Dissertations / Theses on the topic 'Quantum mappings'

This PhD thesis is submitted as a \emph{compendium} of the articles \cite{NS, holographic, topological}. The following has been adapted from their abstracts. Quantum mechanics has been argued to be a coarse--graining of some underlying deterministic theory. Here we support this view by establishing mappings between non-relativistic quantum mechanics and thermodynamic theories, since the latter are the paradigm of an emergent theory. First, we map certain solutions of the Schroedinger equation to solutions of the irrotational Navier--Stokes equation for viscous fluid flow. Although this is formally a generalization of Madelung's hydrodynamical interpretation, the presence of a viscous term leads to a novel interpretation. As a physical model for the fluid itself we propose the quantum probability fluid. It turns out that the (state--dependent) viscosity of this fluid is proportional to Planck's constant, while the volume density of entropy is proportional to Boltzmann's constant. Stationary states have zero viscosity and a vanishing time rate of entropy density. On the other hand, the nonzero viscosity of nonstationary states provides an information--loss mechanism whereby a deterministic theory (a classical fluid governed by the Navier--Stokes equation) gives rise to an emergent theory (a quantum particle governed by the Schroedinger equation). Then, we present a map of standard quantum mechanics onto classical thermodynamics of irreversible processes. In particular, the propagators of the quantum harmonic oscillator are mapped to the conditional probabilities that solve the Chapman-Kolmogorov equation for Markovian Gaussian processes. While no gravity is present in our construction, our map exhibits features that are reminiscent of the holographic principle of quantum gravity. Finally, the classical thermostatics of equilibrium processes is shown to possess a quantum mechanical dual theory with a finite dimensional Hilbert space of quantum states. Specifically, the kernel of a certain Hamiltonian operator becomes the Hilbert space of quasistatic quantum mechanics. The relation of thermostatics to topological field theory is also discussed in the context of the approach of emergence of quantum theory, where the concept of entropy plays a key role.
La presente tesis doctoral se presenta como compendio de las publicaciones \cite{NS, holographic, topological}. El siguiente resumen es una adaptación de sus resumenes. Se ha argumentado que la mecánica cuántica podría emerger como promediado de una teoría determinista subyacente. Se apoya dicha visión estableciendo mapeos entre la mecánica cuántica no relativista y teorías termodinámicas, ya que estas constituyen el paradigma de teoría emergente. Primero, se establece un mapeo entre soluciones de la ecuación de Schroedinger y soluciones de la ecuación de Navier-Stokes irrotacional para fluidos viscosos. Aunque formalmente se trate de una generalización de la interpretación hidrodinámica de Madelung, la presencia del término viscoso sugiere una nueva interpretación. Se propone la probabilidad cuántica como modelo físico del fluido. Se obtiene que la viscosidad (dependiente del estado) es proporcional a la constante de Planck, mientras que la densidad de entropía es proporcional a la constante de Boltzmann. Los estados estacionarios tienen viscosidad y tasa de producción de densidad de entropía nulas. Por otro lado, la viscosidad no nula de los estados no estacionarios proporciona un mecanismo de pérdida de información por el cual una teoría determinista (un fluido clásico gobernado por la ec. de Navier-Stokes) da lugar a una teoría emergente (una partícula cuántica gobernada por la ec. de Schroedinger). Después, se presenta un mapeo entre la mecánica cuántica y la termodinámica clásica de procesos irreversibles. En particular, los propagadores del oscilador armónico cuántico se mapean a las probabilidades condicionales que resuelven la ecuación de Chapman-Kolmogorov para procesos de Markov Gaussianos. Aunque no hay gravedad, el mapeo exhibe propiedades que recuerdan al principio holográfico de la gravedad cuántica. Finalmente, se muestra cómo la termoestática clásica de procesos de equilibrio posee una teoría cuántica dual con un espacio de Hilbert finito - dimensional de estados cuánticos. Concretamente, el núcleo de cierto operador Hamiltoniano se convierte en el espacio de Hilbert de una mecánica cuántica cuasiestática. La relación de la termoestática a la teoría topológica de campos se discute en el contexto de la mecánica cuántica emergente, donde el concepto de entropía juega un papel clave.
Aquesta tesi doctoral es presenta com a compilació de les publicacions \cite{NS, holographic, topological}. El següent resum es una adaptació dels seus resums. S'ha argumentat que la mecànica quàntica podria emergir com a granulat gros d'una teoria determinista subjacent. Es dóna suport a aquesta visió mitjaçant uns mapes entre la mecànica quàntica no relativista i teories termodinàmiques, ja que les darreres són el paradigma de teoria emergent. Primer, s'estableix un mapa entre certes solucions de l'equació de Schroedinger i solucions de l'equació de Navier-Stokes irrotacional per a fluids viscosos. Tot i que formalment es tracte d'una generalització de la interpretació hidrodinàmica de Madelung, la presència del terme viscós ens porta a una nova interpretación. Es proposa la probabilitat quàntica com a model físic del fluid. S'obté que la viscositat del fluid (que depén de l'estat) es proporcional a la constant de Planck, mentre que la densitat d'entropía es proporcional a la constant de Boltzmann. Els estats estacionaris tenen viscositat nul·la i taxa de producció d'entropia nul·la. Per alta banda, la viscositat no nul·la dels estats estacionaris proporciona un mecanisme de pèrdua d'informació pel qual una teoria determinista (un fluid clàssic governat per l'equació de Navier-Stokes) dóna lloc a una teoria emergent (una partícula quàntica governada per l'equació de Schroedinger). Després, es presenta un mapa entre la mecànica quàntica i la termodinàmica clàssica de processos irreversibles. En particular, els propagadors de l'oscil·lador harmònic quàntic es mapejen a les probabilitats condicional que resolen l'ecuació de Chapman-Kolmogorov per a processos de Markov Gaussians. Tot i que no hi ha gravetat present a la nostra construcció, el mapa exhibeix propietats que recorden al principi hologràfic de la gravetat quàntica. Finalment, es mostra cóm la termoestàtica clàssica de processos d'equilibri té una teoria quàntica dual amb un espai de Hilbert de dimensió finita d'estats quàntics. En concret, el nucli de cert operador Hamiltonià es converteix en l'espai de Hilbert d'una mecànica quàntica quasiestàtica. La relació de la termoestàtica a la teoria topològica de camps es dicuteix en el context de la mecànica quàntica emergent, on el concepte d'entropia té un paper clau.
Vázquez Molina, J. (2017). Mappings between Thermodynamics and Quantum Mechanics that support its interpretation as an emergent theory [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/83122
TESIS

