerable number of new applications in the fields of telecommunications, quantum information processing, sensing, and neurophotonics, calling for flexible, reconfigurable, low-cost, compact, and low-power-consuming devices that can cooperate with integrated electronic devices to overcome the limitation expected by the demise of Moore¿s Law. Integrated photonic devices exploiting full programmability are expected to scale from application-specific photonic chips (featuring a relatively low number of functionalities) up to very complex application-agnostic complex subsystems much in the same way as field programmable gate arrays and microprocessors operate in electronics. Two main differences need to be considered. First, as opposed to integrated electronics, programmable integrated photonics will carry analog operations over the signals to be processed. Second, the scale of integration density will be several orders of magnitude smaller due to the physical limitations imposed by the wavelength ratio of electrons and light wave photons. The success of programmable integrated photonics will depend on leveraging the properties of integrated photonic devices and, in particular, on research into suitable interconnection hardware architectures that can offer a very high spatial regularity as well as the possibility of independently setting (with a very low power consumption) the interconnection state of each connecting element. Integrated multiport interferometers and waveguide meshes provide regular and periodic geometries, formed by replicating unit elements and cells, respectively. In the case of waveguide meshes, the cells can take the form of a square, hexagon, or triangle, among other configurations. Each side of the cell is formed by two integrated waveguides connected by means of a Mach¿Zehnder interferometer or a tunable directional coupler that can be operated by means of an output control signal as a crossbar switch or as a variable coupler with independent power division ratio and phase shift. In this paper, we provide the basic foundations and principles behind the construction of these complex programmable circuits. We also review some practical aspects that limit the programming and scalability of programmable integrated photonics and provide an overview of some of the most salient applications demonstrated so far.European Research Council; Conselleria d'Educació, Investigació, Cultura i Esport; Ministerio de Ciencia, Innovación y Universidades; European Cooperation in Science and Technology; Horizon 2020 Framework Programme.Pérez-López, D.; Gasulla Mestre, I.; Dasmahapatra, P.; Capmany Francoy, J. (2020). Principles, fundamentals, and applications of programmable integrated photonics. Advances in Optics and Photonics. 12(3):709-786. https://doi.org/10.1364/AOP.387155709786123Lyke, J. C., Christodoulou, C. G., Vera, G. A., & Edwards, A. H. (2015). An Introduction to Reconfigurable Systems. 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DMRG studies of Chebyshev-expanded spectral functions and quantum impurity models

This thesis is concerned with two main topics: first, the advancement of the density matrix renormalization group (DMRG) and, second, its applications. In the first project of this thesis we exploit the common mathematical structure of the numerical renormalization group and the DMRG, namely, matrix product states (MPS), to implement an efficient numerical treatment of a two-lead, multi-level Anderson impurity model. By adopting a star-like geometry, where each species (spin and lead) of conduction electrons is described by its own so-called Wilson chain, instead of a single Wilson chain we achieve a very significant reduction in the numerical resources required to obtain reliable results. Moreover, we show that it is possible to find an "optimal" chain basis, in which chain degrees of freedom of different Wilson chains become effectively decoupled from each other further out on the Wilson chains. This basis turns out to also diagonalize the model's chain-to-chain scattering matrix. In the second project we show that Chebychev expansions offer numerically efficient representations for calculating spectral functions of one-dimensional lattice models using MPS methods. The main features of this Chebychev matrix product state (CheMPS) approach are: (i) it achieves uniform resolution over the spectral function's entire spectral width; (ii) it offers a well-controlled broadening scheme; (iii) it is based on using MPS tools to recursively calculate a succession of Chebychev vectors, (iv) whose entanglement entropies were found to remain bounded with increasing recursion order for all cases analyzed here. We present CheMPS results for the structure factor of spin-1/2 antiferromagnetic Heisenberg chains and perform a detailed finite-size analysis. Making comparisons to benchmark methods, we find that CheMPS yields results comparable in quality to those of correction vector DMRG, at dramatically reduced numerical cost and agrees well with Bethe Ansatz results for an infinite system, within the limitations expected for numerics on finite systems. Following these technologically focused projects we study the so-called Kondo cloud by means of the DMRG in the third project. The Kondo cloud describes the effect of spatially extended spin-spin correlations of a magnetic moment and the conduction electrons which screen the magnetic moment through the Kondo effect at low temperatures. We focus on the question whether the Kondo screening length, typically assumed to be proportional to the inverse Kondo temperature, can be extracted from the spin-spin correlations. We investigate how perturbations which destroy the Kondo effect, like an applied gate potential or a magnetic field, affect the formation of the screening cloud. In a forth project we address the impact of Quantum (anti-)Zeno physics resulting from repeated single-site resolved observations on the many-body dynamics. We use time-dependent DMRG to obtain the time evolution of the full many-body wave function that is then periodically projected in order to simulate realizations of stroboscopic measurements. For the example of a 1-D lattice of spin-polarized fermions with nearest-neighbor interactions, we find regimes for which many-particle configurations are stabilized and destabilized depending on the interaction strength and the time between observations

