Free field and parafermionic realizations of twisted su(3)(k)((2)) current algebra

Free field and twisted parafermionic representations of twisted su(3)(k)((2)) current algebra are obtained. The corresponding twisted Sugawara energy-momentum tensor is given in terms of three (beta, gamma) pairs and two scalar fields and also in terms of twisted parafermionic currents and one scalar field. Two screening currents of the first kind are presented in terms of the free fields.

Exact solution at integrable coupling of a model for the Josephson effect between small metallic grains

A model is introduced for two reduced BCS systems which are coupled through the transfer of Cooper pairs between the systems. The model may thus be used in the analysis of the Josephson effect arising from pair tunneling between two strongly coupled small metallic grains. At a particular coupling strength the model is integrable and explicit results are derived for the energy spectrum, conserved operators, integrals of motion, and wave function scalar products. It is also shown that form factors can be obtained for the calculation of correlation functions. Furthermore, a connection with perturbed conformal field theory is made.

Integrable coupling in a model for Josephson tunneling between non-identical BCS systems

We extend a recent construction for an integrable model describing Josephson tunneling between identical BCS systems to the case where the BCS systems have different single particle energy levels. The exact solution of this generalized model is obtained through the Bethe ansatz.

R-matrices and the tensor product graph method

A systematic method for constructing trigonometric R-matrices corresponding to the (multiplicity-free) tensor product of any two affinizable representations of a quantum algebra or superalgebra has been developed by the Brisbane group and its collaborators. This method has been referred to as the Tensor Product Graph Method. Here we describe applications of this method to untwisted and twisted quantum affine superalgebras.

Electron exchange coupling for single-donor solid-state spin qubits

Intervalley interference between degenerate conduction band minima has been shown to lead to oscillations in the exchange energy between neighboring phosphorus donor electron states in silicon [B. Koiller, X. Hu, and S. Das Sarma, Phys. Rev. Lett. 88, 027903 (2002); Phys. Rev. B 66, 115201 (2002)]. These same effects lead to an extreme sensitivity of the exchange energy on the relative orientation of the donor atoms, an issue of crucial importance in the construction of silicon-based spin quantum computers. In this article we calculate the donor electron exchange coupling as a function of donor position incorporating the full Bloch structure of the Kohn-Luttinger electron wave functions. It is found that due to the rapidly oscillating nature of the terms they produce, the periodic part of the Bloch functions can be safely ignored in the Heitler-London integrals as was done by Koiller, Hu, and Das Sarma, significantly reducing the complexity of calculations. We address issues of fabrication and calculate the expected exchange coupling between neighboring donors that have been implanted into the silicon substrate using an 15 keV ion beam in the so-called top down fabrication scheme for a Kane solid-state quantum computer. In addition, we calculate the exchange coupling as a function of the voltage bias on control gates used to manipulate the electron wave functions and implement quantum logic operations in the Kane proposal, and find that these gate biases can be used to both increase and decrease the magnitude of the exchange coupling between neighboring donor electrons. The zero-bias results reconfirm those previously obtained by Koiller, Hu, and Das Sarma.

Numerical study of hydrogenic effective mass theory for an impurity P donor in Si in the presence of an electric field and interfaces

In this paper we examine the effects of varying several experimental parameters in the Kane quantum computer architecture: A-gate voltage, the qubit depth below the silicon oxide barrier, and the back gate depth to explore how these variables affect the electron density of the donor electron. In particular, we calculate the resonance frequency of the donor nuclei as a function of these parameters. To do this we calculated the donor electron wave function variationally using an effective-mass Hamiltonian approach, using a basis of deformed hydrogenic orbitals. This approach was then extended to include the electric-field Hamiltonian and the silicon host geometry. We found that the phosphorous donor electron wave function was very sensitive to all the experimental variables studied in our work, and thus to optimize the operation of these devices it is necessary to control all parameters varied in this paper.

Exact results for a tunnel-coupled pair of trapped Bose-Einstein condensates

A model describing coherent quantum tunnelling between two trapped Bose-Einstein condensates is discussed. It is not well known that the model admits an exact solution, obtained some time ago, with the energy spectrum derived through the algebraic Bethe ansatz. An asymptotic analysis of the Bethe ansatz equations leads us to explicit expressions for the energies of the ground and the first excited states in the limit of weak tunnelling and all energies for strong tunnelling. The results are used to extract the asymptotic limits of the quantum fluctuations of the boson number difference between the two Bose-Einstein condensates and to characterize the degree of coherence in the system.

Influence of constraining and confinement in the molecular mobility of low molecular weight materials

