Symmetry and symmetry-breaking have, in the last one hundred and fifty years, become incorporated as central explanatory concepts within the natural sciences and mathematics. An abbreviated review of the incorporation of symmetry within the disciplines of mathematics, physics, philosophy and biology, provides a frame within which to develop of a model of mind. This thesis combines the framework provided by symmetry and symmetry-breaking with a structural understanding of self-referential dynamics in examining the implied Kantian model of mind. It considers that Kant’s assumption of a transcendental self unnecessarily isolates consciousness from being understood as a product of complex natural processes. Kant’s structural model of mind is examined and reformulated in terms of a more fundamental form and process. The space required for any non-reductionist model of mind is proposed as being generated through an enfolding of dimensionality in the occurrence of categorical level symmetry breaking during evolutionary development. The temporally extended function is accounted for in terms of self-referential structural dynamics operating within the primary temporal asymmetry. The model of mind proposed is created through application of naturalistic explanations incorporating symmetry and has attributes that may prove of interest to non-reductionists. The phenomenological geometry established provides a framework to understand the experiential phenomenon of qualia while conforming to the requirements of a natural explanation. Information is conceived as being transmitted inwaveforms propagated across spaces of enfolded dimensionalities through structural framesdemarcating nested spaces and condensing in the synthesis of unity in the object of attention,or image, and returning to distribute, the now reformulated, information outward acrosscontextual frames and spaces. This simplified dynamic is considered to operate at all levels of natural phenomena and involves the reintroduction of Bohm’s concepts of implicate and explicate order. The result is a model of mind employing a minimum structural form and self-referential dynamics that has potential for integration across the discipline theoretic frames of the natural sciences while retaining, for the domain of conscious phenomena, an independent causal significance in terms of a temporal structuralism.

A neutral atom interacting with a single mode of a high finesse cavity provides an opportunity to study uncharted quantum mechanical systems and to explore the field of quantum computing and networking. Ranging from being a deterministic single photon source to a coherent storage unit for quantum information, a strong coupling cavity QED system has proven to be a powerful tool. In this thesis, single atoms are deterministically delivered over long distances and probed in an optical cavity. Once in the cavity, a single atom is stored and continuously observed for over 15 seconds. Progress towards using atoms in the cavity to produce entangled photon pairs is presented. Dual 1D optical lattices are implemented to create a foundation for advancements in two qubit quantum operations and entanglements.

Noncovalent interactions in complex chemical systems are examined by considering model systems which capture the essential physics of the interactions and applying correlated electronic structure techniques to these systems. Noncovalent interactions are critical to understanding a host of energetic and structural properties in complex chemical systems, from base pair stacking in DNA to protein folding in organic solids. Complex chemical and biophysical systems, such as enzymes and proteins, are too large to be studied using computational techniques rigorous enough to capture the subtleties of noncovalent interactions. Thus, the larger chemical system must be truncated to a smaller model system to which rigorous methods can be applied in order to capture the essential physics of the interaction. Computational methodologies which can account for high levels of electron correlation, such as second-order perturbation theory and coupled-cluster theory, must be used. These computational techniques will be used to study several types (pi stacking, S/pi, and C-H/pi) of noncovalent interactions in two chemical contexts: biophysical systems and organic solids.

In this thesis we study the physics of quantum many-body systems confined to one-dimensional geometries. The work was motivated by the recent success of experimentalists in developing atom traps, capable of restricting the motion of the individual atoms to a single spatial dimension. Specifically, we look at aspects of the one-dimensional Bose gas including; excitation spectrum, correlation functions, and dynamical behaviour. In Chapter \ref{ch:excitation1D} we consider the Lieb-Liniger model of interacting bosons in one-dimension. We numerically solve the equations arising from the Bethe ansatz solution for the exact many-body wave function in a finite-size system of up to twenty particles for attractive interactions. We discuss novel features of the solutions, including deviations from the well-known string solutions due to finite size effects. We present excited state string solutions in the limit of strong interactions and discuss their physical interpretation, as well as the characteristics of the quantum phase transition that occurs as a function of interaction strength in the mean-field limit. Our results are compared to those obtained via exact diagonalization of the Hamiltonian in a truncated basis. In Chapter \ref{ch:g2} we analytically calculate the spatial nonlocal pair correlation function for an interacting uniform one dimensional Bose gas at finite temperature and propose an experimental method to measure nonlocal correlations. Our results span six different physical realms, including the weakly and strongly interacting regimes. We show explicitly that the characteristic correlation lengths are given by one of four length scales: the thermal de Broglie wavelength, the mean interparticle separation, the healing length, or the phase coherence length. In all regimes, we identify the profound role of interactions and find that under certain conditions the pair correlation may develop a global maximum at a finite interparticle separation due to the competition between repulsive interactions and thermal effects. In Chapter \ref{ch:casimirdrag} we study the drag force below the critical velocity for obstacles moving in a superfluid. The absence of drag is well established in the context of the mean-field Gross-Pitaevskii theory. We calculate the next order correction due to quantum and thermal fluctuations and find a non-zero force acting on a delta-function impurity moving through a quasi-one-dimensional Bose-Einstein condensate at all subcritical velocities and at all temperatures. The force occurs due to an imbalance in the Doppler shifts of reflected quantum fluctuations from either side of the impurity. Our calculation is based on a consistent extension of Bogoliubov theory to second order in the interaction strength, and finds new analytic solutions to the Bogoliubov-de Gennes equations for a gray soliton. In Chapter \ref{ch:solitons} we study the effect of quantum noise on the stability of a soliton. We find the soliton solutions exactly define the reflectionless potentials of the Bogoliubov-de Gennes equations. This results in complete stability of the solitons in a purely one dimensional system. We look at the modifications to the density profile of a black soliton due to quantum fluctuations.

