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1
Oeckl, Robert. "Quantum geometry and Quantum Field Theory." Thesis, University of Cambridge, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.621912.
Testo completo
2
Midgley, Stuart. "Quantum waveguide theory." University of Western Australia. School of Physics, 2003. http://theses.library.uwa.edu.au/adt-WU2004.0036.
Testo completoAbstract (sommario):
The study of nano-electronic devices is fundamental to the advancement of the semiconductor industry. As electronic devices become increasingly smaller, they will eventually move into a regime where the classical nature of the electrons no longer applies. As the quantum nature of the electrons becomes increasingly important, classical or semiclassical theories and methods will no longer serve their purpose. For example, the simplest non-classical effect that will occur is the tunnelling of electrons through the potential barriers that form wires and transistors. This results in an increase in noise and a reduction in the device?s ability to function correctly. Other quantum effects include coulomb blockade, resonant tunnelling, interference and diffraction, coulomb drag, resonant blockade and the list goes on. This thesis develops both a theoretical model and computational method to allow nanoelectronic devices to be studied in detail. Through the use of computer code and an appropriate model description, potential problems and new novel devices may be identified and studied. The model is as accurate to the physical realisation of the devices as possible to allow direct comparison with experimental outcomes. Using simple geometric shapes of varying potential heights, simple devices are readily accessible: quantum wires; quantum transistors; resonant cavities; and coupled quantum wires. Such devices will form the building blocks of future complex devices and thus need to be fully understood. Results obtained studying the connection of a quantum wire with its surroundings demonstrate non-intuitive behaviour and the importance of device geometry to electrical characteristics. The application of magnetic fields to various nano-devices produced a range of interesting phenomenon with promising novel applications. The magnetic field can be used to alter the phase of the electron, modifying the interaction between the electronic potential and the transport electrons. This thesis studies in detail the Aharonov-Bohm oscillation and impurity characterisation in quantum wires. By studying various devices considerable information can be added to the knowledge base of nano-electronic devices and provide a basis to further research. The computational algorithms developed in this thesis are highly accurate, numerically efficient and unconditionally stable, which can also be used to study many other physical phenomena in the quantum world. As an example, the computational algorithms were applied to positron-hydrogen scattering with the results indicating positronium formation.
3
Schumann, Robert Helmut. "Quantum information theory." Thesis, Stellenbosch : Stellenbosch University, 2000. http://hdl.handle.net/10019.1/51892.
Testo completoAbstract (sommario):
Thesis (MSc)--Stellenbosch University, 2000<br>ENGLISH ABSTRACT: What are the information processing capabilities of physical systems?
As recently as the first half of the 20th century this question did not even have a definite
meaning. What is information, and how would one process it? It took the development of
theories of computing (in the 1930s) and information (late in the 1940s) for us to formulate
mathematically what it means to compute or communicate.
Yet these theories were abstract, based on axiomatic mathematics: what did physical systems
have to do with these axioms? Rolf Landauer had the essential insight - "Information is
physical" - that information is always encoded in the state of a physical system, whose dynamics
on a microscopic level are well-described by quantum physics. This means that we cannot discuss
information without discussing how it is represented, and how nature dictates it should behave.
Wigner considered the situation from another perspective when he wrote about "the unreasonable
effectiveness of mathematics in the natural sciences". Why are the computational techniques
of mathematics so astonishingly useful in describing the physical world [1]? One might begin to
suspect foul play in the universe's operating principles.
Interesting insights into the physics of information accumulated through the 1970s and 1980s
- most sensationally in the proposal for a "quantum computer". If we were to mark a particular
year in which an explosion of interest took place in information physics, that year would have to
be 1994, when Shor showed that a problem of practical interest (factorisation of integers) could be
solved easily on a quantum computer. But the applications of information in physics - and vice
versa - have been far more widespread than this popular discovery. These applications range
from improved experimental technology, more sophisticated measurement techniques, methods
for characterising the quantum/classical boundary, tools for quantum chaos, and deeper insight
into quantum theory and nature.
In this thesis I present a short review of ideas in quantum information theory. The first chapter
contains introductory material, sketching the central ideas of probability and information theory.
Quantum mechanics is presented at the level of advanced undergraduate knowledge, together with
some useful tools for quantum mechanics of open systems. In the second chapter I outline how
classical information is represented in quantum systems and what this means for agents trying
to extract information from these systems. The final chapter presents a new resource: quantum
information. This resource has some bewildering applications which have been discovered in the
last ten years, and continually presents us with unexpected insights into quantum theory and
the universe.<br>AFRIKAANSE OPSOMMING: Tot watter mate kan fisiese sisteme informasie verwerk?
So onlangs soos die begin van die 20ste eeu was dié vraag nog betekenisloos. Wat is informasie,
en wat bedoel ons as ons dit wil verwerk? Dit was eers met die ontwikkeling van die teorieë van
berekening (in die 1930's) en informasie (in die laat 1940's) dat die tegnologie beskikbaar geword
het wat ons toelaat om wiskundig te formuleer wat dit beteken om te bereken of te kommunikeer.
Hierdie teorieë was egter abstrak en op aksiomatiese wiskunde gegrond - mens sou wel kon
wonder wat fisiese sisteme met hierdie aksiomas te make het. Dit was Rolf Landauer wat uiteindelik
die nodige insig verskaf het - "Informasie is fisies" - informasie word juis altyd in 'n fisiese
toestand gekodeer, en so 'n fisiese toestand word op die mikroskopiese vlak akkuraat deur kwantumfisika
beskryf. Dit beteken dat ons nie informasie kan bespreek sonder om ook na die fisiese
voorstelling te verwys nie, of sonder om in ag te neem nie dat die natuur die gedrag van informasie
voorskryf.
Hierdie situasie is vanaf 'n ander perspektief ook deur Wigner beskou toe hy geskryf het
oor "die onredelike doeltreffendheid van wiskunde in die natuurwetenskappe". Waarom slaag
wiskundige strukture en tegnieke van wiskunde so uitstekend daarin om die fisiese wêreld te
beskryf [1]? Dit laat 'n mens wonder of die beginsels waarvolgens die heelal inmekaar steek
spesiaal so saamgeflans is om ons 'n rat voor die oë te draai.