Dissertation presented to obtain a Ph.D. Degree in Chemical Physics

Investigation of Frustrated Quasi-One-Dimensional Quantum Spin-Chain Materials

Copper arsenite CuAs2O4 and Copper antimonite CuSb2O4 are S=1/2 (Cu2+ 3d9 electronic configuration) quasi-one-dimensional quantum spin-chain compounds. Both compounds crystallize with tetragonal structures containing edge sharing CuO6 octahedra chains which experience Jahn-Teller distortions. The basal planes of the octahedra link together to form CuO2 ribbon-chains which harbor Cu2+ spin-chains. These compounds are magnetically frustrated with competing nearest-neighbour and next-nearest-neighbour intrachain spin-exchange interactions. Despite the similarities between CuAs2O4 and CuSb2O4, they exhibit very different magnetic properties. In this thesis work, the physical properties of CuAs2O4 and CuSb2O4 are investigated using a variety of experimental techniques which include x-ray diffraction, magnetic susceptibility measurements, heat capacity measurements, Raman spectroscopy, electron paramagnetic resonance, neutron diffraction, and dielectric capacitance measurements. CuAs2O4 exhibits dominant ferromagnetic nearest-neighbour and weaker antiferromagnetic next-nearest-neighbour intrachain spin-exchange interactions. The ratio of the intrachain interactions amounts to Jnn/Jnnn = -4.1. CuAs2O4 was found to order with a ferromagnetic groundstate below TC = 7.4 K. An extensive physical characterization of the magnetic and structural properties of CuAs2O4 was carried out. Under the effect of hydrostatic pressure, CuAs2O4 was found to undergo a structural phase transition at 9 GPa to a new spin-chain structure. The structural phase transition is accompanied by a severe alteration of the magnetic properties. The high-pressure phase exhibits dominant ferromagnetic next-nearest-neighbour spin-exchange interactions and weaker ferromagnetic nearest-neighbour interactions. The ratio of the intrachain interactions in the high-pressure phase was found to be Jnn/Jnnn = 0.3. Structural and magnetic characterizations under hydrostatic pressure are reported and a relationship between the structural and magnetic properties was established. CuSb2O4 orders antiferromagnetically below TN = 1.8 K with an incommensurate helicoidal magnetic structure. CuSb2O4 is characterized by ferromagnetic nearest-neighbour and antiferromagnetic next-nearest-neighbour spin-exchange interactions with Jnn/Jnnn = -1.8. A (H, T) magnetic phase diagram was constructed using low-temperature magnetization and heat capacity measurements. The resulting phase diagram contains multiple phases as a consequence of the strong intrachain magnetic frustration. Indications of ferroelectricity were observed in the incommensurate antiferromagnetic phase.

Méthode de calcul à N-corps basée sur la G0W0 : étude du couplage électron-phonon dans le C60 et développement d’une approche accélérée pour matériaux organiques

La présente thèse porte sur les limites de la théorie de la fonctionnelle de la densité et les moyens de surmonter celles-ci. Ces limites sont explorées dans le contexte d'une implémentation traditionnelle utilisant une base d'ondes planes. Dans un premier temps, les limites dans la taille des systèmes pouvant être simulés sont observées. Des méthodes de pointe pour surmonter ces dernières sont ensuite utilisées pour simuler des systèmes de taille nanométrique. En particulier, le greffage de molécules de bromophényle sur les nanotubes de carbone est étudié avec ces méthodes, étant donné l'impact substantiel que pourrait avoir une meilleure compréhension de ce procédé sur l'industrie de l'électronique. Dans un deuxième temps, les limites de précision de la théorie de la fonctionnelle de la densité sont explorées. Tout d'abord, une étude quantitative de l'incertitude de cette méthode pour le couplage électron-phonon est effectuée et révèle que celle-ci est substantiellement plus élevée que celle présumée dans la littérature. L'incertitude sur le couplage électron-phonon est ensuite explorée dans le cadre de la méthode G0W0 et cette dernière se révèle être une alternative substantiellement plus précise. Cette méthode présentant toutefois de sévères limitations dans la taille des systèmes traitables, différents moyens théoriques pour surmonter ces dernières sont développés et présentés dans cette thèse. La performance et la précision accrues de l'implémentation résultante laissent présager de nouvelles possibilités dans l'étude et la conception de certaines catégories de matériaux, dont les supraconducteurs, les polymères utiles en photovoltaïque organique, les semi-conducteurs, etc.

The Effect of Antimony Substitution on the Magnetic and Structural Properties of Fe0.75–xSi0.25Sbx Alloys

The results of the investigation of the magnetic and structural properties of the alloy system Fe0.75–xSi0.25Sbx, where x = 0, 0.05, 0.1, 0.15, 0.2, and 0.25 synthesized by mechanical alloying followed by heat treatment are described. The x-ray diffraction reveals that all samples crystallize in the DO3-type cubic phase structure. Substituting Fe by Sb led to a de-crease in the lattice constant and the unit cell volume. The magnetic properties are investigated by vibrating sample magnetometer and show that all the samples are ferromagnetically ordered at room temperature. The Curie temperature is found to decrease linearly from (850 ± 5) K for the parent alloy to (620 ± 5) K for the alloyith x = 0.25. The satura-tion magnetizations at room temperature and at 100 K are found to decrease with increasing the antimony concentration. The above results indicate that Sb dissolves in the cubic structure of this alloy system.

Selection-mutation balance models with epistatic selection

We present an application of birth-and-death processes on configuration spaces to a generalized mutation4 selection balance model. The model describes the aging of population as a process of accumulation of mu5 tations in a genotype. A rigorous treatment demands that mutations correspond to points in abstract spaces. 6 Our model describes an infinite-population, infinite-sites model in continuum. The dynamical equation which 7 describes the system, is of Kimura-Maruyama type. The problem can be posed in terms of evolution of states 8 (differential equation) or, equivalently, represented in terms of Feynman-Kac formula. The questions of interest 9 are the existence of a solution, its asymptotic behavior, and properties of the limiting state. In the non-epistatic 10 case the problem was posed and solved in [Steinsaltz D., Evans S.N., Wachter K.W., Adv. Appl. Math., 2005, 11 35(1)]. In our model we consider a topological space X as the space of positions of mutations and the influence of epistatic potentials

Extension of explicit formulas in Poissonian white noise analysis using harmonic analysis on configuration spaces

Harmonic analysis on configuration spaces is used in order to extend explicit expressions for the images of creation, annihilation, and second quantization operators in L2-spaces with respect to Poisson point processes to a set of functions larger than the space obtained by directly using chaos expansion. This permits, in particular, to derive an explicit expression for the generator of the second quantization of a sub-Markovian contraction semigroup on a set of functions which forms a core of the generator.