Global ETD Search

11	Majorana Representation in Quantum Optics : SU(2) Interferometry and Uncertainty Relations Shabbir, Saroosh January 2017 (has links) The algebra of SU(2) is ubiquitous in physics, applicable both to the atomic spin states and the polarisation states of light. The method developed by Majorana and Schwinger to represent pure, symmetric spin-states of arbitrary value as a product of spin-1/2 states is a powerful tool that allows for a great conceptual and practical simplification. Foremost, it allows the representation of a qudit on the same geometry as a qubit, i.e., the Bloch sphere. An experimental implementation of the Majorana representation in the realm of quantum optics is presented. The technique allows the projection of arbitrary quantum states from a coherent state input. It is also shown that the method can be used to synthesise arbitrary interference patterns with unit visibility, and without resorting to quantum resources. In this context, it is argued that neither the shape nor the visibility of the interference pattern is a good measure of quantumness. It is only the measurement scheme that allows for the perceived quantum behaviour. The Majorana representation also proves useful in delineating uncertainty limits of states with a particular spin value. Issues with traditional uncertainty relations involving the SU(2) operators, such as trivial bounds for certain states and non-invariance, are thereby resolved with the presented pictorial solution. / <p>QC 20170428</p> Majorana representation Quantum optics interferometry SU(2) group angular momentum arbitrary optical gates Atom and Molecular Physics and Optics Atom- och molekylfysik och optik
12	Renormalisation perturbative et T-dualite - Nouvelles metriques d'Einstein et super-espace harmonique Casteill, Pierre-Yves 02 October 2002 (has links) (PDF) Dans la première partie de la thèse, nous étudions le problème de l'équivalence quantique de modèles sigma reliés entre eux par la T-dualité non-abelienne. Nous prouvons que la renormalisabilité à une boucle de divers modèles initiaux implique la renormalisabilité à une boucle de leur partenaire dualisé, et qu'ils partagent les mêmes fonctions beta. Ceci est fait pour tous les modèles sigma principaux (G_L X G_R)/G_D, quelle que soit la brisure de G_R, ainsi que pour la large classe de métriques à quatre dimensions, inhomogènes et d'isométrie SU(2) X U(1). Pour l'exemple simple du modèle sigma T-dualisé SU(2), dont la non-renormalisabilité à deux boucles a été démontrée dans le schéma dimensionel minimal, nous prouvons qu'il est encore possible, à cet ordre, de définir une théorie quantique correcte en modifiant, à l'ordre \hbar, la métrique de l'espace cible de façon finie. Dans la seconde partie, nous construisons de façon explicite, grâce au super-espace harmonique et à l'approche du quotient quaternionique, une extension quaternion-Kähler de la métrique hyper-Kähler à deux centres la plus générale. Elle possède le groupe d'isométrie U(1) X U(1) et contient comme cas particuliers les extensions quaternion-Kähler des métriques de Taub-NUT et d'Eguchi-Hanson. Elle fait aussi apparaître un paramètre supplémentaire qui disparaît dans la limite hyper-Kähler. [PHYS:MPHY] Physics/Mathematical Physics Metrique Einstein super-espace harmonique T-dualite dualisation SU(2) quaternion-kahler kahler
13	Multi-Skyrmion solutions of a sixth order Skyrme model Floratos, Ioannis January 2001 (has links) In this Thesis, we study some of the classical properties of an extension of the Skyrme model defined by adding a sixth order derivative term to the Lagrangian. In chapter 1, we review the physical as well as the mathematical motivation behind the study of the Skyrme model and in chapter 2, we give a brief summary of various extended Skyrme models that have been proposed over the last few years. We then define a new sixth order Skyrme model by introducing a dimensionless parameter λ that denotes the mixing between the two higher order terms, the Skyrme term and the sixth order term. In chapter 3 we compute numerically the multi-skyrmion solutions of this extended model and show that they have the same symmetries with the usual skyrmion solutions. In addition, we analyse the dependence of the energy and radius of these classical solutions with respect to the coupling constant λ. We compare our results with experimental data and determine whether this modified model can provide us with better theoretical predictions than the original one. In chapter 4, we use the rational map ansatz, introduced by Houghton, Manton and Sutcliffe, to approximate minimum energy multi-skyrmion solutions with B ≤ 9 of the SU(2) model and with B ≤ 6 of the SU(3) model. We compare our results with the ones obtained numerically and show that the rational map ansatz works just as well for the generalised model as for the pure Skyrme model, at least for B ≤ 5. In chapter 5, we use a generalisation of the rational map ansatz, introduced by loannidou, Piette and Zakrzewski, to construct analytically some topologically non-trivial solutions of the extended model in SU(3). These solutions are spherically symmetric and some of them can be interpreted as bound states of skyrmions. Finally, we use the same ansatz to construct low energy configurations of the SU(N) sixth order Skyrme model. 539.72
14	Transversal Construction of Topological Gates on Multiqubit Quantum Codes Chauwinoir, Sheila January 2022 (has links) We study the possibility of constructing quantum gates using topological phases, which originate from local SU(2) evolution of entangled multiqubit systems. For this purpose, logical codewords using two-, three- and nine-qubit entangled states are defined and possible implementations of topological gates on these codes, are examined. For two-qubit systems, it is shown that for only two of the Pauli gates, a topological implementation is possible, the third must be non-topological. Furthermore, it is shown that a topological implementation of Hadamard gate is also possible on the two-qubit code. For the three-qubit code, the logical Pauli gates are found to be topologically implementable and a topological implementation of the logical S gate seems to be possible as well. Lastly, for the nine-qubit code, the logical Pauli gates, the logical S gate and the logical T gate are shown to be implementable topologically on the code. It remains an open question whether topological implementation of logical Hadamard gate by invertible local operators is possible on the nine-qubit code. entanglement local SU(2) evolution topological phase factors topological gates transversal gates multiqubit quantum codes Hopf fibration Physical Sciences Fysik