Orientador: Alexandre César Rodrigues da Silva
Abstract: Research in the field of quantum circuits has increased as technology advances in the development of quantum computers. IBM offers access to quantum computers via the cloud service called IBM Q. However, these architectures have some restrictions regarding the types of quantum gates that can be realized. This work proposes a methodology for the mapping of quantum and reversible circuits to the architectures made available by the IBM Q project. The methodology consists in finding CNOT mappings using a set of defined qubits movements to satisfy the architectures constraints by adding as few gates as possible. In order to reduce the number of CNOT gates needing mapping, the permutation of the circuit can be changed. One alternative to find this permutation is trough exhaustive search. However, is not feasible as the number of qubit increases. To solve this problem, the permutation problem was formulated as an Integer Linear Programming problem. The mapping of quantum circuits realized with non-implementable gates and reversible Toffoli circuits to the IBM quantum architectures were proposed in this work as well. This was done by adapting the developed CNOT mappings along with the Integer Linear Programming formulation. The proposed methodology was evaluated by mapping quantum and reversible circuits to an IBM quantum architectures with 5 and 16 qubits. The results were compared with two algorithms that map quantum circuits to IBM architectures. The cost metric used in the evalua... (Complete abstract click electronic access below)
Resumo: Pesquisa no campo de circuitos quânticos tem alavancado conforme a tecnologia avança no desenvolvimento de computadores quânticos. Atualmente, a IBM oferece acesso a computadores quânticos através do serviço em nuvem chamado IBM Q. No entanto, essas arquiteturas têm algumas restrições com relação aos tipos de portas quânticas e qubits em que uma porta CNOT pode ser implementada. Neste trabalho foi proposta uma metodologia para o mapeamento de circuitos quânticos e reversíveis para as arquiteturas disponibilizadas pelo projeto IBM Q. A metodologia consiste em mapear as portas CNOT utilizando uma série de movimentos de qubits, mantendo a permutação do circuito inalterada. A fim de reduzir o número de portas CNOT não implementáveis, a permutação do circuito pode ser alterada. Uma alternativa para encontrar essa permutação é a busca exaustiva. No entanto, é inviável conforme o número de qubits aumenta. Para resolver este problema, o problema de permutação foi formulado como um problema de Programação Linear Inteira. Como a metodologia é facilmente adaptável, o mapeamento de circuitos quânticos utilizando portas quânticas não implementáveis e circuitos reversíveis Toffoli também foram propostas neste trabalho. A avaliação da metodologia proposta foi feita com a realização do mapeamento de circuitos quânticos e reversíveis para arquiteturas quânticas com 5 e 16 qubits. Os resultados foram comparados com dois algoritmos que mapeiam circuitos quânticos para arquiteturas IBM. A métric... (Resumo completo, clicar acesso eletrônico abaixo)
Doutor

El objetivo de esta tesis se centra en el estudio de la transferencia de electrones (ET), una de las reacciones más simples y cruciales en bioquímica. Para dichos procesos, obtener información directa de los factores que lo promueves, asi como del camino de transferencia electronica, no es una tarea trivial. Dicha información a un nivel de conocimiento detallado atómico y electrónico, sin embargo, es muy valiosa en términos de una mejor comprensión del ciclo enzimático, que podría conducir, por ejemplo, a un diseño más eficaz de inhibidores. El objetivo principal de esta tesis es el desarrollo de una metodología para el estudio cuantitativo de la ET en los sistemas biológicos. En este sentido, hemos desarrollado un nuevo método para obtener el camino de transferencia electrónico, llamado QM/MM e-­‐ Pathway, que se puede aplicar en sistemas complejos con ET de largo alcance. El método se basa en una búsqueda sucesiva de residuos importantes para la ET, utilizando la modificación de la región quantica en métodos mixtos QM/MM, y siguiendo la evolución de la densidad de espín dentro de la zona de transferencia. Hemos demostrado la utilidad y la aplicabilidad del algoritmo en el complejo P450cam/Pdx, identificando el papel clave de la Arg112 (en P450cam) y del Asp48 (en Pdx), ambos conocidos en la literatura. Además de obtener caminos de ET, hemos cuantificado su importancia en términos del acoplamiento electrónico entre el dador y aceptor para los diferentes caminos. En este sentido, se realizaron dos estudios de la influencia del solvente y de la temperatura en el acoplamiento electrónico para sistemas modelo oligopéptidos. Ambos estudios revelaron que los valores del acoplamiento electrónico fluctúan fuertemente a lo largo de las trayectorias de dinámica molecular obtenidas, y el mecanismo de transferencia de electrones se ve ampliamente afectado por el espacio conformacional del sistema. La combinación del QM/MM e-­‐pathway y de los cálculos de acoplamiento electronico fueron utilizados finalmente para investigar la ET en el complejo CCP/Cytc. Nuestros hallazgos indican el papel fundamental del Trp191 en localizar un estadio intermedio para la transferencia electronica, así como el camino ET principal que incluye Ala194, Ala193, Gly192 y Trp191. Ambos hallazgos fueron confirmados a través de la literatura. Los resultados obtenidos para el muestro de manios de ET, junto con su evaluación a través de cálculos de acoplamiento electrónico, sugieren un enfoque sencillo y prometedor para investigar ET de largo alcance en proteínas.
The focus of this PhD thesis lies on electron transfer (ET) processes, belonging to the simplest but most crucial reactions in biochemistry. Getting direct information of the forces driving the process and the actual electron pathway is not a trivial task. Such atomic and electronic detailed information, however, is very valuable in terms of a better understanding of the enzymatic cycle, which might lead, for example, to more efficient protein inhibitor design. The main objective of this thesis was the development of a methodology for the quantitative study of ET in biological systems. In this regard, we developed a novel approach to map long-­‐range electron transfer pathways, called QM/MM e-­‐Pathway. The method is based on a successive search for important ET residues in terms of modifying the QM region following the evolution of the spin density of the electron (hole) within a given transfer region. We proved the usefulness and applicability of the algorithm on the P450cam/Pdx complex, indicating the key role of Arg112 of P450cam and Asp48 of Pdx for its ET pathway, both being known to be important from the literature. Besides only identifying the ET pathways, we further quantified their importance in terms of electronic coupling of donor and acceptor incorporating the particular pathway residues. Within this regard, we performed two systematic evaluations of the underlying reasons for the influence of solvent and temperature onto electronic coupling in oligopeptide model systems. Both studies revealed that electronic coupling values strongly fluctuate throughout the molecular dynamics trajectories obtained, and the mechanism of electron transfer is affected by the conformational space the system is able to occupy. Combining both ET mapping and electronic coupling calculations, we finally investigated the electron transfer in the CcP/Cytc complex. Our findings indicate the key role of Trp191 being the bridge-­‐localized state of the ET as well as the main pathway consisting of Ala194, Ala193, Gly192 and Trp191 between CcP and Cytc. Both findings were confirmed through the literature. Moreover, our calculations on several snapshots state a nongated ET mechanism in this protein complex. The methodology developed along this thesis, mapping ET pathways together with their evaluation through electronic coupling calculations, suggests a straightforward and promising approach to investigate long-­‐range ET in proteins.