Die fisika van informasie het in die 1970's en 1980's heelwat interessante insigte opgelewer,
waarvan die mees opspraakwekkende sekerlik die gedagte van 'n kwantumrekenaar is. As ons
één jaar wil uitsonder as die begin van informasiefisika, is dit die jaar 1994 toe Shor ontdek
het dat 'n belangrike probleem van algemene belang (die faktorisering van groot heelgetalle)
moontlik gemaak word deur 'n kwantumrekenaar. Die toepassings van informasie in fisika,
en andersom, strek egter veel wyer as hierdie sleutel toepassing. Ander toepassings strek van
verbeterde eksperimentele metodes, deur gesofistikeerde meetmetodes, metodes vir die ondersoek
en beskrywing van kwantumchaos tot by dieper insig in die samehang van kwantumteorie en die
natuur.
In hierdie tesis bied ek 'n kort oorsig oor die belangrikste idees van kwantuminformasie teorie.
Die eerste hoofstuk bestaan uit inleidende materiaal oor die belangrikste idees van waarskynlikheidsteorie
en klassieke informasie teorie. Kwantummeganika word op 'n gevorderde voorgraadse
vlak ingevoer, saam met die nodige gereedskap van kwantummeganika vir oop stelsels.
In die tweede hoofstuk spreek ek die voorstelling van klassieke informasie en kwantumstelsels
aan, en die gepaardgaande moontlikhede vir 'n agent wat informasie uit sulke stelsels wil kry.
Die laaste hoofstuk ontgin 'n nuwe hulpbron: kwantuminformasie. Gedurende die afgelope tien
jaar het hierdie nuwe hulpbron tot verbysterende nuwe toepassings gelei en ons keer op keer tot
onverwagte nuwe insigte oor kwantumteorie en die heelal gelei.
4
Shin, Ghi Ryang. "Quantum transport theory." Diss., The University of Arizona, 1993. http://hdl.handle.net/10150/186508.
Testo completoAbstract (sommario):
Within the framework of the quantum transport theory based on the Wigner transform of the density matrix I study first in non-relativistic and subsequently in relativistic formulation a number of applications. I also develop further the recently proposed relativistic theory: the classical limit is carefully derived and the integral equations of the relativistic Wigner function derived explicitly. I show how it is possible to obtain the Schwinger like particle production rate from relativistic quantum transport equations. Noteworthy numerical results address the shape of the relativistic Wigner function of a given quantum state. Other numerical studies are primarily oriented towards the time evolution of the Wigner function--I can presently solve only the nonrelativistic case in which there is no mixing between particle production and flow phenomena: I consider numerically the fate of the muon after muon catalyzed fusion.
5
Gupta, Neha. "Homotopy quantum field theory and quantum groups." Thesis, University of Warwick, 2011. http://wrap.warwick.ac.uk/38110/.
Testo completoAbstract (sommario):
The thesis is divided into two parts one for dimension 2 and the other for dimension 3. Part one (Chapter 3) of the thesis generalises the definition of an n-dimensional HQFT in terms of a monoidal functor from a rigid symmetric monoidal category X-Cobn to any monoidal category A. In particular, 2-dimensional HQFTs with target K(G,1) taking values in A are generated from any Turaev G-crossed system in A and vice versa. This is the generalisation of the theory given by Turaev into a purely categorical set-up. Part two (Chapter 4) of the thesis generalises the concept of a group-coalgebra, Hopf group-coalgebra, crossed Hopf group-coalgebra and quasitriangular Hopf group-coalgebra in the case of a group scheme. Quantum double of a crossed Hopf group-scheme coalgebra is constructed in the affine case and conjectured for the more general non-affine case. We can construct 3-dimensional HQFTs from modular crossed G-categories. The category of representations of a quantum double of a crossed Hopf group-coalgebra is a ribbon (quasitriangular) crossed group-category, and hence can generate 3-dimensional HQFTs under certain conditions if the category becomes modular. However, the problem of systematic finding of modular crossed G-categories is largely open.
6
Poletti, Stephen John. "Geometry, quantum field theory and quantum cosmology." Thesis, University of Newcastle Upon Tyne, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.315921.
Testo completo
7
Kerr, Steven. "Topological quantum field theory and quantum gravity." Thesis, University of Nottingham, 2014. http://eprints.nottingham.ac.uk/14094/.
Testo completoAbstract (sommario):
This thesis is broadly split into two parts. In the first part, simple state sum models for minimally coupled fermion and scalar fields are constructed on a 1-manifold. The models are independent of the triangulation and give the same result as the continuum partition functions evaluated using zeta-function regularisation. Some implications for more physical models are discussed. In the second part, the gauge gravity action is written using a particularly simple matrix technique. The coupling to scalar, fermion and Yang-Mills fields is reviewed, with some small additions. A sum over histories quantisation of the gauge gravity theory in 2+1 dimensions is then carried out for a particular class of triangulations of the three-sphere. The preliminary stage of the Hamiltonian analysis for the (3+1)-dimensional gauge gravity theory is undertaken.
8
Whitt, Brian. "Gravity : a quantum theory?" Thesis, University of Cambridge, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.304522.
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9
Hamilton, Craig S. "Measurements in quantum theory." Thesis, University of Strathclyde, 2009. http://oleg.lib.strath.ac.uk:80/R/?func=dbin-jump-full&object_id=11885.
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10
Hele, Timothy John Harvey. "Quantum transition-state theory." Thesis, University of Cambridge, 2014. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.708197.
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11
Galvão, Ernesto Fagundes. "Foundations od quantum theory and quantum information applications." Thesis, University of Oxford, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.249255.
Testo completo
12
Cortese, John A. Preskill John P. "Quantum information theory : classical communication over quantum channels /." Diss., Pasadena, Calif. : California Institute of Technology, 2004. http://resolver.caltech.edu/CaltechETD:etd-02172004-173217.
Testo completo
13
Palmer, Matthew. "Relativistic quantum information theory and quantum reference frames." Thesis, The University of Sydney, 2013. http://hdl.handle.net/2123/9891.