15	Lee-Yang zeros analysis of finite density lattice QCD Crompton, P. R. January 2001 (has links) No description available. 539.72
16	Self-interacting dark matter of an SU(2) gauged dark sector Liu, Ruochuan 04 September 2018 (has links) This thesis investigates the possibility that the gauge boson in a certain hypothetical SU(2) gauged sector can constitute all the non-baryonic dark matter. The gauge bosons acquire mass from the Higgs mechanism as in the Standard Model and scatter elastically among themselves non-gravitationally. It is expected that this self interaction of the dark gauge bosons would resolve the various discrepancies between the ΛCDM model and astrophysical observations on small (e.g. galactic or galaxy cluster) scales. Parameter space within the domain of validity of perturbation theory satisfying the constraints of dark matter abundance, the elastic self-scattering momentum transfer cross-section suggested by recent astrophysical observations, and consideration of the Big-Bang nucleosynthesis was found to be non-empty in the “forbidden” regime where the mass of the dark Higgs boson is greater than the mass of the dark gauge boson. / Graduate Self-interacting dark matter Dark matter Thermal dark matter Non-abelian gauge theory Yang-Mills theory dark Higgs boson Higgs mechanism Higgs portal Dark gauge boson Massive gauge boson Elastically self-interacting dark matter SU(2)
17	An Efficient Quantum Algorithm and Circuit to Generate Eigenstates Of SU(2) and SU(3) Representations Sainadh, U Satya January 2013 (has links) (PDF) Many quantum computation algorithms, and processes like measurement based quantum computing, require the initial state of the quantum computer to be an eigenstate of a specific unitary operator. Here we study how quantum states that are eigenstates of finite dimensional irreducible representations of the special unitary (SU(d)) and the permutation (S_n) groups can be efficiently constructed in the computational basis formed by tensor products of the qudit states. The procedure is a unitary transform, which first uses Schur-Weyl duality to map every eigenstate to a unique Schur basis state, and then recursively uses the Clebsch - Gordan transform to rotate the Schur basis state to the computational basis. We explicitly provide an efficient quantum algorithm, and the corresponding quantum logic circuit, to generate any desired eigenstate of SU(2) and SU(3) irreducible representations in the computational basis. Quantum Mechanics Quantum Algorithms Quantum Circuits Computational Complexity Schur Transform Eigenstate - SU(2) Eigenstate - SU(3) High Energy Physics
18	Applications of the coupled cluster method to pairing problems Snape, Christopher January 2010 (has links) The phenomenon of pairing in atomic and nuclear many-body systems gives rise to a great number of different physical properties of matter, from areas as seemingly diverse as the shape of stable nuclei to superconductivity in metals and superfluidity in neutron stars. With the experimental realisation of the long sought BCS-BEC crossover observed in trapped atomic gases - where it is possible to fine tune the s-wave scattering length a of a many-fermion system between a dilute, correlated BCS-like superfluid of Cooper pairs and a densely packed BEC of composite bosons - pairing problems in atomic physics have found renewed interest in recent years. Given the high precision techniques involved in producing these trapped gas condensates, we would like to employ a suitably accurate many-body method to study such systems, preferably one which goes beyond the simple mean-field picture.The Coupled Cluster Method (CCM) is a widely applied and highly successful ab initio method in the realm of quantum many-body physics and quantum chemistry, known to be capable of producing extremely accurate results for a wide variety of different many-body systems. It has not found many applications in pairing problems however, at least not in a general sense. Our aim, therefore, is to study various models of pairing using a variety of CCM techniques - we are interested in studying the generic features of pairing problems and in particular, we are especially interested in probing the collective modes of a system which exhibits the BCS-BEC crossover, in either the BCS or BEC limit. The CCM seems a rather good candidate for the job, given the high precision results it can produce. 539.7
19	Field Theoretic Lagrangian From Off-shell Supermultiplet Gauge Quotients Katona, Gregory 01 January 2013 (has links) 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, [phi] = 1.61803, Ref [52]. It is further determined that these Lagrangians allow an N = 3 - > 4 supersymmetric extension to the Chiral-Chiral and Chiral-twistedChiral multiplet, while a subset admits two inequivalent such extensions. In a natural proiii gression, 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. Supersymmetry superspace supermultiplet adinkra automata adiankraic tensor product decomposition group theoretic lorentz group su(2) so(3) gauge quotient isomorphism surjective bijective image mapping indefinite adiankraic network sequence super poincare group haag lopuszanski sohnius theorem string theory m theory f theory nonlinear sigma model (numerical) algebraic geometry algebraic paradigms worldsheet worldsheet stacks supersymmetric lagrangians ansatz templates super potentials quantum mechanics field theory fermionic bosonic (super) zeeman background flux fields supergravity superfields young tableaux susy tableaux controlled chaos supercharge continuum chiral chiral twisted chiral Physics

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