Les algèbres L(g,n,H) ont été introduites par Alekseev-Grosse-Schomerus et Buffenoir-Roche au milieu des années 1990, dans le cadre de la quantification combinatoire de l'espace de modules des G-connexions plates sur la surface S(g,n) de genre g avec n disques ouverts enlevés. L'algèbre de Hopf H, appelée algèbre de jauge, était à l'origine le groupe quantique U_q(g), avec g=Lie(G). Dans cette thèse nous appliquons les algèbres L(g,n,H) à la topologie en basses dimensions (groupe de difféotopie et algèbres d'écheveaux des surfaces), sous l'hypothèse que H est une algèbre de Hopf de dimension finie, factorisable et enrubannée mais pas nécessairement semi-simple, l'exemple phare d'une telle algèbre de Hopf étant le groupe quantique restreint associé à sl(2) (à une racine 2p-ième de l'unité). D'abord, nous construisons en utilisant L(g,n,H) une représentation projective des groupes de difféotopie de S(g,0)D et de S(g,0) (où D est un disque ouvert). Nous donnons des formules pour les représentations d'un ensemble de twists de Dehn qui engendre le groupe de difféotopie; en particulier ces formules nous permettent de montrer que notre représentation est équivalente à celle construite par Lyubashenko-Majid et Lyubashenko via des méthodes catégoriques. Pour le tore S(1,0) avec le groupe quantique restreint associé à sl(2) comme algèbre de jauge, nous calculons explicitement la représentation de SL(2,Z) en utilisant une base convenable de l'espace de représentation et nous en déterminons la structure.Ensuite, nous introduisons une description diagrammatique de L(g,n,H) qui nous permet de définir de façon très naturelle l'application boucle de Wilson W. Cette application associe un élément de L(g,n,H) à chaque entrelac dans (S(g,n)D) x [0,1] qui est parallélisé, orienté et colorié par des H-modules. Quand l'algèbre de jauge est le groupe quantique restreint associé à sl(2), nous utilisons W et les représentations de L(g,n,H) pour construire des représentations des algèbres d'écheveaux S_q(S(g,n)). Pour le tore S(1,0) nous étudions explicitement cette représentation
The algebras L(g,n,H) have been introduced by Alekseev-Grosse-Schomerus and Buffenoir-Roche in the middle of the 1990's, in the program of combinatorial quantization of the moduli space of flat G-connections over the surface S(g,n) of genus g with n open disks removed. The Hopf algebra H, called gauge algebra, was originally the quantum group U_q(g), with g = Lie(G). In this thesis we apply these algebras L(g,n,H) to low-dimensional topology (mapping class groups and skein algebras of surfaces), under the assumption that H is a finite dimensional factorizable ribbon Hopf algebra which is not necessarily semisimple, the guiding example of such a Hopf algebra being the restricted quantum group associated to sl(2) (at a 2p-th root of unity).First, we construct from L(g,n,H) a projective representation of the mapping class groups of S(g,0)D and of S(g,0) (D being an open disk). We provide formulas for the representations of Dehn twists generating the mapping class group; in particular these formulas allow us to show that our representation is equivalent to the one constructed by Lyubashenko-Majid and Lyubashenko via categorical methods. For the torus S(1,0) with the restricted quantum group associated to sl(2) for the gauge algebra, we compute explicitly the representation of SL(2,Z) using a suitable basis of the representation space and we determine the structure of this representation.Second, we introduce a diagrammatic description of L(g,n,H) which enables us to define in a very natural way the Wilson loop map W. This maps associates an element of L(g,n,H) to any link in (S(g,n)D) x [0,1] which is framed, oriented and colored by H-modules. When the gauge algebra is the restricted quantum group associated to sl(2), we use W and the representations of L(g,n,H) to construct representations of the skein algebras S_q(S(g,n)). For the torus S(1,0) we explicitly study this representation

Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering, 2010.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 67-70).
This thesis accomplishes three tasks. First, it verifies the EC-Kit under different water source conditions by comparing it to a laboratory standard method, the IDEXX Quanti-Tray[tm]. The EC-Kit is a simple, inexpensive field test kit that contains complementary tests for Escherichia coli and total coliform: the Colilert[tm] 10-milliliter presence/absence test and 3MTMS Petrifilm[tm] test. This work was executed by analyzing 521 water samples collected in Capiz Province, Philippines as well as 40 water samples from the Charles River in Cambridge, Massachusetts. Second, it determines the risk level for drinking water sources according to E.coli and total coliform levels in Capiz Province for difference locations and source types. Third, this study contributes to an ongoing mapping project, aimed at creating an interactive, searchable map of water quality results from EC-Kit and Quanti-Tray[tm]. The results of the study reveal that each component of EC-Kit and the entire kit itself is correlated to Quanti-Tray[tm] in a statistically significant way. Moreover, from the calculations of error and proportional reduction in error for unimproved/improved water sources, it is possible to make better predictions with just the use of the Colilert[tm] test, but not just the use of the TM T Petrifilm . This is because the detection limits for PetrifilmTM are an order of magnitude higher than Colilert[tm], namely PetrifilmTM colony counts of 1-10/1 mL sample results fall within the High and colony counts of 10-100/1 mL of sample fall within the Very High risk level categories, whereas positive Colilert[tm] results fall within the Intermediate, High, and Very High risk level categories. Most importantly, the EC-Kit allows for the best reduction in error, with a proportional reduction in error of 63% for unimproved water sources and 60% for improved water sources. This finding is significant because it means that a simple, inexpensive field kit can change our understanding of the safety of drinking water compared to simply knowing the United Nations infrastructure designation of improved versus unimproved water sources. Furthermore, the statistical analysis revealed that while the EC-Kit does not exactly match the Quanti-Tray[tm] results, it still provides useful information for assessing at-risk water sources.
by Patty Chuang.
M.Eng.

Dans notre thèse nous nous sommes intéressés à l'étude des fluctuations de courant, de l'admittance quantique ainsi que la densité d'états pour un nano système en interaction. Notre travail se divise en deux parties. Dans la première partie, nous avons étudié les fluctuations de courant et l'admittance pour un conducteur unidimensionnel, en décrivant le système par un liquide de Tomonaga-Luttinger. Nous avons utilisé les techniques de bosonisation et de refermionisation afin d'aboutir à des résultats exacts pour tous les régimes de température, toutes les valeurs de la tension appliquée et toute la gamme des fréquences. Les résultats obtenus sont appliqués à un conducteur cohérent couplé à un quantum de résistance, et aux états de bord dans le régime de l'effet Hall quantique fractionnaire. Dans le cas d'un conducteur cohérent, le bruit non symétrisé à fréquence finie exhibe un profil différent de celui de la théorie de la diffusion, et la conductance à fréquence finie est directement liée au courant. Dans le cas du régime de l'effet Hall quantique fractionnaire, nous avons pu établir que dans certaines limites, il existe une relation entre les corrélations de courant à l'admittance quantique. En particulier, les singularités qui apparaissent dans les corrélations de courant sont celles de l'admittance. Dans la deuxième partie, nous avons étudié un fil quantique connecté à deux réservoirs qui sont représentés par deux impuretés. Le système est décrit par un liquide de Tomonaga-Luttinger. Nous avons établi et résolu l'équation de Dyson pour la fonction de Green retardée. Ce qui permet de calculer la densité d'états pour un fil quantique homogène puis inhomogène. Dans le cas d'un paramètre d'interaction homogène, l'effet des impuretés modifie le profil de la densité d'états. Dans le cas d'un paramètre d'interaction inhomogène, le calcul de la densité d'états est plus difficile et une approche numérique est indispensable.

Cette thèse comporte des interprétations homologiques de certains invariants quantiques, plus particulièrement ceux associés aux groupes de tresses. Le Chapitre 3 étudie des groupes d'homologie localement finie, relative et à coefficients dans un système local abélien sur des espaces de configurations de points dans le disque épointé. Nous munissons ces complexes d'une action du groupe quantique sl(2) dans une version entière, et nous reconnaissons un produit tensoriel de modules de Verma entiers. Enfin, nous retrouvons une action naturelle du groupe des tresses (par homéomorphisme) sur ces modules homologiques, et nous montrons qu'il s'agit de la représentation obtenue par la R-matrice de la catégorie de modules de sl(2). Les représentations homologiques obtenues sont une généralisation des représentations de Lawrence, donc elles sont fidèles. Elles permettent de retrouver homologiquement plusieurs propriétés de la catégorie de modules sur sl(2). Nous donnons des bases entières de l'homologie (i.e. des bases en tant que module sur un anneau entier de polynômes de Laurent). L'action de sl(2), ainsi que celle du groupe des tresses, respectent cette structure, tout comme l'isomorphisme vers le produit tensoriel de modules de Verma. Ce travail étend le théorème de Kohno (retrouvé via une jolie opération homologique) dans plusieurs directions : • il relie les représentations homologiques à tout le produit tensoriel de modules de Verma (et plus seulement aux vecteurs de plus haut poids) • il inclue une interprétation homologique de l'action de sl(2), dont les définitions sont inspirées par un travail de Felder - Wieczerkowski dans lequel l'aspect homologique restait jusqu'ici conjectural. • il en est une version entière, c'est à dire qu'il préserve la structure d'anneau entier sur les polynômes de Laurent, exhibant ainsi précisément les conditions de généricité précédemment requises par le théorème de Kohno. Ce modèle homologique (pour les représentations quantiques de tresses) est ensuite appliqué aux nœuds vus comme des clôtures de tresses dans le Chapitre 4, et permet d'obtenir une formule des traces (homologiques) pour les polynômes de Jones coloriés, qui s'apparente à une somme pondérée de nombres de Lefschetz abélianisés. Le manuscrit contient également un chapitre (Chapitre 2) d'étude concrète de "petits cas" (car les représentations homologiques sont une famille graduée de représentations). Nous montrons explicitement que les représentations de Gassner du groupe des tresses sont des représentations quantiques, et nous donnons des matrices pour une version colorée des représentations de Bigelow-Krammer-Lawrence - construites au préalable. Nous étudions également le premier niveau de graduation de la représentation du groupe modulaire de la sphère à quatre pointes obtenue via la TQFT non semi-simple (construite par Blanchet - Costantino - Geer - Patureau), nous retrouvons une représentation de nature homologique, ce qui aboutit à la fidélité de cette représentation
We provide homological interpretations for some quantum invariants. We recall basic notions involved in this work: topological ones on one hand (braids, mapping class groups, and homological representations of the latter) and algebaic ones on the other hand (Hopf algebra, quantum groups, categories of modules, braiding). Then, we study "small cases": We show that the Gassner representation is contained in quantum representations of the braid group. We build Bigelow-Krammer-Lawrence representations in a colored version and we give matrices for the action. Finally we study the non semi-simple TQFT (built by Blanchet - Costantino - Geer - Patureau) representation of the mapping class group of the sphere with 4 punctures. We recognize homological representation inside of it, and this leads to the faithfulness of the representation. In the last chapter, we study modules of relative and locally finite homology modules with coefficients in an abelian local system, over configuration spaces of punctured disks. We endow them with an algebra representation of the quantized algebra of sl(2) in an integral version. We recognize a tensor product of integral Verma modules. We identify the natural braid group representation induced on this homology (by mapping class) with the ones obtain by the braiding of the quantized algebra of sl(2). This work extends Kohno's theorem (recovered via a nice homological operation) in several directions: • it relates homological representations to the entire tensor product of Verma modules (and not only to the highest weight vectors) • it includes a homological interpretation for the action of quantum sl(2), whose definitions are inspired by a work of Felder - Wieczerkowski for which the homological aspect remained conjectural. • it is an integral version of Kohno's theorem, namely it preserves the integral structure on Laurent polynomials, thus exposes conditions of genericity previously required by Kohno's theorem. We finally reach the level of knot invariants: in Chapter 4, this homological model for quantum braid representations allows us to show that colored Jones polynomials compute some weighted sum of abelianized Lefschetz numbers