In this thesis we study the physics of quantum many-body systems confined to one-dimensional geometries. The work was motivated by the recent success of experimentalists in developing atom traps, capable of restricting the motion of the individual atoms to a single spatial dimension. Specifically, we look at aspects of the one-dimensional Bose gas including; excitation spectrum, correlation functions, and dynamical behaviour. In Chapter \ref{ch:excitation1D} we consider the Lieb-Liniger model of interacting bosons in one-dimension. We numerically solve the equations arising from the Bethe ansatz solution for the exact many-body wave function in a finite-size system of up to twenty particles for attractive interactions. We discuss novel features of the solutions, including deviations from the well-known string solutions due to finite size effects. We present excited state string solutions in the limit of strong interactions and discuss their physical interpretation, as well as the characteristics of the quantum phase transition that occurs as a function of interaction strength in the mean-field limit. Our results are compared to those obtained via exact diagonalization of the Hamiltonian in a truncated basis. In Chapter \ref{ch:g2} we analytically calculate the spatial nonlocal pair correlation function for an interacting uniform one dimensional Bose gas at finite temperature and propose an experimental method to measure nonlocal correlations. Our results span six different physical realms, including the weakly and strongly interacting regimes. We show explicitly that the characteristic correlation lengths are given by one of four length scales: the thermal de Broglie wavelength, the mean interparticle separation, the healing length, or the phase coherence length. In all regimes, we identify the profound role of interactions and find that under certain conditions the pair correlation may develop a global maximum at a finite interparticle separation due to the competition between repulsive interactions and thermal effects. In Chapter \ref{ch:casimirdrag} we study the drag force below the critical velocity for obstacles moving in a superfluid. The absence of drag is well established in the context of the mean-field Gross-Pitaevskii theory. We calculate the next order correction due to quantum and thermal fluctuations and find a non-zero force acting on a delta-function impurity moving through a quasi-one-dimensional Bose-Einstein condensate at all subcritical velocities and at all temperatures. The force occurs due to an imbalance in the Doppler shifts of reflected quantum fluctuations from either side of the impurity. Our calculation is based on a consistent extension of Bogoliubov theory to second order in the interaction strength, and finds new analytic solutions to the Bogoliubov-de Gennes equations for a gray soliton. In Chapter \ref{ch:solitons} we study the effect of quantum noise on the stability of a soliton. We find the soliton solutions exactly define the reflectionless potentials of the Bogoliubov-de Gennes equations. This results in complete stability of the solitons in a purely one dimensional system. We look at the modifications to the density profile of a black soliton due to quantum fluctuations.

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.

Made available in DSpace on 2014-06-11T19:27:15Z (GMT). No. of bitstreams: 0 Previous issue date: 2010-04-04Bitstream added on 2014-06-13T19:26:13Z : No. of bitstreams: 1 silva_rmc_me_ift.pdf: 461180 bytes, checksum: 92f4f89859c7a0a67572084d80b54ceb (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Neste estudo iremos aplicar supersimetria em teorias como mecânica quântica, teoria de cordas e teoria de campos em D = 3. Apesar de todas essas teorias terem aplicações em campos completamente diferentes iremos encontrar semelhanças entre elas através da algebra supersimétrica. Discutiremos tamb em vários resultados que supersimetrização traz para cada uma dessas teorias / In this study we'll use supersymmetry in diferent theories like quantum mechanics, string theory and eld theory in D = 3. Although all these theories have aplication in diferent areas of physics, we'll nd similarities among them. To nish we'll discuss some results that supersymmetry bring to each of these theories