Testo completoAbstract (sommario):
This thesis is a compilation of research in relativistic quantum information theory, and research in quantum reference frames. The research in the former category provides a fundamental construction of quantum information theory of localised qubits in curved spacetimes. For example, this concerns quantum experiments on free-space photons and electrons in the vicinity of the Earth. From field theory a description of localised qubits that traverse classical trajectories in curved spacetimes is obtained, for photons and massive spin-1/2 fermions. The equations governing the evolution of the two-dimensional quantum state and its absolute phase are determined. Quantum information theory of these qubits is then developed. The Stern-Gerlach measurement formalism for massive spin-1/2 fermions is also derived from field theory. In the latter category of research, I consider the process of changing reference frames in the case where the reference frames are quantum systems. I find that, as part of this process, decoherence is necessarily induced on any quantum system described relative to these frames. I explore this process with examples involving quantum reference frames for phase and orientation. Quantifying the effect of changing quantum reference frames provides a theoretical description for this process in quantum experiments, and serves as a first step in developing a relativity principle for theories in which all objects including reference frames are necessarily quantum.
14
Patrascu, A. T. "The universal coefficient theorem and quantum field theory." Thesis, University College London (University of London), 2016. http://discovery.ucl.ac.uk/1476590/.
Testo completoAbstract (sommario):
During the end of the 1950's Alexander Grothendieck observed the importance of the coefficient groups in cohomology. Three decades later, he presented his ``Esquisse d'un Programme" to the main french funding body. This program also included the use of different coefficient groups in the definition of various (co)homologies. His proposal was rejected. Another three decades later, in the 21st century, his research proposal is considered one of the most inspiring and important collection of ideas in pure mathematics. His ideas brought together algebraic topology, geometry, Galois theory, etc. becoming the origin for several new branches of mathematics. Today, less than one year after his death, Grothendieck is considered one of the most influential mathematicians worldwide. His ideas were important for the proofs of some of the most remarkable mathematical problems like the Weil Conjectures, Mordell Conjectures and the solution of Fermat's last theorem. Grothendieck's dessins d'enfant have been used in mathematical physics in various domains. Seiberg-Witten curves, N=1 and N=2 gauge theories and matrix models are a few examples where his insights are relevant. In this thesis I try to connect the idea of cohomology with coefficients in various sheaves to some areas of modern research in physics. The applications are manifold: the universal coefficient theorem presents connections to the topological genus expansion invented by 't Hooft and applied to quantum chromodynamics (QCD) and string theory, but also to strongly coupled electronic systems or condensed matter physics. It also appears to give a more intuitive explanation for topological recursion formulas and the holomorphic anomaly equations. The counting of BPS states may also profit from this new perspective. Indeed, the merging of cohomology classes when a change in coefficient groups is implemented may be related to the wall-crossing formulas and the phenomenon of decay or coupling of BPS states while crossing stability walls. The $Ext$ groups appearing in universal coefficient theorems may be regarded as obstructions characterizing the phenomena occurring when BPS stability walls are being crossed. Another important aspect is the existence of dualities. These are the non-perturbative analogue of symmetry transformations. Until now, they were discovered more by accident or by educated guesswork. I show in this thesis that there exists an underlying structure to the dualities, a structure that connects them the number fields used as coefficients in (co)homologies. This observation makes a nontrivial connection between number theory and physics.
15
Eakins, Jonathan Simon. "Classical and quantum causality in quantum field theory, or, "the quantum universe"." Thesis, University of Nottingham, 2004. http://eprints.nottingham.ac.uk/10069/.
Testo completoAbstract (sommario):
Based on a number of experimentally verified physical observations, it is argued that the standard principles of quantum mechanics should be applied to the Universe as a whole. Thus, a paradigm is proposed in which the entire Universe is represented by a pure state wavefunction contained in a factorisable Hilbert space of enormous dimension, and where this statevector is developed by successive applications of operators that correspond to unitary rotations and Hermitian tests. Moreover, because by definition the Universe contains everything, it is argued that these operators must be chosen self-referentially; the overall dynamics of the system is envisaged to be analogous to a gigantic, self-governing, quantum computation. The issue of how the Universe could choose these operators without requiring or referring to a fictitious external observer is addressed, and this in turn rephrases and removes the traditional Measurement Problem inherent in the Copenhagen interpretation of quantum mechanics. The processes by which conventional physics might be recovered from this fundamental, mathematical and global description of reality are particularly investigated. Specifically, it is demonstrated that by considering the changing properties, separabilities and factorisations of both the state and the operators as the Universe proceeds though a sequence of discrete computations, familiar notions such as classical distinguishability, particle physics, space, time, special relativity and endo-physical experiments can all begin to emerge from the proposed picture. A pregeometric vision of cosmology is therefore discussed, with all of physics ultimately arising from the relationships occurring between the elements of the underlying mathematical structure. The possible origins of observable physics, including physical objects positioned at definite locations in an arena of apparently continuous space and time, are consequently investigated for a Universe that incorporates quantum theory as a fundamental feature. Overall, a framework for quantum cosmology is introduced and explored which attempts to account for the existence of time, space, matter and, eventually, everything else in the Universe, from a physically consistent perspective.
16
Rosaler, Joshua S. "Inter-theory relations in physics : case studies from quantum mechanics and quantum field theory." Thesis, University of Oxford, 2013. http://ora.ox.ac.uk/objects/uuid:1fc6c67d-8c8e-4e92-a9ee-41eeae80e145.
Testo completoAbstract (sommario):
I defend three general claims concerning inter-theoretic reduction in physics. First, the popular notion that a superseded theory in physics is generally a simple limit of the theory that supersedes it paints an oversimplified picture of reductive relations in physics. Second, where reduction specifically between two dynamical systems models of a single system is concerned, reduction requires the existence of a particular sort of function from the state space of the low-level (purportedly more accurate and encompassing) model to that of the high-level (purportedly less accurate and encompassing) model that approximately commutes, in a specific sense, with the rules of dynamical evolution prescribed by the models. The third point addresses a tension between, on the one hand, the frequent need to take into account system-specific details in providing a full derivation of the high-level theory’s success in a particular context, and, on the other hand, a desire to understand the general mechanisms and results that under- write reduction between two theories across a wide and disparate range of different systems; I suggest a reconciliation based on the use of partial proofs of reduction, designed to reveal these general mechanisms of reduction at work across a range of systems, while leaving certain gaps to be filled in on the basis of system-specific details. After discussing these points of general methodology, I go on to demonstrate their application to a number of particular inter-theory reductions in physics involving quantum theory. I consider three reductions: first, connecting classical mechanics and non-relativistic quantum mechanics; second,connecting classical electrodynamics and quantum electrodynamics; and third, connecting non-relativistic quantum mechanics and quantum electrodynamics. I approach these reductions from a realist perspective, and for this reason consider two realist interpretations of quantum theory - the Everett and Bohm theories - as potential bases for these reductions. Nevertheless, many of the technical results concerning these reductions pertain also more generally to the bare, uninterpreted formalism of quantum theory. Throughout my analysis, I make the application of the general methodological claims of the thesis explicit, so as to provide concrete illustration of their validity.
