Na primeira parte do trabalho estudamos a equação de Schrödinger logarítmica com um delta potencial; $V(x)=-\\gamma \\,\\delta(x)$, onde $\\delta$ é a distribuição de Dirac na origem e o parâmetro real $\\gamma$ descreve a intensidade do potencial. Estabelecemos a existência e unicidade das soluções do problema de Cauchy associado em um espaço de funções adequado. No caso do potencial atrativo ($\\gamma>0$), calculamos de forma explícita o seu único ground state e mostramos a sua estabilidade orbital.\\\\ A segunda parte trata detalhadamente da equação de Schrödinger logarítmica com um delta derivada potencial; $V(x)=-\\gamma\\, \\delta^{\\prime}(x)$. A boa colocação global para o problema de Cauchy é verificada em um espaço de funções adequado. No caso do potencial atrativo ($\\gamma>0$), o conjunto dos ground states é completamente determinado. Mais precisamente: se $0<\\gamma\\leq2$, então há um único ground state e é uma função ímpar; se $\\gamma>2$, então existem dois ground states não-simétricos. Em adição, provamos que cada ground state é orbitalmente estável através de uma abordagem variacional. Finalmente, usando a teoria de extensão de operadores simétricos, também mostramos um resultado de instabilidade para $\\gamma>2$. / The first part of this thesis deals with the logarithmic Schrödinger equation with a delta potential; $V(x)=-\\gamma \\,\\delta(x)$, where $\\delta$ is the Dirac distribution at the origin and the real parameter $\\gamma$ is interpreted as the strength of the potential. We establish the existence and uniqueness of the solutions of the associated Cauchy problem in a suitable functional framework. In the attractive potential case ($\\gamma>0$), we explicitly compute the unique ground state and we show their orbital stability .\\\\ The second part deals with the case of the logarithmic Schrödinger equation with a delta prime potential; $V(x)=-\\gamma\\, \\delta^{\\prime}(x)$. Global well-posedness is verified for the Cauchy problem in a suitable functional space. In the attractive potential case ($\\gamma>0$), the set of the ground state is completely determined. More precisely: if $0<\\gamma\\leq2$, then there is a single ground state and it is an odd function; if $\\gamma>2$, then there exist two non-symmetric ground states. Moreover, we show that every ground state is orbitally stable via a variational approach. Finally, by applying the theory of extensions of symetric operators, we also prove a result of instability for $\\gamma>2$.

Na primeira parte do trabalho estudamos a equação de Schrödinger logarítmica com um delta potencial; $V(x)=-\\gamma \\,\\delta(x)$, onde $\\delta$ é a distribuição de Dirac na origem e o parâmetro real $\\gamma$ descreve a intensidade do potencial. Estabelecemos a existência e unicidade das soluções do problema de Cauchy associado em um espaço de funções adequado. No caso do potencial atrativo ($\\gamma>0$), calculamos de forma explícita o seu único ground state e mostramos a sua estabilidade orbital.\\\\ A segunda parte trata detalhadamente da equação de Schrödinger logarítmica com um delta derivada potencial; $V(x)=-\\gamma\\, \\delta^{\\prime}(x)$. A boa colocação global para o problema de Cauchy é verificada em um espaço de funções adequado. No caso do potencial atrativo ($\\gamma>0$), o conjunto dos ground states é completamente determinado. Mais precisamente: se $0<\\gamma\\leq2$, então há um único ground state e é uma função ímpar; se $\\gamma>2$, então existem dois ground states não-simétricos. Em adição, provamos que cada ground state é orbitalmente estável através de uma abordagem variacional. Finalmente, usando a teoria de extensão de operadores simétricos, também mostramos um resultado de instabilidade para $\\gamma>2$. / The first part of this thesis deals with the logarithmic Schrödinger equation with a delta potential; $V(x)=-\\gamma \\,\\delta(x)$, where $\\delta$ is the Dirac distribution at the origin and the real parameter $\\gamma$ is interpreted as the strength of the potential. We establish the existence and uniqueness of the solutions of the associated Cauchy problem in a suitable functional framework. In the attractive potential case ($\\gamma>0$), we explicitly compute the unique ground state and we show their orbital stability .\\\\ The second part deals with the case of the logarithmic Schrödinger equation with a delta prime potential; $V(x)=-\\gamma\\, \\delta^{\\prime}(x)$. Global well-posedness is verified for the Cauchy problem in a suitable functional space. In the attractive potential case ($\\gamma>0$), the set of the ground state is completely determined. More precisely: if $0<\\gamma\\leq2$, then there is a single ground state and it is an odd function; if $\\gamma>2$, then there exist two non-symmetric ground states. Moreover, we show that every ground state is orbitally stable via a variational approach. Finally, by applying the theory of extensions of symetric operators, we also prove a result of instability for $\\gamma>2$.

