No / Budesonide is a mixture of 22R and 22S epimers. The epimeric content of budesonide was reported in both British and European pharmacopoeias to be within the range of 60-49/40-51 for R and S epimers, respectively. In this work, contribution of the two epimers to the overall infrared spectrum of budesonide has been investigated by quantum chemical calculations.

The nuclear spin response to a rotating field H has been theoretically investigated from the 1930s to the 1950s. Building upon Majorana's probability theory, the behavior of spin 1/2 is well-illustrated in the joint review by Rabi, Ramsey, andSchwinger, and their spin wave function ψ is succinctly restated by Gottfried: ψ(t) = e-iIzωt/ℏe-i[Iz(ω0-ω)+Ixω1]t/ℏψ(0). However, the complexity involved in evaluating the wave function ψ in terms of probability amplitudes Cm attributed to the noncommutative nature of spin operators [Ix, Iz] ≠0, hinders the application of this well-established theory to spins with arbitrary values I > 1/2. In a recent study by Hall and Klemm, a conjectural form of the spin wave function was suggested. Here, we present an alternative formulation of the wave function ψ by controlling doubly rotating coordinates: ψ(t) = e-iIzωt/ℏ e-iIyθ/ℏ e-iIzΩt/ℏ eiIyθ/ℏ ψ(0). This formulation facilitates the computation of general state transitions from an initial state ψ(0)=∑mCm(0)ψm(0) to ψ(t)=∑m'Cm'(t)ψm'(t). Moreover, by assuming an analogous form of the total electron spin J to that of the nucleus I, we can explore hyperfine structures in atoms and/or molecules traversing in the magnetic field H in terms of the nuclear-electronic spin interaction (I·J). Through this approach, we not only formulate wave functions more effectively but also bridge quantum mechanics and algebraic perspectives.

Usando as Regras de Soma da QCD, testamos se a nova estrutura estreita, X(4350) recentemente observada pela Colaboração Belle, pode ser descrita como um estado molecular D8D80 exótico JPC = 1+. Consideramos as contribuições dos condensados de dimensão oito, trabalhamos com os termos dominantes em 8 mantendo os termos lineares na massa do quark estranho m8. A massa obtida é igual a mD8D80 = (5.05±0.19) GeV. Consideramos também uma corrente molecular 1+, DD0 e obtemos mDD0 = (4.92 ± 0.08) GeV. Concluímos que não é possível descrever a estrutura X(4350) como um estado molecular 1+ D8D80. / Using the QCD sum rules we test if the new narrow structure, the X(4350) recently observed by the Belle Collaboration, can be described as a JPC = 1+ exotic D8D80 molecular state. We consider the contributions of condensates up to dimension eight, we work at leading order in s and we keep terms which are linear in the strange quark mass ms. The mass obtained for such state is mD8D80 =(5.05 ± 0.19) GeV. We also consider a molecular 1+, DD0 current and we obtain mDD0 = (4.92 ± 0.08) GeV. We conclude that it is not possible to describe the X(4350) structure as a 1+ D8D80 molecular state.

Usando as Regras de Soma da QCD, testamos se a nova estrutura estreita, X(4350) recentemente observada pela Colaboração Belle, pode ser descrita como um estado molecular D8D80 exótico JPC = 1+. Consideramos as contribuições dos condensados de dimensão oito, trabalhamos com os termos dominantes em 8 mantendo os termos lineares na massa do quark estranho m8. A massa obtida é igual a mD8D80 = (5.05±0.19) GeV. Consideramos também uma corrente molecular 1+, DD0 e obtemos mDD0 = (4.92 ± 0.08) GeV. Concluímos que não é possível descrever a estrutura X(4350) como um estado molecular 1+ D8D80. / Using the QCD sum rules we test if the new narrow structure, the X(4350) recently observed by the Belle Collaboration, can be described as a JPC = 1+ exotic D8D80 molecular state. We consider the contributions of condensates up to dimension eight, we work at leading order in s and we keep terms which are linear in the strange quark mass ms. The mass obtained for such state is mD8D80 =(5.05 ± 0.19) GeV. We also consider a molecular 1+, DD0 current and we obtain mDD0 = (4.92 ± 0.08) GeV. We conclude that it is not possible to describe the X(4350) structure as a 1+ D8D80 molecular state.