17
Timpson, Christopher Gordon. "Quantum information theory and the foundations of quantum mechanics." Thesis, University of Oxford, 2004. http://ora.ox.ac.uk/objects/uuid:457a0257-016d-445d-a6b2-f1bdd2648523.
Testo completoAbstract (sommario):
This thesis is a contribution to the debate on the implications of quantum information theory for the foundational problems of quantum mechanics. In Part I an attempt is made to shed some light on the nature of information and quantum information theory. It is emphasized that the everyday notion of information is to be firmly distinguished from the technical notions arising in information theory; however it is maintained that in both settings ‘information’ functions as an abstract noun, hence does not refer to a particular or substance. The popular claim ‘Information is Physical’ is assessed and it is argued that this proposition faces a destructive dilemma. Accordingly, the slogan may not be understood as an ontological claim, but at best, as a methodological one. A novel argument is provided against Dretske’s (1981) attempt to base a semantic notion of information on ideas from information theory. The function of various measures of information content for quantum systems is explored and the applicability of the Shannon information in the quantum context maintained against the challenge of Brukner and Zeilinger (2001). The phenomenon of quantum teleportation is then explored as a case study serving to emphasize the value of recognising the logical status of ‘information’ as an abstract noun: it is argued that the conceptual puzzles often associated with this phenomenon result from the familiar error of hypostatizing an abstract noun. The approach of Deutsch and Hayden (2000) to the questions of locality and information flow in entangled quantum systems is assessed. It is suggested that the approach suffers from an equivocation between a conservative and an ontological reading; and the differing implications of each is examined. Some results are presented on the characterization of entanglement in the Deutsch-Hayden formalism. Part I closes with a discussion of some philosophical aspects of quantum computation. In particular, it is argued against Deutsch that the Church-Turing hypothesis is not underwritten by a physical principle, the Turing Principle. Some general morals are drawn concerning the nature of quantum information theory. In Part II, attention turns to the question of the implications of quantum information theory for our understanding of the meaning of the quantum formalism. Following some preliminary remarks, two particular information-theoretic approaches to the foundations of quantum mechanics are assessed in detail. It is argued that Zeilinger’s (1999) Foundational Principle is unsuccessful as a foundational principle for quantum mechanics. The information-theoretic characterization theorem of Clifton, Bub and Halvorson (2003) is assessed more favourably, but the generality of the approach is questioned and it is argued that the implications of the theorem for the traditional foundational problems in quantum mechanics remains obscure.
18
Di, Mauro Marco. "Flavor mixing in quantum field theory and quantum information." Doctoral thesis, Universita degli studi di Salerno, 2011. http://hdl.handle.net/10556/194.
Testo completoAbstract (sommario):
2009 - 2010<br>After reviewing the formalism for describing flavor mixing, both in Quantum Mechanics
and Quantum Field Theory, some consequences along three different directions are studied.
First, it is proposed that flavor mixing can be a viable candidate for spontaneous
supersymmetry breaking, due to the nontrivial vacuum structure induced by it. After
the statement of the conjecture, an explicit proof in a simple case is given. Second, the
properties of flavor states as entangled states both in QM and QFT are studied. By interpreting
such states as multipartite mode–entangled states, both the correlation content and
the decoherence effects are studied. Third, a possible new interpretation of flavor mixing
as induced by an external vector field is proposed, and it is shown how this solves some
problems of the usual formalism in connection with Lorentz and Poincar´e violation. Some
phenomenological consequences of this picture are pointed out, as well as some intriguing
physical interpretations. [edited by author]<br>IX n.s.
19
Sentís, Manuel Lorenzo. "Quantum theory of open systems." Zürich : ETH, Eidgenössische Technische Hochschule Zürich, Institut für Theoretische Physik, 2002. http://e-collection.ethbib.ethz.ch/show?type=dipl&nr=172.
Testo completo
20
García, Díaz María. "The theory of quantum coherence." Doctoral thesis, Universitat Autònoma de Barcelona, 2020. http://hdl.handle.net/10803/670162.
Testo completoAbstract (sommario):
La coherència quàntica, o la propietat dels sistemes que es troben en
una superposició d’estats capaç de donar lloc a patrons d’interferència en els
experiments adequats, és el segell distintiu de la mecànica quàntica. Més enllà
de les seves fascinants implicacions epistemològiques, la coherència quàntica
resulta també un recurs valuós a l’hora de dur a terme diferents tasques
quàntic-informacionals i ha estat fins i tot emprada en la descripció de certs
processos biològics. Per aquest motiu s’ha fet necessari el desenvolupament
d’una teoria de recursos que formalitzi rigorosament la noció de coherència, i
que permeti així quantificar la coherència present en els sistemes físics, així
com estudiar la seva manipulació amb vista a un millor aprofitament d’aquest
recurs. Aquesta tesi doctoral pretén contribuir a la teoria de la coherència de
la següent manera.
En primer lloc, demostrem que la coherència, tal com la teoria la formalitza,
està sòlidament ancorada en la física dels interferòmetres —almenys en el
context de les Operacions Estrictament Incoherents—, i encarna, per tant, el
seu propi principi operacional.
En segon lloc, després de fer notar que els estats poden ser entesos com a
canals de “output” constant, emprenem la generalització de la teoria de la
coherència dels estats a la teoria dels canals. En concret, proposem diverses
maneres de mesurar el contingut en coherència d’un canal quàntic i el calculem
considerant dues classes diferents d’operacions del tipus “free”: Operacions
Incoherents i Operacions Màximament Incoherents.
Finalment, investiguem si la coherència pot ser també testimoni d’alguna
manifestació de no classicitat diferent dels propis efectes interferomètrics.