Ultrafast photophysics and energy losses in emerging photovoltaic materials and devices

The mechanisms that govern the transformation and dissipation of energy in semiconductors must be understood to advance optoelectronic technologies to their fullest extent. This thesis aims to unravel the evolution and energy losses of electronically excited states in novel solution-processed materials for photovoltaics. This is achieved by implementing ultrafast laser spectroscopies devised to target efficiency-limiting processes in conditions relevant to device operation. Part of the research herein examines the deleterious relaxation of high-energy ("hot") charge carriers in metal-halide perovskites and their nanocrystal analogues using an all-optical "pump-push-probe" approach. The results show that carrier "cooling" in these materials is dictated by the lattice composition, and unlike other low-dimensional semiconductors, insensitive to the crystal size or surface properties. The multi-pulse methodology also reveals that hot carriers can lose their energy to cold carriers, which highlights a previously unaddressed competition between carrier-carrier and carrier-lattice interactions in these materials. The remainder of the thesis deals with charge separation at the interface between electron-donating and accepting organic semiconductors. Spectroscopies with optical, emission and photocurrent detection convey slower charge separation when the donor and acceptor are more closely aligned in energy. In spite of the slower dynamics and small "driving energy" of these systems, efficient long-range delocalisation of charges occurs in a manner that does not entail inexorable non-radiative recombination. Moreover, the electric field inside working solar cells is discovered to directly aid the preliminary step to this process, contrary to conventional wisdom. Both research strands of the thesis bring unique insight into the photophysics of "soft" semiconductors, and also establish frameworks for the design of high-performance solar cells based on molecular and/or nanoscale materials. These guidelines and the device-oriented approaches developed herein could be instrumental in unlocking the functionality of other up-and-coming materials systems for energy, photonic and nanoelectronic applications.Open Acces

Matrix product state clculations for one-dimensional quantum chains and quantum impurity models