Exact solution of the Schr&ouml / dinger equation with some potentials is obtained. The normal and supersymmetric cases are considered. Deformed ring-shaped potential is solved in the parabolic and spherical coordinates. By taking appropriate values for the parameter q, similar results are obtained for Hulth&eacute / n and exponential type screened potentials. Similarly, Morse, P&ouml / schl-Teller and Hulth&eacute / n potentials are solved for the supersymmetric case. Supersymmetric solution of PT-/non-PT-symmetric and non-Hermitian Morse potential is also studied. The Nikiforov-Uvarov and Hamiltonian Hierarchy methods are used in the calculations. Eigenfunctions and corresponding energy eigenvalues are calculated analytically. Results are in good agreement with ones obtained before.

This PhD thesis is submitted as a \emph{compendium} of the articles \cite{NS, holographic, topological}. The following has been adapted from their abstracts. Quantum mechanics has been argued to be a coarse--graining of some underlying deterministic theory. Here we support this view by establishing mappings between non-relativistic quantum mechanics and thermodynamic theories, since the latter are the paradigm of an emergent theory. First, we map certain solutions of the Schroedinger equation to solutions of the irrotational Navier--Stokes equation for viscous fluid flow. Although this is formally a generalization of Madelung's hydrodynamical interpretation, the presence of a viscous term leads to a novel interpretation. As a physical model for the fluid itself we propose the quantum probability fluid. It turns out that the (state--dependent) viscosity of this fluid is proportional to Planck's constant, while the volume density of entropy is proportional to Boltzmann's constant. Stationary states have zero viscosity and a vanishing time rate of entropy density. On the other hand, the nonzero viscosity of nonstationary states provides an information--loss mechanism whereby a deterministic theory (a classical fluid governed by the Navier--Stokes equation) gives rise to an emergent theory (a quantum particle governed by the Schroedinger equation). Then, we present a map of standard quantum mechanics onto classical thermodynamics of irreversible processes. In particular, the propagators of the quantum harmonic oscillator are mapped to the conditional probabilities that solve the Chapman-Kolmogorov equation for Markovian Gaussian processes. While no gravity is present in our construction, our map exhibits features that are reminiscent of the holographic principle of quantum gravity. Finally, the classical thermostatics of equilibrium processes is shown to possess a quantum mechanical dual theory with a finite dimensional Hilbert space of quantum states. Specifically, the kernel of a certain Hamiltonian operator becomes the Hilbert space of quasistatic quantum mechanics. The relation of thermostatics to topological field theory is also discussed in the context of the approach of emergence of quantum theory, where the concept of entropy plays a key role. / La presente tesis doctoral se presenta como compendio de las publicaciones \cite{NS, holographic, topological}. El siguiente resumen es una adaptación de sus resumenes. Se ha argumentado que la mecánica cuántica podría emerger como promediado de una teoría determinista subyacente. Se apoya dicha visión estableciendo mapeos entre la mecánica cuántica no relativista y teorías termodinámicas, ya que estas constituyen el paradigma de teoría emergente. Primero, se establece un mapeo entre soluciones de la ecuación de Schroedinger y soluciones de la ecuación de Navier-Stokes irrotacional para fluidos viscosos. Aunque formalmente se trate de una generalización de la interpretación hidrodinámica de Madelung, la presencia del término viscoso sugiere una nueva interpretación. Se propone la probabilidad cuántica como modelo físico del fluido. Se obtiene que la viscosidad (dependiente