En particular, analitzem la connexió de la coherència amb la no classicitat
dels processos estocàstics quàntics, tant en el règim markovià com en el no
markovià.<br>La coherencia cuántica, o la propiedad de los sistemas que se encuentran en
una superposición de estados capaz de dar lugar a patrones de interferencia en
los experimentos adecuados, es el sello distintivo de la mecánica cuántica. Más
allá de sus fascinantes implicaciones epistemológicas, la coherencia cuántica
resulta también un recurso valioso a la hora de llevar a cabo diferentes tareas
cuántico-informacionales y ha sido incluso empleada en la descripción de
ciertos procesos biológicos. Por este motivo se ha hecho necesario el desarrollo
de una teoría de recursos que formalice rigurosamente la noción de coherencia,
y que permita así cuantificar la coherencia presente en los sistemas físicos, así
como estudiar su manipulación con vistas a un mejor aprovechamiento de este
recurso. Esta tesis doctoral pretende contribuir a la teoría de la coherencia
del siguiente modo.
En primer lugar, demostramos que la coherencia, tal y como la teoría la
formaliza, está sólidamente anclada en la física de los interferómetros —al
menos en el contexto de las Operaciones Estrictamente Incoherentes—, con
lo que encarna su propio principio operacional.
En segundo lugar, tras hacer notar que los estados pueden ser entendidos
como canales de “output” constante, emprendemos la generalización de la
teoría de la coherencia de los estados a la teoría de los canales. En concreto,
proponemos diversas maneras de medir el contenido en coherencia de un
canal cuántico y lo calculamos considerando dos clases diferentes de opera-
ciones de tipo “free”: Operaciones Incoherentes y Operaciones Máximamente
Incoherentes.
Finalmente, investigamos si la coherencia puede ser también testigo de
alguna manifestación de no clasicidad distinta de los propios efectos inter-
ferométricos. En particular, analizamos la conexión de la coherencia con
la no clasicidad de los procesos estocásticos cuánticos, tanto en el régimen
markoviano como en el no markoviano.<br>Quantum coherence, or the property of systems which are in a superpo-
sition of states yielding interference patterns in suitable experiments, is the
main hallmark of departure of quantum mechanics from classical physics.
Besides its fascinating epistemological implications, quantum coherence also
turns out to be a valuable resource for quantum information tasks, and has
even been used in the description of fundamental biological processes. This
calls for the development of a resource theory which rigorously formalizes
the notion of coherence, that further allows both to quantify the coherence
present in physical systems and to study its manipulation in order to better
leverage it. This thesis intends to make a contribution to the recently built
resource theory of coherence in a number of ways.
First, we show that coherence, as formalized by its resource theory, is
soundly grounded in the physics of interferometers—at least in the con-
text of Strictly Incoherent Operations—and thus embodies its operational
foundations.
Second, we note that states can be thought of as constant-output channels,
and start to generalize the coherence theory of states to that of channels.
In particular, we propose several measures of the coherence content of a
channel and further compute them when considering two different classes
of free operations: Incoherent Operations and the largest set of Maximally
Incoherent Operations.
Finally, we investigate the question whether coherence can witness some
other manifestations of non-classicality (we mean, beyond interference effects).
In particular, we analyze the connection of coherence to the non-classicality of
quantum stochastic processes both in the Markovian and in the non-Markovian
regimes.
21
Esposito, Massimiliano. "Kinetic theory for quantum nanosystems." Doctoral thesis, Universite Libre de Bruxelles, 2004. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/211088.
Testo completoAbstract (sommario):
In this thesis, we investigate the emergence of kinetic processes in finite quantum systems. We first generalize the Redfield theory to describe the dynamics of a small quantum system weakly interacting with an environment of finite heat capacity. We then study in detail the spin-GORM model, a model made of a two-level system interacting with a random matrix environment. By doing this, we verify our new theory and find a critical size of the environment over which kinetic processes occur. We finally study the emergence of a diffusive transport process, on a finite tight-binding subsystem interacting with a fast environment, when the size of subsystem exceeds a critical value.<br>Doctorat en sciences, Spécialisation chimie<br>info:eu-repo/semantics/nonPublished
22
Wilkins, Andrew H. "Topics in modern quantum theory /." Title page, table of contents and abstract only, 1998. http://web4.library.adelaide.edu.au/theses/09PH/09phw6837.pdf.
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23
Faghfoor, Maghrebi Mohammad. "Information gain in quantum theory." Thesis, University of British Columbia, 2008. http://hdl.handle.net/2429/2724.
Testo completoAbstract (sommario):
In this thesis I address the fundamental question that how the information
gain is possible in the realm of quantum mechanics where a single measurement
alters the state of the system. I study an ensemble of particles in some unknown (but product) state in detail and suggest an optimal way of gaining the maximum information and also quantify the corresponding information exactly. We find a rather novel result which is quite different from other well-known definitions of the information gain in quantum theory.
24
Galiautdinov, Andry. "Quantum theory of elementary processes." Diss., Georgia Institute of Technology, 2002. http://hdl.handle.net/1853/28007.
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25
Vedral, Vlatko. "Quantum information theory of entanglement." Thesis, Imperial College London, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.299786.
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26
Ivin, Marko. "Topics in quantum field theory." Thesis, Imperial College London, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.410042.
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27
Kirrander, Adam. "Quantum defect theory of molecules." Thesis, University of Oxford, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.422660.
Testo completo
28
Girolami, Davide. "Quantum correlations in information theory." Thesis, University of Nottingham, 2013. http://eprints.nottingham.ac.uk/13397/.
Testo completoAbstract (sommario):
The project concerned the study of quantum correlations (QC) in compound systems, i.e. statistical correlations more general than entanglement which are predicted by quantum mechanics but not described in any classical scenario. I aimed to understand the technical and operational properties of the measures of QC, their interplay with entanglement quantifiers and the experimental accessibility. In the first part of my research path, after having acquired the conceptual and technical rudiments of the project, I provided solutions for some computational issues: I developed analytical and numerical algorithms for calculating bipartite QC in finite dimensional systems. Then, I tackled the problem of the experimental detection of QC. There is no Hermitian operator associated with entanglement measures, nor with QC ones. However, the information encoded in a density matrix is redundant to quantify them, thus the full knowledge of the state is not required to accomplish the task. I reported the first protocol to measure the QC of an unknown state by means of a limited number of measurements, without performing the tomography of the state. My proposal has been implemented experimentally in a NMR (Nuclear Magnetic Resonance) setting. In the final stage of the project, I explored the foundational and operational merits of QC. I showed that the QC shared by two subsystems yield a genuinely quantum kind of uncertainty on single local observables. The result is a promising evidence of the potential exploitability of separable (unentangled) states for quantum metrology in noisy conditions.
