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Quasi-one-dimensional quantum models are ideal for theoretically exploring the physical phenomena associated with strong correlations. In this thesis we study three examples where strong correlations play an important role in the static or dynamic properties of the system. Firstly, we examine the behaviour of a doped fermionic two-leg ladder in which umklapp interactions are present. Such interactions arise at special band fillings and can be induced by the formation of charge density wave order in an array of two-leg ladders with long-range (three-dimensional) interactions. For the umklapp which arises from the half-filling of one of the bands, we show that the low-energy theory has a number of phases, including a strong coupling regime in which the dominant fluctuations are superconducting in nature. These superconducting fluctuations carry a finite wave vector – they are the one-dimensional analogue of Fulde-Ferrell-Larkin-Ovchinnikov superconductivity. In a second example, we consider a quantum spin model which captures the essential one-dimensional physics of CoNb₂O₆, a quasi-one-dimensional Ising ferromagnet. Motivated by high-resolution inelastic neutron scattering experiments, we calculate the dynamical structure in the paramagnetic phase and show that a small misalignment of the transverse field can lead to quasi-particle breakdown – a surprising broadening in the single particle mode observed in experiment. Finally, we study the out-of-equilibrium dynamics of a model with tuneable integrability breaking. When integrability is broken by the presence of weak interactions, we show that the system relaxes to a non-thermal state on intermediate time scales, the so-called “prethermalization plateau”. We describe the approximately stationary behaviour in this regime by constructing a generalised Gibbs ensemble with charges deformed to leading order in perturbation theory. Expectation values of these charges are time-independent, but interestingly the charges do not commute with the Hamiltonian to leading order in perturbation theory. Increasing the strength of the integrability breaking interactions leads to behaviour compatible with thermalisation. In each case we use a combination of perturbative analytical calculations and non-perturbative numerical computations to study the problem at hand.

Thesis (MSc (Physics))--University of Stellenbosch, 2010. / ENGLISH ABSTRACT: Non-commutative quantum mechanics is a generalisation of quantum mechanics which incorporates the notion of a fundamental shortest length scale by introducing non-commuting position coordinates. Various theories of quantum gravity indicate the existence of such a shortest length scale in nature. It has furthermore been realised that certain condensed matter systems allow effective descriptions in terms of non-commuting coordinates. As a result, non-commutative quantum mechanics has received increasing attention recently. A consistent formulation and interpretation of non-commutative quantum mechanics, which unambiguously defines position measurement within the existing framework of quantum mechanics, was recently presented by Scholtz et al. This thesis builds on the latter formalism, extends it to many-particle systems and links it up with non-commutative quantum field theory via second quantisation. It is shown that interactions of particles, among themselves and with external potentials, are altered as a result of the fuzziness induced by non-commutativity. For potential scattering, generic increases are found for the differential and total scattering cross sections. Furthermore, the recovery of a scattering potential from scattering data is shown to involve a suppression of high energy contributions, disallowing divergent interaction forces. Likewise, the effective statistical interaction among fermions and bosons is modified, leading to an apparent violation of Pauli’s exclusion principle and foretelling implications for thermodynamics at high densities. / AFRIKAANSE OPSOMMING: Nie-kommutatiewe kwantummeganika is ’n veralgemening van kwantummeganika wat die idee van ’n fundamentele kortste lengteskaal invoer d.m.v. nie-kommuterende ko¨ordinate. Verskeie teorie¨e van kwantum-grawitasie dui op die bestaan van so ’n kortste lengteskaal in die natuur. Dit is verder uitgewys dat sekere gekondenseerde materie sisteme effektiewe beskrywings in terme van nie-kommuterende koordinate toelaat. Gevolglik het die veld van nie-kommutatiewe kwantummeganika onlangs toenemende aandag geniet. ’n Konsistente formulering en interpretasie van nie-kommutatiewe kwantummeganika, wat posisiemetings eenduidig binne bestaande kwantummeganika raamwerke defineer, is onlangs voorgestel deur Scholtz et al. Hierdie tesis brei uit op hierdie formalisme, veralgemeen dit tot veeldeeltjiesisteme en koppel dit aan nie-kommutatiewe kwantumveldeteorie d.m.v. tweede kwantisering. Daar word gewys dat interaksies tussen deeltjies en met eksterne potensiale verander word as gevolg van nie-kommutatiwiteit. Vir potensiale verstrooi ¨ıng verskyn generiese toenames vir die differensi¨ele and totale verstroi¨ıngskanvlak. Verder word gewys dat die herkonstruksie van ’n verstrooi¨ıngspotensiaal vanaf verstrooi¨ıngsdata ’n onderdrukking van ho¨e-energiebydrae behels, wat divergente interaksiekragte verbied. Soortgelyk word die effektiewe statistiese interaksie tussen fermione en bosone verander, wat ly tot ’n skynbare verbreking van Pauli se uitsluitingsbeginsel en dui op verdere gevolge vir termodinamika by ho¨e digthede.