This thesis contributes to the field of strongly correlated electron systems with studies in two distinct fields thereof: the specific nature of correlations between electrons in one dimension and quantum quenches in quantum impurity problems. In general, strongly correlated systems are characterized in that their physical behaviour needs to be described in terms of a many-body description, i.e. interactions correlate all particles in a complex way. The challenge is that the Hilbert space in a many-body theory is exponentially large in the number of particles. Thus, when no analytic solution is available - which is typically the case - it is necessary to find a way to somehow circumvent the problem of such huge Hilbert spaces. Therefore, the connection between the two studies comes from our numerical treatment: they are tackled by the density matrix renormalization group (DMRG) [1] and the numerical renormalization group (NRG) [2], respectively, both based on matrix product states. The first project presented in this thesis addresses the problem of numerically finding the dominant correlations in quantum lattice models in an unbiased way, i.e. without using prior knowledge of the model at hand. A useful concept for this task is the correlation density matrix (CDM) [3] which contains all correlations between two clusters of lattice sites. We show how to extract from the CDM, a survey of the relative strengths of the system’s correlations in different symmetry sectors as well as detailed information on the operators carrying long-range correlations and the spatial dependence of their correlation functions. We demonstrate this by a DMRG study of a one-dimensional spinless extended Hubbard model [4], while emphasizing that the proposed analysis of the CDM is not restricted to one dimension. The second project presented in this thesis is motivated by two phenomena under ongoing experimental and theoretical investigation in the context of quantum impurity models: optical absorption involving a Kondo exciton [5, 6, 7] and population switching in quantum dots [8, 9, 10, 11, 12, 13, 14, 15]. It turns out that both phenomena rely on the various manifestations of Anderson orthogonality (AO) [16], which describes the fact that the response of the Fermi sea to a quantum quench (i.e. an abrupt change of some property of the impurity or quantum dot) is a change of the scattering phase shifts of all the single-particle wave functions, therefore drastically changing the system. In this context, we demonstrate that NRG, a highly accurate method for quantum impurity models, allows for the calculation of all static and dynamic quantities related to AO and present an extensive NRG study for population switching in quantum dots.In dieser Doktorarbeit werden zwei Felder aus dem Gebiet der stark korrelierten elektronischen Systeme behandelt: die spezifische Natur von Korrelationen zwischen Elektronen in einer Dimension und die Folgen eines Quanten-Quenches in Quanten-Störstellenmodellen. Ganz allgemein sind stark korrelierte Systeme dadurch charakterisiert, dass ihr physikalisches Verhalten durch eine Vielteilchentheorie beschrieben werden muss, d.h. Wechselwirkungen korrelieren alle Teilchen auf komplexe Weise. Die Herausforderung hierbei ist, dass der Hilbertraum in einer Vielteilchentheorie exponentiell groß ist in der Anzahl der Teilchen. Wenn also keine analytische Lösung verfügbar ist - was typischerweise der Fall ist - ist es notwendig das Problem solch großer Hilberträume irgendwie zu umgehen. Daher besteht die Verbindung zwischen den beiden Studien in dieser Arbeit aus ihrer numerischen Behandlung: sie machen Gebrauch von der Dichtematrix-Renormierungsgruppe (DMRG) [1] bzw. der numerischen Renormierungsgruppe (NRG) [2], die beide auf Matrixproduktzuständen basieren. Das erste Projekt dieser Arbeit behandelt das Problem wie man auf numerische Weise die dominanten Korrelationen in Quanten-Gittermodellen finden kann, und zwar unvoreingenommen, also ohne Vorwissen über das aktuelle Modell. Ein nützliches Konzept dafuür ist die Korrelations-Dichtematrix (CDM) [3], die alle Korrelationen zwischen zwei Gruppen von Gitterplätzen beinhaltet. Wir zeigen wie man aus der CDM einen Überblick über die relative Stärke der Korrelationen aus verschiedenen Symmetriesektoren extrahieren kann. Weiterhin wird gezeigt wie man detaillierte Informationen über die Operatoren gewinnt, die langreichweitige Korrelationen besitzen, wie die räumliche Abhängigkeit ihrer Korrelationsfunktionen. Wir demonstrieren dies mittels einer DMRG-Studie eines eindimensionalen, spinlosen, erweiterten Hubbard-Modells [4], wobei betont werden muss, dass die vorgeschlagene Analyse der CDM nicht auf eine Dimension beschränkt ist. Das zweite Projekt dieser Arbeit ist motiviert durch zwei Phänomene aus dem Gebiet der Quanten-Störstellenmodelle, deren experimentelle und theoretische Behandlung immer noch andauert: optische Absorption im Zusammenhang mit einem Kondo-Exziton [5, 6, 7] und Besetzungsvertauschung in Quantenpunkten [8, 9, 10, 11, 12, 13, 14, 15]. Es stellt sich heraus, dass beide Phänomene auf den zahlreichen Aspekten der Anderson-Orthogonalität (AO) [16] beruhen. Diese beschreibt die Tatsache, dass die Reaktion des Fermisees auf einen Quanten-Quench (also einer abrupten Änderung einer Eigenschaft der Störstelle oder des Quantenpunktes) die Änderung aller Streuphasenverschiebungen aller Einteilchenwellenfunktionen ist, wodurch das System drastisch verändert wird. In diesem Zusammenhang zeigen wir dass NRG (eine äußerst genaue Methode für Quanten-Störstellenmodelle) für die Berechnung aller statischen und dynamischen Größen im Zusammenhang mit AO geeignet ist. Darauf aufbauend präsentieren wir eine ausführliche NRG-Studie der Besetzungsvertauschung in Quantenpunkten

Damage and repair identification in reinforced concrete beams modelled with various damage scenarios using vibration data

This research aims at developing a novel vibration-based damage identification technique that can efficiently be applied to real-time large data for detection, classification, localisation and quantification of the potential structural damage