Made available in DSpace on 2015-05-14T12:14:13Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 607405 bytes, checksum: 901b07535dd697c3ac45d2bdfef30f70 (MD5) Previous issue date: 2014-08-08 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this thesis, we study the generalized harmonic oscillator with frequency dependent mass and time and subjected to a friction force whose speed depends on the time, of classical and quantum points of view. Obtained the solutions of the classical equation of motion of this system for some special cases, we derive an equation of motion that describes three systems. Then, with the help of quadratic invariant operators the light of the method of dynamical invariants we find the exact solutions of the Schrodinger equation for this system. We derive the geometric, dynamic and Berry for this system non-stationary phases and we evaluate this phases for three special cases. After this, we construct coherent states for this quantized system and employ them to investigate some properties quantum properties such as quantum uctuations of the coordinate and momentum as well as the product of the uncertainties. We then use a linear invariant operator light of the method of dynamical invariants in the intention of finding exact Schrodinger equation for the damped harmonic oscillator for forced time-dependent solutions. As described in our contribution we built solutions in the form of Gaussian wave packets as well as calculate the quantum uctuations of the coordinates and time, as well as the correlations between them. Finally, we show that the width of the uctuations and correlations of the Gaussian packet does not depend on the external force / Na presente tese, estudamos o oscilador harmônico generalizado com massa e frequência dependentes do tempo e submetido a uma força de fricção linear na velocidade cujo coeficiente de fricção depende do tempo, do ponto de vista clássico e quântico. Obtivemos as soluções da equação de movimento clássica deste sistema para alguns casos particulares e derivamos uma equação de movimento que descreve simultaneamente três sistemas diferentes. Em seguida, com a ajuda dos operadores invariantes quadráticos e à luz do método de invariantes dinâmicos encontramos as soluções exatas da equação de Schrodinger para este sistema. Também derivamos as fases geométrica, dinâmica e de Berry para este sistema não-estacionário e as avaliamos para três casos especiais. Ainda construímos estados coerentes para este sistema quantizado e os empregamos para investigar algumas propriedades quânticas tais como utuações quânticas da coordenada e momento bem como do produto das incertezas. Em seguida, utilizamos um operador invariante linear e usamos o método de invariantes dinâmicos para encontrar soluções exatas da equação de Schrodinger para um oscilador harmônico amortecido e forçado dependente do tempo. Com as soluções desta equação, construímos soluções na forma de pacotes de onda Gaussianos assim como calculamos as utuações quânticas das coordenadas e momentos, bem como as correlações entre ambos. Finalmente, mostramos que a largura das utuações e correlações do pacote Gaussiano não dependem da força externa.