del estado) es proporcional a la constante de Planck, mientras que la densidad de entropía es proporcional a la constante de Boltzmann. Los estados estacionarios tienen viscosidad y tasa de producción de densidad de entropía nulas. Por otro lado, la viscosidad no nula de los estados no estacionarios proporciona un mecanismo de pérdida de información por el cual una teoría determinista (un fluido clásico gobernado por la ec. de Navier-Stokes) da lugar a una teoría emergente (una partícula cuántica gobernada por la ec. de Schroedinger). Después, se presenta un mapeo entre la mecánica cuántica y la termodinámica clásica de procesos irreversibles. En particular, los propagadores del oscilador armónico cuántico se mapean a las probabilidades condicionales que resuelven la ecuación de Chapman-Kolmogorov para procesos de Markov Gaussianos. Aunque no hay gravedad, el mapeo exhibe propiedades que recuerdan al principio holográfico de la gravedad cuántica. Finalmente, se muestra cómo la termoestática clásica de procesos de equilibrio posee una teoría cuántica dual con un espacio de Hilbert finito - dimensional de estados cuánticos. Concretamente, el núcleo de cierto operador Hamiltoniano se convierte en el espacio de Hilbert de una mecánica cuántica cuasiestática. La relación de la termoestática a la teoría topológica de campos se discute en el contexto de la mecánica cuántica emergente, donde el concepto de entropía juega un papel clave. / Aquesta tesi doctoral es presenta com a compilació de les publicacions \cite{NS, holographic, topological}. El següent resum es una adaptació dels seus resums. S'ha argumentat que la mecànica quàntica podria emergir com a granulat gros d'una teoria determinista subjacent. Es dóna suport a aquesta visió mitjaçant uns mapes entre la mecànica quàntica no relativista i teories termodinàmiques, ja que les darreres són el paradigma de teoria emergent. Primer, s'estableix un mapa entre certes solucions de l'equació de Schroedinger i solucions de l'equació de Navier-Stokes irrotacional per a fluids viscosos. Tot i que formalment es tracte d'una generalització de la interpretació hidrodinàmica de Madelung, la presència del terme viscós ens porta a una nova interpretación. Es proposa la probabilitat quàntica com a model físic del fluid. S'obté que la viscositat del fluid (que depén de l'estat) es proporcional a la constant de Planck, mentre que la densitat d'entropía es proporcional a la constant de Boltzmann. Els estats estacionaris tenen viscositat nul·la i taxa de producció d'entropia nul·la. Per alta banda, la viscositat no nul·la dels estats estacionaris proporciona un mecanisme de pèrdua d'informació pel qual una teoria determinista (un fluid clàssic governat per l'equació de Navier-Stokes) dóna lloc a una teoria emergent (una partícula quàntica governada per l'equació de Schroedinger). Després, es presenta un mapa entre la mecànica quàntica i la termodinàmica clàssica de processos irreversibles. En particular, els propagadors de l'oscil·lador harmònic quàntic es mapejen a les probabilitats condicional que resolen l'ecuació de Chapman-Kolmogorov per a processos de Markov Gaussians. Tot i que no hi ha gravetat present a la nostra construcció, el mapa exhibeix propietats que recorden al principi hologràfic de la gravetat quàntica. Finalment, es mostra cóm la termoestàtica clàssica de processos d'equilibri té una teoria quàntica dual amb un espai de Hilbert de dimensió finita d'estats quàntics. En concret, el nucli de cert operador Hamiltonià es converteix en l'espai de Hilbert d'una mecànica quàntica quasiestàtica. La relació de la termoestàtica a la teoria topològica de camps es dicuteix en el context de la mecànica quàntica emergent, on el concepte d'entropia té un paper clau. / Vázquez Molina, J. (2017). Mappings between Thermodynamics and Quantum Mechanics that support its interpretation as an emergent theory [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/83122 / TESIS