Manipulating light by controlling surface plasmons on metals is being discussed as a means for bridging the size gap between micrometer-sized photonic circuits and nanometer-sized integrated electronics. Plasmonic waveguides based on metal nanoparticles are of particular interest for circumventing the diffraction limit, thereby enabling high-speed communication over short-range distances in miniaturized micro-components. However, scalable, inexpensive fine-tuning of particle assemblies remains a challenge and near-field probing is required to reveal plasmonic interactions. In this thesis, self-assembled waveguides should be produced on DNA scaffolds. DNA origami is an extremely versatile and robust self-assembly method which allows scalable production of nanostructures with a fine control of assemblies at the nanoscale. To form the plasmonic waveguides, six-helix bundle DNA origami nanotubes are used as templates for attachment of highly monodisperse and monocrystalline gold nanoparticles with an inter-particle distance of 1-2 nm. In the first part of this thesis, the effects of parameters which are involved in assembly reactions are systematically investigated. The assembly yield and binding occupancy of the gold nanoparticles are determined by an automated, high-throughput image analysis of electron micrographs of the formed complexes. As a result, unprecedented binding site occupancy and assembly yield are achieved with the optimized synthesis protocol. In addition, waveguides with different sizes of gold nanoparticles and different inter-particle distances, quantum dots attachments to the waveguides and multimerization of the waveguides are successfully realized. In the second part of this thesis, direct observation of energy transport through a self-assembled waveguide towards a fluorescent nanodiamond is demonstrated. High-resolution, near-field mapping of the waveguides are studied by electron energy loss spectroscopy and cathodoluminescence imaging spectroscopy. The experimental and simulation results reveal that energy propagation through the waveguides is enabled by coupled surface plasmon modes. These surface plasmon modes are probed at high spatial and spectral resolutions. The scalable self-assembly approach presented here will enable the construction of complex, sub diffraction plasmonic devices for applications in high-speed optical data transmission, quantum information technology, and sensing
Die Manipulation des Lichts durch die Kontrolle von Oberflächenplasmonen auf metallischen Oberflächen und Nanopartikeln gilt als vielversprechende Methode zur Überbrückung der Größen-Lücke zwischen Mikrometer-großen photonischen und nanometer-großen elektronischen Schaltkreisen. Plasmonische Wellenleiter basierend auf metallischen Nanopartikeln sind vom besonderen Interesse, da sie die Umgehung des Beugungslimits und somit eine Hochgeschwindigkeitskommunikation über kurze Distanzen in immer kleiner werdenden Schaltkreisen ermöglichen könnten. Allerdings ist die skalierbare und kostengünstige Anordnung von Partikeln eine große Herausforderung und es werden Nahfelduntersuchungen benötigt um plasmonische Interaktionen detektieren zu können. Das Ziel dieser Arbeit ist die Selbstassemblierung von multi-partikel Wellenleitern auf DNA Gerüsten. Die Verwendung von DNA-Origami bietet eine äußerst vielseitige Plattform zur skalierbaren Herstellung von Nanostrukturen mittels Selbstassemblierung und ermöglicht eine präzise Kontrolle der Anordnungen im Nanobereich. Für den Aufbau der plasmonischen Wellenleiter werden DNA-Origami Nanoröhren, bestehend aus sechs Helices als Templat für die Anbindung von monodispersen und monokristallinen Goldnanopartikeln mit einem interpartikulären Abstand von 1-2 nm verwendet. Im ersten Abschnitt dieser Arbeit werden die beeinflussenden Faktoren dieser Assemblierungsreaktion systematisch untersucht. Die Ausbeute der assemblierten Strukturen und die Besetzung der Bindungsstellen werden durch eine automatisierte und effiziente Bildanalyse von Elektronenmikroskopieaufnahmen ausgewertet. Durch die Entwicklung eines optimierten Syntheseprotokolls werden bisher unerreichte Assemblierungsausbeuten ermöglicht. Zusätzlich erfolgen die experimentelle Realisierung von Strukturen mit verschieden großen Goldnanopartikeln und unterschiedlichen interpartikulären Abständen, sowie die Anbindung von Quantenpunkten an die Wellenleiter und eine Verknüpfung der assemblierten Strukturen. Der zweite Abschnitt dieser Dissertation befasst sich mit der Untersuchung des Energietransports in selbstassemblierten Wellenleitern über einen fluoreszierenden Nanodiamanten. Dazu erfolgen hochaufgelöste Nahfeldmessungen der Wellenleiter mittels Elektronenenergieverlustspektroskopie und Kathodolumineszenz-mikroskopie. Die experimentellen Ergebnisse und zusätzlich durchgeführte Simulationen bestätigen eine durch gekoppelte Oberflächenplasmonenmoden induzierte Weitergabe der Energie innerhalb des Wellenleiters. Diese Oberflächenplasmonenmoden werden bei hoher räumlicher und spektraler Auflösung untersucht. Das hier umgesetzte Konzept der Selbstassemblierung wird den Aufbau komplexer plasmonischer Geräte für Anwendungen im Bereich der optischen Hochgeschwindigkeitsdatenübertragung, der Quanteninformations-technolgie und der Sensorik ermöglichen