The knowledge of the packing behaviour of small organic compounds in crystal lattices is of great importance for industries dealing with solid state materials. The properties of materials depend on how the molecules arrange themselves in a crystalline environment. Crystal structure prediction provides a theoretical approach through the application of computational strategies to seek possible crystal packing arrangements (or polymorphs) a compound may adopt. Based on the chemical diagrams, this thesis investigates polymorphism of several small organic compounds. Plausible crystal packings of those compounds are generated, and their lattice energies are minimised using molecular mechanics and/or quantum mechanics methods. Most of the work presented here is conducted using two software packages commercially available in this field, Polymorph Predictor of Materials Studio 4.0 and GRACE 1.0. In general, the computational techniques implemented in GRACE are very good at reproducing the geometries of the crystal structures corresponding to the experimental observations of the compounds, in addition to describing their solid state energetics correctly. Complementing the CSP results obtained using GRACE with isostructurality offers a route by which new potential polymorphs of the targeted compounds might be crystallised using the existing experimental data. Based on all calculations in this thesis, four new potential polymorphs for four different compounds, which have not yet been determined experimentally, are predicted to exist and may be obtained under the right crystallisation conditions. One polymorph is expected to crystallise under pressure. The remaining three polymorphs might be obtained by using a seeding technique or the utilisation of suitable tailor made additives.

In this thesis I develop a formalism for analyzing quantum optics in photonic crystal slab cavities which may be coupled, lossy, and non-orthogonal. Using a tight-binding approximation I find classical coupled-cavity quasimodes which overlap in space and frequency. These classical modes are used to develop a multiphoton basis for quantum optics with non-orthogonal photon states. I develop creation and annihilation operators with a novel commutation relation as a consequence of the nonorthogonality of the quasimodes. With these operators the effective Hamiltonian, number operator, electric field operator and quadrature operators are obtained. The quantum jump technique is applied to handle the effects of loss. This technique is compared with the master equation, and conditions for the quantum jump technique being preferable are described. The quantum jump technique is implemented numerically, allowing for time-dependent linear and X(2) non-linear pumping. I use a combination of analytic results and characteristic functions to examine the evolution of coherent and squeezed states in a single lossy quasimode. The analysis is then extended to two nonorthogonal quasimodes. States are investigated using reduced characteristic functions. / Thesis (Master, Physics, Engineering Physics and Astronomy) -- Queen's University, 2013-09-27 12:00:10.281

Resource identification and quantification is an essential element of both classical and quantum information theory. Entanglement is one of these resources, arising when quantum communication and nonlocal operations are expensive to perform. In the first part of this thesis we quantify the effective entanglement when operations are additionally restricted to account for both fundamental restrictions on operations, such as those arising from superselection rules, as well as experimental errors arising from the imperfections in the apparatus. For an important class of errors we find a linear relationship between the usual and effective higher dimensional generalization of concurrence, a measure of entanglement. Following the treatment of effective entanglement, we focus on a related concept of nonlocality in the presence of superselection rules (SSR). Here we propose a scheme that may be used to activate nongenuinely multipartite nonlocality, in that a single copy of a state is not multipartite nonlocal, while two or more copies exhibit nongenuinely multipartite nonlocality. The states used exhibit the more powerful genuinely multipartite nonlocality when SSR are not enforced, but not when they are, raising the question of what is needed for genuinely multipartite nonlocality. We show that whenever the number of particles is insufficient, the degrading of genuinely multipartite to nongenuinely multipartite nonlocality is necessary. While in the first few chapters we focus our attention on understanding the resources present in quantum states, in the final part we turn the picture around and instead treat operations themselves as a resource. We provide our observers with free access to classical operations - ie. those that cannot detect or generate quantum coherence. We show that the operation of interest can then be used to either generate or detect quantum coherence if and only if it violates a particular commutation relation. Using the relative entropy, the commutation relation provides us with a measure of nonclassicality of operations. We show that the measure is a sum of two contributions, the generating power and the distinguishing power, each of which is separately an essential ingredient in quantum communication and information processing. The measure also sheds light on the operational meaning of quantum discord - we show it can be interpreted as the difference in superdense coding capacity between a quantum state and a classical state.

The Interactive Physics Laboratory is a project created at MFF UK. The idea is to provide access to interesting physical experiments to high-school students. This paper describes installation of experiments covering the topic "Physics of the microworld". After the topic is analysed, several suitable experiments are chosen, made oparational and supporting manuals and worksheets created. At the very end, actual high school students are brought in for testing. Powered by TCPDF (www.tcpdf.org)

[pt] O propósito deste trabalho é apresentar uma demonstração simplificada do Teorema da Composicionalidade de Coecke, o qual diz respeito ao processamento de informação quântica agregada a estados emaranhados hpartidos. Utilizando a propriedade da universalidade do produto tensorial em nossa prova, veremos que é possível considerar todos os estados relevantes como sendo estados-produto, o que torna a demonstração bem mais fácil. Apresentaremos ainda o processo de teleportação de estados quânticos, tão comentado nos dias de hoje, e verificaremos finalmente que tal processo é uma aplicação trivial do teorema de Coecke. / [en] The purpose of this work is to present a simplified demonstration of Co- ecke's Compositionality Theorem, which refers to the quantum information processing associated to n-partite entangled states. By using the universal property of the tensor product in our proof, we will see that is possible to consider all the relevant states as being product states, which turns the demonstration much easier. We will present also the teleportation process of quantum states, so called nowadays, and verify finally that such a process is a trivial application of Coecke's theorem