<p>Open quantum systems have become a rapidly developing sector for research. Such systems present novel physical phenomena, such as topological chirality, enhanced sensitivity, and unidirectional invisibility resulting from both their non-equilibrium dynamics and the presence of exceptional points.</p> <p><br></p> <p>We begin by introducing the core features of open systems governed by non-Hermitian Hamiltonians, providing the PT -dimer as an illustrative example. Proceeding, we introduce the Lindblad master equation which provides a working description of decoherence in quantum systems, and investigate its properties through the Decohering Dimer and periodic potentials. We then detail our preferred experimental apparatus governed by the Lindbladian. Finally, we introduce the Liouvillian, its relation to non-Hermitian Hamiltonians and Lindbladians, and through it investigate multiple properties of open quantum systems.</p>

Submitted by Rosivalda Pereira (mrs.pereira@ufma.br) on 2017-05-26T20:32:19Z No. of bitstreams: 1 CamilaSoares.pdf: 1320447 bytes, checksum: e69a85013513d267e1ce15c2864ee0bf (MD5) / Made available in DSpace on 2017-05-26T20:32:19Z (GMT). No. of bitstreams: 1 CamilaSoares.pdf: 1320447 bytes, checksum: e69a85013513d267e1ce15c2864ee0bf (MD5) Previous issue date: 2017-03-03 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Fundação de Amparo à Pesquisa e ao Desenvolvimento Científico e Tecnológico do Maranhão (FAPEMA) / In this work, we study the formalism of the supersimmetric quantum mechanics (SUSY QM) starting with hamiltonian fatorization method of the bosonic harmonic oscillator (BHO) by means of ladders operators and we extended to hamiltonian of oscillators in general, inclusive of the fermionic harmonic oscillator (FHO), with their respective properties. We show that the SUSY QM for bound states, connect hamiltonians, potentials, and eigenvalues energy of different systems which are called supersymmetric partners. In the case scattering states, we notice that SUSY QM applies only in shape invariant potentials (SIPs). Despite this restriction, the SIPs are commonly used in literature by its wide applicability as in particles physics as in condensed matter. Therefore, we study the scattering states to the problem of massive relativistic fermions under the influence of modified Pöschl-Teller potential (PT), which is shape invariant. We calculate the transmission (T) and reflection (R) coefficients, just knowing the superpotential, which was carried out in a simple and elegant form. Thus, the study of the quantum scattering via SUSY QM becomes a powerful tool in the calculations of T and R. / Neste trabalho, estudamos o formalismo da mecânica quântica supersimétrica (MQS) partindo do método de fatoração do hamiltoniano do oscilador harmônico bosônico (OHB) por meio dos operadores escada e estendemos para o hamiltoniano de osciladores em geral, inclusive o oscilador harmônico fermiônico (OHF), com suas respectivas propriedades. Mostramos que a MQS, para estados ligados, associa hamiltonianos, potenciais e autovalores de energia de sistemas diferentes, que são denominados parceiros supersimétricos. No caso dos estados de espalhamento, observamos que a MQS aplica-se somente em potenciais invariantes de forma (PIFs). Apesar desta restrição, os PIFs são comumente utilizados na literatura, por sua larga aplicabilidade tanto na física de partículas quanto na matéria condensada. Sendo assim, estudamos os estados de espalhamento para o problema dos férmions relativísticos com massa sob influência do potencial de Pöschl-Teller modificado (PT), que é invariante de forma. Calculamos os coeficientes de transmissão (T) e reflexão (R), conhecendo apenas seu superpotencial, o que foi realizado de uma forma simples e elegante. Desse modo, o estudo do espalhamento quântico via MQS torna-se, uma ferramenta poderosa nos cálculos de T e R.

The supersymmetric solutions of PT-/non-PT symmetric and Hermitian/non-Hermitian forms of quantum systems are obtained by solving the Schr&Auml / odinger equation with the deformed Morse, Hulth&para / en, P&Auml / oschl-Teller, Hyperbolic Kratzer-like, Screened Coulomb, and Exponential-Cosine Screened Coulomb (ECSC) potentials. The Hamiltonian hi- erarchy method is used to get the real energy eigenvalues and corresponding wave functions.

The path integral formulation of quantum mechanics generalizes the action principle of classical mechanics. The Feynman path integral is, roughly speaking, a sum over all possible paths that a particle can take between fixed endpoints, where each path contributes to the sum by a phase factor involving the action for the path. The resulting sum gives the probability amplitude of propagation between the two endpoints, a quantity called the propagator. Solutions of the Feynman path integral formula exist, however, only for a small number of simple systems, and modifications need to be made when dealing with more complicated systems involving singular potentials, including the Coulomb potential. We derive a generalized path integral formula, that can be used in these cases, for a quantity called the pseudo-propagator from which we obtain the fixed-energy amplitude, related to the propagator by a Fourier transform. The new path integral formula is then successfully solved for the Hydrogen atom in two and three dimensions, and we obtain integral representations for the fixed-energy amplitude. / Vägintegral-formuleringen av kvantmekanik generaliserar minsta-verkanprincipen från klassisk mekanik. Feynmans vägintegral kan ses som en summa över alla möjliga vägar en partikel kan ta mellan två givna ändpunkter A och B, där varje väg bidrar till summan med en fasfaktor innehållande den klassiska verkan för vägen. Den resulterande summan ger propagatorn, sannolikhetsamplituden att partikeln går från A till B. Feynmans vägintegral är dock bara lösbar för ett fåtal simpla system, och modifikationer behöver göras när det gäller mer komplexa system vars potentialer innehåller singulariteter, såsom Coulomb--potentialen. Vi härleder en generaliserad vägintegral-formel som kan användas i dessa fall, för en pseudo-propagator, från vilken vi erhåller fix-energi-amplituden som är relaterad till propagatorn via en Fourier-transform. Den nya vägintegral-formeln löses sedan med framgång för väteatomen i två och tre dimensioner, och vi erhåller integral-representationer för fix-energi-amplituden.