Recent efforts to classify off-shell representations of supersymmetry without a central charge have focused upon directed, supermultiplet graphs of hypercubic topology known as Adinkras. These encodings of Super Poincare algebras, depict every generator of a chosen supersymmetry as a node-pair transformtion between fermionic / bosonic component fields. This research thesis is a culmination of investigating novel diagrammatic sums of gauge quotients by supersymmetric images of other Adinkras, and the correlated building of field theoretic worldline Lagrangians to accommodate both classical and quantum venues. We find Ref [40], that such gauge quotients do not yield other stand alone or ”proper” Adinkras as afore sighted, nor can they be decomposed into supermultiplet sums, but are rather a connected ”Adinkraic network”. Their iteration, analogous to Weyl's construction for producing all finite-dimensional unitary representations in Lie algebras, sets off chains of algebraic paradigms in discrete-graph and continuous-field variables, the links of which feature distinct, supersymmetric Lagrangian templates. Collectively, these Adiankraic series air new symbolic genera for equation to phase moments in Feynman path integrals. Guided in this light, we proceed by constructing Lagrangians actions for the N = 3 supermultiplet YI /(iDI X) for I = 1, 2, 3, where YI and X are standard, Salam-Strathdee superfields: YI fermionic and X bosonic. The system, bilinear in the component fields exhibits a total of thirteen free parameters, seven of which specify Zeeman-like coupling to external background (magnetic) fluxes. All but special subsets of this parameter space describe aperiodic oscillatory responses, some of which are found to be surprisingly controlled by the golden ratio, ? ? 1.61803, Ref [52]. It is further determined that these Lagrangians allow an N = 3 ? 4 supersymmetric extension to the Chiral-Chiral and Chiral-twisted- Chiral multiplet, while a subset admits two inequivalent such extensions. In a natural progression, a continuum of observably and usefully inequivalent, finite-dimensional off-shell representations of worldline N = 4 extended supersymmetry are explored, that are variate from one another but in the value of a tuning parameter, Ref [53]. Their dynamics turns out to be nontrivial already when restricting to just bilinear Lagrangians. In particular, we find a 34-parameter family of bilinear Lagrangians that couple two differently tuned supermultiplets to each other and to external magnetic fluxes, where the explicit parameter dependence is unremovable by any field redefinition and is therefore observable. This offers the evaluation of X-phase sensitive, off-shell path integrals with promising correlations to group product decompositions and to deriving source emergences of higher-order background flux-forms on 2-dimensional manifolds, the stacks of which comprise space-time volumes. Application to nonlinear sigma models would naturally follow, having potential use in M- and F- string theories.
Ph.D.
Doctorate
Physics
Sciences
Physics

Bibliography: leaves 143-146
vii, 147 leaves ; 30 cm.
Title page, contents and abstract only. The complete thesis in print form is available from the University Library.
Thesis (Ph.D.)--University of Adelaide, Dept. of Mathematical Physics, 1986

Indiana University-Purdue University Indianapolis (IUPUI)
I study d-bar and Dirac operators on classical and quantum domains subject to the APS boundary conditions, APS like boundary conditions, and other types of global boundary conditions. Moreover, the inverse or inverse modulo compact operators to these operators are computed. These inverses/parametrices are also shown to be bounded and are also shown to be compact, if possible. Also the index of some of the d-bar operators are computed when it doesn't have trivial index. Finally a certain type of limit statement can be said between the classical and quantum d-bar operators on specialized complex domains.

Quantum information processing is of interest as it offers the potential for a new generation of very powerful computers supporting novel computational paradigms. Over the last couple of decades, different aspects of quantum computers ranging from quantum algorithms to quantum physical design have received growing attention. One of the most important research areas is the synthesis and post-synthesis optimization of reversible and quantum circuits. Many synthesis and optimization approaches can be found in the literature, yet, due to the complexity of the problem, finding approaches leading to optimal, or near optimal, results is still an open problem. The synthesized circuits are usually evaluated based on quantum cost models. Therefore, they are often technology mapped to circuits of more primitive gates. To this end, various technology mapping approaches have also been proposed in the past few years. Related work shows an existing gap in optimized technology mapping for reversible and quantum circuits. In this dissertation, an optimized technology mapping design flow is introduced for mapping reversible circuits to quantum circuits. The contributions of this dissertation are classified as follows: - New reversible circuit optimization methods. - Optimized reversible to quantum mapping approaches. - New quantum gate libraries and new cost models for reversible gates based on the new libraries. - Quantum circuit optimization approaches. The steps above, form an optimized flow for mapping reversible circuits to quantum circuits. At each step of the design flow optimized and consistent approaches are suggested with the goal of reducing the quantum cost of the synthesized reversible circuits. The evaluations show that the proposed mapping methodology leads to significant improvement in the quantum cost of the existing benchmark circuits.
Graduate