29
Mackman, Stephen William. "Gauge fields and quantum theory." Thesis, Durham University, 1996. http://etheses.dur.ac.uk/5183/.
Testo completoAbstract (sommario):
This thesis investigates the problems within quantum mechanics for the Bohm model caused by Lorentz invariance and the existence of photons. A model describing the electromagnetic interactions of fermions is produced which does not use photons and avoids these problems. It is then shown how these techniques can be extended to linearised gravitational interactions. Finally semi-classical gravity and the possibility of gravitationally induced collapse are considered. In the first part of the thesis two modifications to the Bohm model are proposed. One takes account of Lorentz invariance, and the other is capable of describing photons. The main part of the thesis is devoted to describing interactions in a way which does not need extra gauge particles, and so is in the same spirit as the Bohm model. Electromagnetic interactions are formed using a 4-potential operator which is calculated directly, without imposing commutation relations on the 4-potential. This leads to an expression for the 4-potential in terms of the Dirac field, and results in there being no photon states. There are various ways of constructing the theory and the scattering matrix of standard QED is compared to the scattering matrix of the version which appears to be most similar. Considering only the matrix elements between fermion states, they are found to be in agreement at the order e(^2), but disagree at the order e(^4). It follows that this model, which otherwise appears to be a self consistent theory of QED, cannot agree with experiment. The same techniques can be used to quantise General Relativity when it is linearised about the Minkowski metric. The metric operator is calculated in terms of the Dirac field. The interaction is similar to that of electrodynamics, being of order 4 in the Dirac field. Finally issues relating to gravitational collapse are discussed.
30
Russell, I. H. "Calculations in quantum field theory." Thesis, University of Newcastle Upon Tyne, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.328134.
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31
Mander, Gillian Linda. "Quantum theory of laser amplifiers." Thesis, University of Essex, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.290741.
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32
Butterley, Paul. "Topics in quantum information theory." Thesis, University of York, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.444697.
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33
Roberts, Justin Deritter. "Quantum invariants via skein theory." Thesis, University of Cambridge, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.319336.
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34
Lai, Yinchieh. "Quantum theory of optical solitons." Thesis, Massachusetts Institute of Technology, 1991. http://hdl.handle.net/1721.1/42512.
Testo completoAbstract (sommario):
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1991.<br>Includes bibliographical references (leaves 93-98).<br>v by Yinchieh Lai.<br>Ph.D.
35
Maynard, Glenn. "Complex Numbers in Quantum Theory." Thesis, University of North Texas, 2015. https://digital.library.unt.edu/ark:/67531/metadc804988/.
Testo completoAbstract (sommario):
In 1927, Nobel prize winning physicist, E. Schrodinger, in correspondence with Ehrenfest, wrote the following about the new theory: “What is unpleasant here, and indeed directly to be objected to, is the use of complex numbers. Psi is surely fundamentally a real function.” This seemingly simple issue remains unexplained almost ninety years later. In this dissertation I elucidate the physical and theoretical origins of the complex requirement. I identify a freedom/constraint situation encountered by vectors when, employed in accordance with adopted quantum representational methodology, and representing angular momentum states in particular. Complex vectors, quite simply, provide more available adjustable variables than do real vectors. The additional variables relax the constraint situation allowing the theory’s representational program to carry through. This complex number issue, which lies at the deepest foundations of the theory, has implications for important issues located higher in the theory. For example, any unification of the classical and quantum accounts of the settled order of nature, will rest squarely on our ability to account for the introduction of the imaginary unit.
36
Oniga, Teodora. "Theory of quantum gravitational decoherence." Thesis, University of Aberdeen, 2016. http://digitool.abdn.ac.uk:80/webclient/DeliveryManager?pid=231085.
Testo completoAbstract (sommario):
As quantum systems can never be isolated from their environment entirely, it is expected that the spacetime fluctuations will influence their evolution. In particular, the environmental interaction may cause the loss of quantum superpositions, or decoherence. In this thesis, we examine the effects of the quantised environmental background on a range of bosonic fields in the formalism of open quantum systems. We first quantise linearised gravity in a gauge invariant way, using Dirac's constraint quantisation. We then use the influence functional technique to obtain an exact master equation for general bosonic matter interacting with weak gravity. As an application of this, we investigate the decoherence of free scalar, electromagnetic and gravitational fields. For long-time decoherence, under the Markov approximation, the dissipative terms in the master equation vanish, leading to no decay of quantum interferences. As a short-time effect, we study the master equation for a many particle state of a free scalar field, massive or massless and relativistic or non-relativistic. We find that in this case, the particles exhibit a counterintuitive behaviour of bundling towards the same quantum state that is not shared by the single particle master equation. Such collective effects, as well as possible long-time decoherence for fields in an external potential may have important implications in setting limits for precision measurements and astronomical observations.
37
Abeyesinghe, Anura Yamesh Preskill John P. "Unification of quantum information theory /." Diss., Pasadena, Calif. : Caltech, 2006. http://resolver.caltech.edu/CaltechETD:etd-05252006-222551.
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38
Allen, John-Mark. "Reality, causality, and quantum theory." Thesis, University of Oxford, 2017. http://ora.ox.ac.uk/objects/uuid:01413eef-0944-4ec5-ad53-ac8378bcf4be.