Made available in DSpace on 2015-05-14T12:14:20Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 650048 bytes, checksum: 434d6fa42298be2011c48aa4e06477c3 (MD5) Previous issue date: 2008-06-20 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this thesis, we use linear invariants and the method of dynamical invariants to obtain exact solutions of the Schr¨odinger equation for the generalized time-dependent forced harmonic oscillator in terms of the solutions of a second order ordinary differential equation that describes the amplitude of the classical unforced damped oscillator. In addition, we construct gaussian wave packet solutions and calculate the fluctuations in coordinate and momentum as well as the quantum correlations between them. It is shown that the width of the Gaussian packet, fluctuations and correlations do not depend on the external force. As a particular case, we consider the forced Caldirola-Kanai oscillator. In addition, we use the Coulomb gauge, linear invariants and the method of dynamical invariants in the framework of the Schr¨odinger equation to obtain a quantum description of the light propagation through a homogeneous conducting linear media with no charge density. We obtain exact wave functions for this problem in terms of solutions of a second order ordinary differential equation which describes the amplitude of the classical damped harmonic oscillator. Furthermore, we construct gaussian wave packet solutions and calculate the fluctuations in coordinate and momentum as well as the quantum correlations for every mode of the quantized electromagnetic field. We also use quadratic invariants together method of dynamical invariants to study the light propagation in a conducting media. We obtain exact solutions of the time-dependent Schr¨odinger equation for this case and construct coherent and squeezed states for the quantized electromagnetic waves. Yet, we evaluate the quantum fluctuations in coordinate and momentum as well as the uncertainty product for every mode of the electromagnetic field. Finally, we use quadratic invariants and the dynamical invariant method for obtain exact wavefunctions of the Schr¨odinger equation for a particle trapped by oscillating fields. / Na presente tese, usamos operadores invariantes lineares à luz do método de invariantes dinâmicos para encontrar as soluções exatas da equação de Schrödinger para um oscilador harmônico forçado generalizado dependente do tempo em termos das soluções de uma equação diferencial de segunda ordem que descreve a amplitude de um oscilador harmônico amortecido não-for¸cado. Construimos as soluções do tipo pacotes de ondas gaussianos e calculamos as flutuações quânticas das coordenadas e momentos, bem como da correlação entre ambos. Como destaque, mostramos que a largura das flutuações e as correlações do pacote gaussiano não dependem da força externa. Como caso particular, aplicamos nosso formalismo ao conhecido oscilador forçado de Caldirola-Kanai. Depois, fazemos uma descrição quântica da propagação da luz num meio condutor, homogêneo, linear e com densidade de carga nula, usando o modelo de oscilador harmônico dependente de tempo numa abordagem fenomenológica usando o gauge de Coulomb, invariantes lineares e o método do invariante dinâmico. Obtemos as funções de onda exatas para este problema em termos de soluções de uma equação diferencial de segunda ordem que descreve a amplitude do oscilador amortecido clássico. Além disso, construimos soluções do tipo pacotes de onda gaussianos e calculamos as flutuações e as correlações quânticas para cada modo do campo eletromagnético quantizado. Em seguida, estendemos nossa investiga ção utilizando também um operador invariante quadrático. Encontramos as funções de onda exatas para a equação de Schrödinger para a luz num meio condutor com frequência dependente do tempo. Concluímos a presente tese abordando o problema de encontrar funções de onda (soluções da equação de Schrodinger) exatas, com dependência temporal, para uma partícula aprisionada por campos oscilantes.

Made available in DSpace on 2015-05-14T13:21:35Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 1225184 bytes, checksum: aea7240aacf52c5036cf6d487576423c (MD5) Previous issue date: 2009-10-14 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / The intramolecular hydrogen bond occurs when the same molecules has both proton donor and proton acceptor groups in satisfactory configuration space for the formation of this interaction. It is important to note the changes in the structural, electronic and vibrational properties that occur due to the formation of this interaction. In the hydrogen bonding formation is an important phenomenon called charge transfer , where part of the electronic density of the proton acceptor species, Y, is transferred o the proton donor specie, HX. With respect to the vibrational spectrum are observed changes in the way of straightening of donor and acceptor proton species. Di-carbonyl compounds (C3H2O2R2) with their substituent groups (R=CH3, CN, H, NH2, OH and SH) were studied focusing on the energetic, structural, vibrational and electron density analysis. Initially the energy and structural analysis were carried out starting from the molecules optimized geometry. We also evaluated of the strength s hydrogen bonding and the length s intramolecular bond. The QTAIM study was performed to obtain the electron density s values and the electron density s Laplacian values and verify the existence of the bond critical point in the intramolecular hydrogen bond. From the harmonic vibrational spectra was possible to identify changes in the vibrational modes, related the intramolecular interaction s formation. / A ligação de hidrogênio intramolecular ocorre quando uma mesma molécula apresenta, simultaneamente, um grupo doador e outro receptor de próton, em configuração espacial favorável à formação dessa interação. É importante salientar as mudanças nas propriedades estruturais, eletrônicas e vibracionais que ocorrem devido à formação dessa interação. Na formação da ligação de hidrogênio ocorre um fenômeno importante denominado de transferência de carga , onde parte da densidade eletrônica da espécie receptora de próton, Y, é transferida para a espécie doadora de próton, HX. Com respeito aos espectros vibracionais, são observadas modificações nos modos de estiramento das espécies doadora e receptora de próton. Compostos di-carbonílicos (C3H2O2R2) com suas substituições (R=CH3, CN, H, NH2, OH e SH) foram estudados enfocando as análises energética, estrutural, vibracional e de densidade eletrônica. Inicialmente foram realizadas as análises energéticas e estruturais a partir da geometria otimizada das moléculas. Foram avaliados a força da ligação de hidrogênio e do comprimento da ligação intramolecular. O estudo usando a QTAIM foi realizado para adquirir os valores de densidade eletrônica e do Laplaciano da densidade eletrônica e verificar a existência do ponto crítico de ligação na ligação de hidrogênio intramolecular. A partir dos espectros vibracionais harmônicos foi possível identificar as variações no infravermelho, referentes à formação da interação intramolecular.