Realizamos uma caracterização estrutural e eletrônica dos inibidores enzimáticos E-64 e CA030 utilizando técnicas de química quântica. Otimizações de geometria são realizadas em nível ab initio com os métodos Hartree-Fock e Teoria do Funcional da Densidade e estas estruturas são então comparadas com os resultados cristalográficos obtidos do Protein Data Bank. O cálculo do espectro de vibração infravermelho foi realizado para assegurar que as estruturas eram pontos de mínimo. Nós também fizemos a atribuição das freqüências vibracionais aos grupos funcionais das moléculas. A caracterização eletrônica é obtida com o cálculo do espectro de absorção ultravioleta-visível. Efeitos de solvente são contabilizados através da teoria de Campo de Reação Auto-Consistente. Uma análise detalhada das excitações do espectro calculado do E-64 e do CA030 é realizada e nós estudamos particularmente as transições características em torno de 200 nm. Tanto para o E-64 como para o CA030 nós identificamos o cromóforo responsável pela transição característica dos inibidores. Adicionalmente, nós levamos em consideração a influência da interação do CA030 com a catepsina B através do cálculo do espectro ultravioleta-visível do inibidor com o aminoácido cisteína. / We have made a structural and electronic characterization of the enzyme inhibitors E-64 and CA030 using quantum chemistry techniques. Geometry optimizations are performed in the ab initio level with the Hartree-Fock and Density Functional Theory methods and these structures are then compared with crystallographic results obtained from the Protein Data Bank. The infrared vibration spectrum calculation has been carried out to assure that the theoretical structures are true minima. We also have made an assignment of the vibrational frequencies to the functional groups of the molecules. The electronic characterization is performed with the calculation of the ultraviolet-visible absorption spectrum. Solvent effects are taken into account the Self Consistent Reaction Field theory. A detailed analysis of the calculated spectra of E-64 and CA030 excitations is given and we have particularly studied the characteristic transitions around 200 nm. For both the E-64 and the CA030 we have identified the chromophore responsible for the characteristic transition of the inhibitors. In addition, we have considered the influence of the interaction of the CA030 with the enzyme cathepsin B by calculating the ultraviolet-visible spectrum of the inhibitor with the cysteine amino acid.

Utilizamos um formalismo de operadores e a técnica de grupo de renormalizacao de Dasgupta, Ma e Hu para analisar o efeito de distribuições inomogêneas dos parâmetros sobre o comportamento crítico de um modelo estocástico simples. O processo de contato em uma dimensão constitui talvez o modelo mais simples que apresenta uma transição de fase para um estado absorvente. Nós usamos as seqüências de Fibonacci, duplicação de período e triplicação de período para introduzir inomogeneidades aperiódicas no processo de contato unidimensional e em uma cadeia quântica de spin. Usando procedimento de grupo de renormalização de desordem forte, estabelecemos algumas relações entre propriedades dos operadores renormalizados e grandezas termodinâmicas ou médias. Fomos capazes de testar o critério de relevância de flutuações geométricas de Harris-Luck, de obter vários expoentes críticos, e de observar aspectos característicos de dinâmica lenta e oscilações log-periódicas. A sequência de triplicação de período nos leva aos expoentes = ln (7/9)/ ln (4/9), = ln (9/7)/ ln 4, = ln 3/ ln (3/2) e k = ln 2/ ln (3/2). Usamos técnicas de Monte Carlo para confirmar os resultados de grupo de renormalização. As simulações numéricas indicam a validade do critério de relevância de Harris-Luck, e corroboram o caráter universal do comportamento crítico desses sistemas aperiódicos. / We use an operator formalism and the renormalization-group technique of Dasgupta, Ma and Hu to analyze the effects of a nonhomogeneous distribution of parameters on the critical behavior of simple stochastic model system. The contact process in one dimension is perhaps the simplest model to display a phase transition to an absorbing stationary state. We use the Fibonacci, period-doubling and period-tripling sequences for introducing aperiodic inhomogeneities in the one dimensional contact process and in a quantum Ising chain. Using strong-disorder renormalization-group procedures, we establish some relations between properties of renormalized operator and of thermodynamic or mean quantities. We were able to test a well-known criterion of relevance of geometric fluctuations, to obtain a number of critical exponents, and to point out features of slow-dynamics and log-periodic oscillations. The period-tripling sequence leads to the critical exponents = ln (7/9)/ ln (4/9), = ln (9/7)/ ln 4, = ln 3/ ln (3/2) and k = ln 2/ ln (3/2). We then used Monte Carlo techniques to check renormalization-group results. The numerical simulations indicate the validity of the Harris-Luck criterion of relevance of the geometric fluctuations, and generally support the universal character of the critical behavior of these aperiodic systems.