Testo completoAbstract (sommario):
Quantum theory describes our universe incredibly successfully. To our classically-inclined brains, however, it is a bizarre description that requires a reimagining of what fundamental reality, or 'ontology', could look like. This thesis examines different ontological features in light of the success of quantum theory, what it requires, and what it rules out. While these investigations are primarily foundational, they also have relevance to quantum information, quantum communication, and experiments on quantum systems. The way that quantum theory describes the state of a system is one of its most unintuitive features. It is natural, therefore, to ask whether a similarly strange description of states is required on an ontological level. This thesis proves that almost all quantum superposition states for d > 3 dimensions must be real - that is, present in the ontology in a well-defined sense. This is a strong requirement which prevents intuitive explanations of the many quantum phenomena which are based on superpositions. A new theorem is also presented showing that quantum theory is incompatible with macro-realist ontologies, where certain physical quantities must always have definite values. This improves on the Leggett-Garg argument, which also aims to prove incompatibility with macro-realism but contains loopholes. Variations on both of these results that are error-tolerant (and therefore amenable to experimentation) are presented, as well as numerous related theorems showing that the ontology of quantum states must be somewhat similar to the quantum states themselves in various specific ways. Extending these same methods to quantum communication, a simple proof is found showing that an exponential number of classical bits are required to communicate a linear number of qubits. That is, classical systems are exponentially bad at storing quantum data. Causal influences are another part of ontology where quantum theory demands a revision of our classical notions. This follows from the outcomes of Bell experiments, as rigorously shown in recent analyses. Here, the task of constructing a native quantum framework for reasoning about causal influences is tackled. This is done by first analysing the simple example of a common cause, from which a quantum version of Reichenbach's principle is identified. This quantum principle relies on an identification of quantum conditional independence which can be defined in four ways, each naturally generalising a corresponding definition for classical conditional independence. Not only does this allow one to reason about common causes in a quantum experiments, but it can also be generalised to a full framework of quantum causal models (mirroring how classical causal models generalise Reichenbach's principle). This new definition of quantum causal models is illustrated by examples and strengthened by it's foundation on a robust quantum Reichenbach's principle. An unusual, but surprisingly fruitful, setting for considering quantum ontology is found by considering time travel to the past. This provides a testbed for different ontological concepts in quantum theory and new ways to compare classical and quantum frameworks. It is especially useful for comparing computational properties. In particular, time travel introduces non-linearity to quantum theory, which brings (sometimes implicit) ontological assumptions to the fore while introducing strange new abilities. Here, a model for quantum time travel is presented which arguably has fewer objectionable features than previous attempts, while remaining similarly well-motivated. This model is discussed and compared with previous quantum models, as well as with the classical case. Together, these threads of investigation develop a better understanding of how quantum theory affects possible ontologies and how ontological prejudices influence quantum theory.
39
Ho, Ki-hiu, and 何其曉. "Study of quantum low density parity check and quantum degeneratecodes." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2009. http://hub.hku.hk/bib/B41897109.
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40
Månsson, Anders. "Quantum State Analysis : Probability theory as logic in Quantum mechanics." Doctoral thesis, KTH, Mikroelektronik och tillämpad fysik, MAP, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-4417.
Testo completoAbstract (sommario):
Quantum mechanics is basically a mathematical recipe on how to construct physical models. Historically its origin and main domain of application has been in the microscopic regime, although it strictly seen constitutes a general mathematical framework not limited to this regime. Since it is a statistical theory, the meaning and role of probabilities in it need to be defined and understood in order to gain an understanding of the predictions and validity of quantum mechanics. The interpretational problems of quantum mechanics are also connected with the interpretation of the concept of probability. In this thesis the use of probability theory as extended logic, in particular in the way it was presented by E. T. Jaynes, will be central. With this interpretation of probabilities they become a subjective notion, always dependent on one's state of knowledge or the context in which they are assigned, which has consequences on how things are to be viewed, understood and tackled in quantum mechanics. For instance, the statistical operator or density operator, is usually defined in terms of probabilities and therefore also needs to be updated when the probabilities are updated by acquisition of additional data. Furthermore, it is a context dependent notion, meaning, e.g., that two observers will in general assign different statistical operators to the same phenomenon, which is demonstrated in the papers of the thesis. It is also presented an alternative and conceptually clear approach to the problematic notion of "probabilities of probabilities", which is related to such things as probability distributions on statistical operators. In connection to this, we consider concrete numerical applications of Bayesian quantum state assignment methods to a three-level quantum system, where prior knowledge and various kinds of measurement data are encoded into a statistical operator, which can then be used for deriving probabilities of other measurements. The thesis also offers examples of an alternative quantum state assignment technique, using maximum entropy methods, which in some cases are compared with the Bayesian quantum state assignment methods. Finally, the interesting and important problem whether the statistical operator, or more generally quantum mechanics, gives a complete description of "objective physical reality" is considered. A related concern is here the possibility of finding a "local hidden-variable theory" underlying the quantum mechanical description. There have been attempts to prove that such a theory cannot be constructed, where the most well-known impossibility proof claiming to show this was given by J. S. Bell. In connection to this, the thesis presents an idea for an interpretation or alternative approach to quantum mechanics based on the concept of space-time.<br>QC 20100810
41
Månsson, Anders. "Quantum state analysis : probability theory as logic in Quantum mechanics /." Stockholm : Department of Microelectronics and Applied Physics, Royal Institute of Technology, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-4417.
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Thorwart, Joerg Christian Hermann. "Quantum cosmology and the decoherent histories approach to quantum theory." Thesis, Imperial College London, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.397623.
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Constantin, Carmen Maria. "Sheaf-theoretic methods in quantum mechanics and quantum information theory." Thesis, University of Oxford, 2015. https://ora.ox.ac.uk/objects/uuid:788d9d90-8fb1-4e1d-a0fa-346ba64d228a.
Testo completoAbstract (sommario):
In this thesis we use the language of sheaf theory in an attempt to develop a deeper understanding of some of the fundamental differences - such as entanglement, contextuality and non-locality - which separate quantum from classical physics. We first present, based on the work of Abramsky and Brandenburger [2], how sheaves, defined over certain posets of physically meaningful contexts, give a natural setting for capturing and analysing important quantum mechanical phenomena, such as quantum non-locality and contextuality. We also describe how this setting naturally leads to a three level hierarchy of quantum contextuality: weak contextuality, logical non-locality and strong contextuality. One of the original contributions of this thesis is to use these insights in order to classify a particular class of multipartite entangled states, which we have named balanced states with functional dependencies. Almost all of these states turn out to be at least logically non-local, and a number of them even turn out to be strongly contextual. We then further extend this result by showing that in fact all n-qubit entangled states, with the exception of tensor products of single-qubit and bipartite maximally-entangled states, are logically non-local. Moreover, our proof is constructive: given any n-qubit state, we present an algorithm which produces n + 2 local observables witnessing its logical non-locality. In the second half of the thesis we use the same basic principle of sheaves defined over physically meaningful contexts, in order to present an elegant mathematical language, known under the name of the Topos Approach [62], in which many quan- tum mechanical concepts, such as states, observables, and propositions about these, can be expressed. This presentation is followed by another original contribution in which we show that the language of the Topos Approach is as least as expressive, in logical terms, as traditional quantum logic. Finally, starting from a topos-theoretic perspective, we develop the construction of contextual entropy in order to give a unified treatment of classical and quantum notions of information theoretic entropy.