Solving quantum dynamics is an exponentially difficult problem. Thus, an exact numerical solution is inaccessible for any condensed matter system. A promising approach is to divide the system into a quantum subsystem containing degrees of freedom which are of greater interest or those which have more profound quantum character (e.g., have smaller mass) and a classical bath containing the rest of the system. Imposing such a partition and treating the bath classically results in quantum-classical dynamics. The quantum-classical Liouville equation is a general equation in the Hilbert space of quantum degrees of freedom while it resides in the phase space of the classical degrees of freedom. Any numerical solution to this equation requires representation of the quantum subsystem in some basis. Solutions to this equation have been already proposed in the subsystem, adiabatic and force bases, each with its own cons and pros. In this work, the quantum-classical equations of motion are cast in the subsystem basis and subsequently mapped to a number of fictitious harmonic oscillators. The result is quantum-classical dynamics in the mapping basis which treats both quantum and classical degrees of freedom on the same footing, i.e., in phase space. Neglecting a portion of the back reaction of the quantum-subsystem to classical bath results in an expression for the time evolution of an operator (density matrix) equal to its Poisson bracket with the Hamiltonian. This equation can be solved in terms of characteristics to provide a computationally tractable method for calculating quantum-classical dynamical properties. The expressions for expectation values and correlation functions in this formalism are derived. Calculations on spin-boson system, barrier crossing models---the so called Tully models---and the Fenna-Mathews-Olson pigments show very good agreement between the results of this method and numerical solutions to the Schrödinger equation.

博士
國立交通大學
物理研究所
103
In this work, we fabricated a series of (Cu/Al)/AlOx/Y planar tunnel junctions which are on the different location of the phase diagram for two-impurity Kondo effect. In (Cu/Al)/AlOx/Y tunnel junctions, the Y atoms will diffuse into AlOx barrier to be treated as the spin-½ magnetic impurities and result in Kondo effect. We tune the coupling strength between magnetic impurity and electrode by modulating barrier properties. We measured the differential conductance G(V,T) in a dozen of (Cu/Al)/AlOx/Y tunnel junctions. For all junctions, we can observe the weak coupling behavior, i.e. G(0,T) is -logT dependence, between about 10 – 35 K. And a quantum critical regime also can be observed in the range about 2 – 25 K, in which shows non-Fermi liquid behavior. G(V,T) obeys the two-impurity Kondo universal scaling form. As the temperature further decreases, the G(V,T) of tunnel junctions will cross over to three different behaviors. First one is the Kondo screened ground state (Fermi liquid behavior), second one is the RKKY local spin singlet state (Fermi liquid behavior), and the other one is in the vicinity around quantum critical point. G(V,T) clearly shows three different behavior with varying temperature, bias voltage and applied magnetic field. Furthermore, the versatile tunnel junction can achieve very high TK (~ 40 K) to explore quantum phase transition in a wide window, and may be of potential relevance to many strongly correlated electron systems.

In this thesis, the strength of the LBIC system is enhanced in different aspects that includes its feasibility as a non-destructive characterization tool, the signal analysis and development of analytical solution to have better understanding on the defects and inhomogeneities in the quantum dot based hetero-structures for device applications, finally understanding its limits due to the size of the laser beam and interpretation of artefacts in the signal appearance due to the presence of co-devices. Chapter#1 provides the introduction and literature survey of the LBIC system. It covers the importance and area of application of the LBIC. Chapter#2 various tools and instrumentation are discussed briefly for the systems that are developed in the lab as well as standard tools utilised for the material characterization. A LBIC instrumentation a novel colloidal quantum dots (CQD) thin film deposition system is discussed. In the last part along with the standard characterization systems a software tool (semiconductor device simulator) is discussed, which is used to visualize and understand the LBIC profile that is obtained experimentally. Chapter#3 provides the information of colloidal synthesis of PbS and HgxCd1-xTe quantum dots. Device fabrication process is explained step by step for the following devices. p-n junction silicon diodes, PbS-CQD/Si hetero-structures, ITO/PbS-CQD/Al crossbar structures and HgCdTe-CQD/Si hetero-structures. Chapter#4 deals with the major constraints imposed on the LBIC due to the need of Ohmic contacts. To overcome this major limitation, in this work, the origin of the signal is studied with the remote contact geometry for silicon p-n junction devices. It was observed that the signals can be collected with the capacitively coupled remote contacts, where LBIC was ultimately demonstrated as contactless measurement tool without any compromise on the measurements and thus obtained physical parameters. The effect of finite laser beam size is also described, which was found to have effect on the actual dimensions measured with the LBIC images. LBIC utility is further enhanced with the Si/CQD based hetero-structure devices, which are the potential candidates in the evolving device technology to be utilized in various modular systems such as PDs and LED applications. Chapter#5 discusses the origin and possible mechanisms for lateral photo-voltage which is closely monitored in the PbS-CQD/Si hetero-junction device systems. Interestingly, it is observed that there are two different line profiles for n and p type Si substrates. Different mechanisms that give rise to this kind of profiles were found to be distinct and are related to the band alignment of the CQD/Si hetero-structure. It lead to the revelation of an interesting phenomenon and believed to be universally observed irrespective of the materials involved in the formation of hetero-junction. Simulations and experimental results are quite consistent and in agreement with each other, which confirm the underlying physical mechanism that connects the LBIC anomalies with the band alignment. Chapter#6 deals with the spatial variations in the transverse photocurrent in the PbS-CQD film which is studied as a function of applied bias. Analytical equation is setup for the photocurrent in the CQD film under applied bias with the help of available transport mechanism and equations from the literature. The spatial non-uniformity that exists in the photocurrent proved to be the result of spatial inhomoginities in the physical parameters. By correlating the spatial data to the analytical equation, it is shown that the inhomoginities can be predicted. This approach is important for the devices, where monolithic detectors are fabricated by depositing CQD film on Read-Out-Integrated-Circuit (ROIC), where the manifestation of non-uniformity can be understood and probably fixed. Chapter#7 HgCdTe CQD based devices are studied for the purpose of photo-detector applications in MWIR (3  5 μm) region. HgxCd1-xTe Colloidal quantum dots are technologically important due to their wide absorption range that covers different regions of the atmospheric window. HgxCd1-xTe are successfully synthesised, which covers the absorption edge up to ~6.25 m in the IR region. Absorption and photo-response studies are carried out on HgxCd1-xTe/Si hetero-junctions under incident IR radiation. It is observed that the band gap of the quantum dots can be tuned easily by controlling the growth time as a parameter, thus moulded HgxCd1-xTe CQD/Si hetero-structures were found to have good photo-response. Chapter#8 the summary and the future direction and scope of the work is discussed. This includes the interesting observations during this thesis work which are not reported here in details.