Studying nuclei beyond the proton dripline can provide valuable information on the structure of nuclei at the limits of stability, where the strong nuclear force starts to be overcome by Coulomb repulsion between protons. Simple experimental observables, such as excitation energies and lifetimes of excited states in these proton-unbound nuclei can provide information on the nuclear wave function. Experimental data, such as that presented in this work, can then be used to improve models of nuclear structure at the proton dripline. This thesis presents data from a recoil-decay tagged differential plunger experiment undertaken at the University of Jyvaskyla in 2014. A fusion-evaporation reaction was used to populate excited states in the deformed ground-state proton emitter 113Cs. The JUROGAM-RITU-GREAT experimental setup was used to correlate gamma rays emitted from these excited states with protons emitted from 113Cs and the differential plunger for unbound nuclear states (DPUNS) was placed at the target position to measure the excited state lifetimes. The lifetime of the (11/2+) state in the most intense rotational band of 113Cs was measured to be tau = 24(6) ps, while a limit of tau is less than or equal to 5 ps was found for the lifetime of the higher energy (15/2+) state. The lifetime of proton emission was measured to be tau = 24.2(2) microseconds. The experimental data were used to test the predictions of a non adiabatic quasi-particle model for proton-emitting nuclei, which was employed to deduce the deformation of the states in 113Cs. Wave functions from the non adiabatic quasi-particle model were used to independently calculate proton-emission rates, gamma-ray transition rates and excited state energies as functions of deformation. The deformation of 113Cs could then be extracted from the intersection of the different theoretical values and experimental observables. A deformation of beta2 = 0.22(6)was extracted from the (11/2+) excitation energy and lifetime. The deformation values taken from the proton-emission rate and the lifetime limit of the (15/2+) state were also consistent with this value. The consistency of the different deformations calculated shows the effectiveness of the non adiabatic quasi-particle method when used to calculate the properties of deformed ground-state proton-emitters.

We consider the Cauchy problem for the focusing energy critical NLS with inverse square potential. The energy of the solution, which consists of the kinetic energy and potential energy, is conserved for all time. Due to the focusing nature, solution with arbitrary energy may exhibit various behaviors: it could exist globally and scatter like a free evolution, persist like a solitary wave, blow up at finite time, or even have mixed behaviors. Our goal in this thesis is to fully characterize the solution when the energy is below or at the level of the energy of the ground state solution $W_a$. Our main result contains two parts. First, we prove that when the energy and kinetic energy of the initial data are less than those of the ground state solution, the solution exists globally and scatters. Second, we show a rigidity result at the level of ground state solution. We prove that among all solutions with the same energy as the ground state solution, there are only two (up to symmetries) solutions $W_a^+, W_a^-$ that are exponential close to $W_a$ and serve as the threshold of scattering and blow-up. All solutions with the same energy will blow up both forward and backward in time if they go beyond the upper threshold $W_a^+$; all solutions with the same energy will scatter both forward and backward in time if they fall below the lower threshold $W_a^-$. In the case of NLS with no potential, this type of results was first obtained by Kenig-Merle \cite{R: Kenig focusing} and Duyckaerts-Merle \cite{R: D Merle}. However, as the potential has the same scaling as $\Delta$, one can not expect to extend their results in a simple perturbative way. We develop crucial spectral estimates for the operator $-\Delta+a/|x|^2$, we also rely heavily on the recent understanding of the operator $-\Delta+a/|x|^2$ in \cite{R: Harmonic inverse KMVZZ}.