44
Farhi, David. "Jets and Metastability in Quantum Mechanics and Quantum Field Theory." Thesis, Harvard University, 2016. http://nrs.harvard.edu/urn-3:HUL.InstRepos:26718743.
Testo completoAbstract (sommario):
I give a high level overview of the state of particle physics in the introduction, accessible without any background in the field. I discuss improvements of theoretical and statistical methods used for collider physics. These include telescoping jets, a statistical method which was claimed to allow jet searches to increase their sensitivity by considering several interpretations of each event. We find that indeed multiple interpretations extend the power of searches, for both simple counting experiments and powerful multivariate fitting experiments, at least for h->bb at the LHC. Then I propose a method for automation of background calculations using SCET by appropriating the technology of Monte Carlo generators such as MadGraph.
In the third chapter I change gears and discuss the future of the universe. It has long been known that our pocket of the standard model is unstable; there is a lower-energy configuration in a remote part of the configuration space, to which our universe will, eventually, decay. While the timescales involved are on the order of 10^400 years (depending on how exactly one counts) and thus of no immediate worry, I discuss the shortcomings of the standard methods and propose a more physically motivated derivation for the decay rate. I then make various observations about the structure of decays in quantum field theory.<br>Physics
45
Burns, Daniel Kevin. "Matter quantum corrections in the quantum theory of Einstein gravity." Thesis, University of Manchester, 2015. https://www.research.manchester.ac.uk/portal/en/theses/matter-quantum-corrections-in-the-quantum-theory-of-einstein-gravity(f3b070c6-74d2-4eee-9953-6eab423673ca).html.
Testo completoAbstract (sommario):
In this thesis, we revisit the calculation of matter quantum effects on the graviton self-energy on a flat Minkowski background, with the aim to acquire a deeper understanding of the mechanism that renders the graviton massless. We first review some essential background material of the framework of quantum field theory pertaining to the understanding of the classification of massless states on the Hilbert space. Using these techniques, along with the development of some preliminaries of general relativity, we show that the gravitational wave obtained through the linearised gravity equation must have only two polarisations of helicity σ = ±2; we infer that these correspond to massless graviton states of the same helicity. Then, by considering an Abelian Higgs model with minimal coupling to gravity, we argue that the graviton propagator obtained after radiative corrections must have a pole corresponding to the propagation of a massless particle if the graviton propagator is transverse. To show this transversality, we derive a new low-energy theorem which directly relates the radiative corrections of thecosmological constant to the longitudinal modes of the graviton self-energy to all orders in perturbation theory; we show this relation explicitly at the one-loop level. In the same Abelian Higgs model, we also calculate the matter quantum corrections to the Newtonian potential and present new formulae in terms of modified Bessel and Struve functions of the particle masses in the loop. We show that the correction to the Newtonian potential exponentially falls-off with the distance r, once the nonrelativistic limit with respect to the nonzero loop masses are carefully considered. For massless scalars, fermions, and gauge bosons in the loops, we recover the well-known results presented in the literature.
46
Ho, Ki-hiu. "Study of quantum low density parity check and quantum degenerate codes." Click to view the E-thesis via HKUTO, 2009. http://sunzi.lib.hku.hk/hkuto/record/B41897109.
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Cui, Ping. "Quantum dissipation theory and applications to quantum transport and quantum measurement in mesoscopic systems /." View abstract or full-text, 2006. http://library.ust.hk/cgi/db/thesis.pl?CHEM%202006%20CUI.
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Dorier, Vincent. "Quantum theory of light in linear media : applications to quantum optics and quantum plasmonics." Thesis, Bourgogne Franche-Comté, 2020. http://www.theses.fr/2020UBFCK006.
Testo completoAbstract (sommario):
Nous développons une méthode de quantification du champ électromagnétique en interaction linéaire avec les milieux passifs d'une part, et les milieux actifs (plasmoniques) d'autre part. Cette méthode repose sur la construction d'une structure Hamiltonienne compatible avec les équations de Maxwell, puis sur un principe de correspondence et la définition d'un espace de Fock des états quantiques. Nous utilisons les résultats de la théorie quantique pour étudier la propagation de photons dans des environnements diéléctriques et l'émission de plasmons uniques<br>We develop a method of quantization of the electromagnetic field interacting with passive media on one hand, and active (plasmonic) media on the other hand. This method relies on the construction of a Hamiltonian structure compatible with the Maxwell equations, and then on a principle of correspondence and the definition of a Fock space of quantum states. We use the results of the quantum theory to study the propagation of photons in dielectric environments and the emission of single plasmons
49
Rondelli, Andrea. "Functional methods in quantum field theory." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2018. http://amslaurea.unibo.it/15839/.
Testo completoAbstract (sommario):
Iniziamo introducendo l'integrazione su manifold di Hilbert, tramite l'approssimazione dello spazio tangente alla varietà. Passiamo poi a descrivere due tecniche per regolarizzare integrali funzionali o di cammino quadratici (che presentano un laplaciano nell'azione): la regolarizzazione e rinormalizzazione tramite zeta function e il cutoff nel tempo proprio. Cerchiamo di confrontare i due diversi risultati (finiti) così ottenuti. Sussessivamente applichiamo l'integrazione funzionale agli integrali di cammino usando il formalismo della quantizzazione in qp-simboli ottenendo così un'ampiezza di probabilità. Infine iniziamo a sviluppare questi argomenti per le teorie di gauge. In particolare ci soffermeremo su vari aspetti geometrici dei campi di gauge, quali la connessione e la curvatura (usando il formalismo dei fibrati). In ultimo introduciamo l'integrazione funzionale per le teorie di gauge.
50
at, Andreas Cap@esi ac. "Quantum Field Theory as Dynamical System." ESI preprints, 2001. ftp://ftp.esi.ac.at/pub/Preprints/esi1055.ps.
Testo completo