Manipulating light by controlling surface plasmons on metals is being discussed as a means for bridging the size gap between micrometer-sized photonic circuits and nanometer-sized integrated electronics. Plasmonic waveguides based on metal nanoparticles are of particular interest for circumventing the diffraction limit, thereby enabling high-speed communication over short-range distances in miniaturized micro-components. However, scalable, inexpensive fine-tuning of particle assemblies remains a challenge and near-field probing is required to reveal plasmonic interactions. In this thesis, self-assembled waveguides should be produced on DNA scaffolds. DNA origami is an extremely versatile and robust self-assembly method which allows scalable production of nanostructures with a fine control of assemblies at the nanoscale. To form the plasmonic waveguides, six-helix bundle DNA origami nanotubes are used as templates for attachment of highly monodisperse and monocrystalline gold nanoparticles with an inter-particle distance of 1-2 nm. In the first part of this thesis, the effects of parameters which are involved in assembly reactions are systematically investigated. The assembly yield and binding occupancy of the gold nanoparticles are determined by an automated, high-throughput image analysis of electron micrographs of the formed complexes. As a result, unprecedented binding site occupancy and assembly yield are achieved with the optimized synthesis protocol. In addition, waveguides with different sizes of gold nanoparticles and different inter-particle distances, quantum dots attachments to the waveguides and multimerization of the waveguides are successfully realized. In the second part of this thesis, direct observation of energy transport through a self-assembled waveguide towards a fluorescent nanodiamond is demonstrated. High-resolution, near-field mapping of the waveguides are studied by electron energy loss spectroscopy and cathodoluminescence imaging spectroscopy. The experimental and simulation results reveal that energy propagation through the waveguides is enabled by coupled surface plasmon modes. These surface plasmon modes are probed at high spatial and spectral resolutions. The scalable self-assembly approach presented here will enable the construction of complex, sub diffraction plasmonic devices for applications in high-speed optical data transmission, quantum information technology, and sensing.
Die Manipulation des Lichts durch die Kontrolle von Oberflächenplasmonen auf metallischen Oberflächen und Nanopartikeln gilt als vielversprechende Methode zur Überbrückung der Größen-Lücke zwischen Mikrometer-großen photonischen und nanometer-großen elektronischen Schaltkreisen. Plasmonische Wellenleiter basierend auf metallischen Nanopartikeln sind vom besonderen Interesse, da sie die Umgehung des Beugungslimits und somit eine Hochgeschwindigkeitskommunikation über kurze Distanzen in immer kleiner werdenden Schaltkreisen ermöglichen könnten. Allerdings ist die skalierbare und kostengünstige Anordnung von Partikeln eine große Herausforderung und es werden Nahfelduntersuchungen benötigt um plasmonische Interaktionen detektieren zu können. Das Ziel dieser Arbeit ist die Selbstassemblierung von multi-partikel Wellenleitern auf DNA Gerüsten. Die Verwendung von DNA-Origami bietet eine äußerst vielseitige Plattform zur skalierbaren Herstellung von Nanostrukturen mittels Selbstassemblierung und ermöglicht eine präzise Kontrolle der Anordnungen im Nanobereich. Für den Aufbau der plasmonischen Wellenleiter werden DNA-Origami Nanoröhren, bestehend aus sechs Helices als Templat für die Anbindung von monodispersen und monokristallinen Goldnanopartikeln mit einem interpartikulären Abstand von 1-2 nm verwendet. Im ersten Abschnitt dieser Arbeit werden die beeinflussenden Faktoren dieser Assemblierungsreaktion systematisch untersucht. Die Ausbeute der assemblierten Strukturen und die Besetzung der Bindungsstellen werden durch eine automatisierte und effiziente Bildanalyse von Elektronenmikroskopieaufnahmen ausgewertet. Durch die Entwicklung eines optimierten Syntheseprotokolls werden bisher unerreichte Assemblierungsausbeuten ermöglicht. Zusätzlich erfolgen die experimentelle Realisierung von Strukturen mit verschieden großen Goldnanopartikeln und unterschiedlichen interpartikulären Abständen, sowie die Anbindung von Quantenpunkten an die Wellenleiter und eine Verknüpfung der assemblierten Strukturen. Der zweite Abschnitt dieser Dissertation befasst sich mit der Untersuchung des Energietransports in selbstassemblierten Wellenleitern über einen fluoreszierenden Nanodiamanten. Dazu erfolgen hochaufgelöste Nahfeldmessungen der Wellenleiter mittels Elektronenenergieverlustspektroskopie und Kathodolumineszenz-mikroskopie. Die experimentellen Ergebnisse und zusätzlich durchgeführte Simulationen bestätigen eine durch gekoppelte Oberflächenplasmonenmoden induzierte Weitergabe der Energie innerhalb des Wellenleiters. Diese Oberflächenplasmonenmoden werden bei hoher räumlicher und spektraler Auflösung untersucht. Das hier umgesetzte Konzept der Selbstassemblierung wird den Aufbau komplexer plasmonischer Geräte für Anwendungen im Bereich der optischen Hochgeschwindigkeitsdatenübertragung, der Quanteninformations-technolgie und der Sensorik ermöglichen.