This thesis presents an implementation of path integral molecular dynamics (PIMD) for sampling equilibrium and dynamical properties within the molecular modelling toolkit (MMTK) [J. Comp. Chem. 21, 79 (2000)], an open source Python package. Rigorous simulation using this code serves to benchmark this implementation as well as the robust- ness of the path integral Langevin equation as a thermostat [J. Chem. Phys. 133, 124104 (2010)]. PIMD is used to calculate equilibrium properties for clusters of HeN-CO2 at low- temperatures, with comparison to experimental and exact results. We characterize the convergence of structural and energetic properties as a function of path-integral discretiza- tion error. The radial and angular distribution of these clusters is studied as a function of size in the absence of rotation and bosonic exchange. These distributions are subsequently used to calculate vibrational shifts of CO2. This result is compared to high-accuracy path integral Monte Carlo simulations which include rotational and exchange effects. These sim- ulations indicate that the neglect of rotational degrees of freedom leads to an unphysical localization of helium atoms and incorrect vibrational shifts when compared to experiment. Approximate real-time quantum dynamics is presented for doped helium clusters using the ring-polymer molecular dynamics (RPMD) method. The accuracy of RPMD is tested iii for low-temperature simulations and compared to exact results. Preliminary calculation of the dynamics of the helium solvated CO2 dopant with respect to the center of mass of the cluster is presented. The effect of a cartesian integrator versus a normal-mode integrator for quantum dynamics is addressed. The path integral ground-state method is applied in order to calculate T = 0 properties. A convergence study of the ground-state energy of the quantum harmonic oscillator with respect to sampling time and path discretization is shown. As a final application of this implementation, a sugar in a periodic water box is simulated at T = 300K. The calculation of rotamer populations and a dipole autocorrelation indicate negligible change with the inclusion of quantum effects. This work offers a comprehensive foundation from which to base future PIMD centered research.

Ground state depletion with individual molecule return (GSDIM) super-resolution microscopy is used to interrogate the location of individual fluorescence bursts from two different nanoparticle-fluorophore systems. The first system consists of fluorophore-labeled DNA molecules on gold nanowire surfaces. In this system carboxytetramethyl rhodamine-labeled double-stranded DNA molecules were bound to the surface of gold nanowires via gold-thiol linkages. The second system focuses on mesoporous silica coated nanorods with dye embedded into the silica coating. The dye molecule, Rhodamine 6G, was incorporated into the silica shell during the nanorod coating procedure. Individual fluorescence bursts were spatially localized using point spread function fitting and used to reconstruct the image of the underlying nanowire or nanorod. / text

The research presented in this dissertation was performed in the Atomic, Molecular and Optical (AMO) physics laboratory at the University of Manitoba. Atomic beams of the two-valence-electron heavy atom systems, barium and ytterbium, were investigated with low energy electron scattering and optical emission studies. Both the ground states and laser excited states were investigated as a function of incident electron beam energy from 10 eV to 50 eV. Measurements of relative cross sections and polarization for 583 nm and 554 nm line emission from the (6s7p)1P1 and (6s6p)1P1 states of barium excited by electron impact from both the ground states and the optically pumped metastable (6s5d)1D2 are reported. Data are normalized to absolute cross sections for the ground state (6s2)1S0→(6s6p)1P1 state transition due to electron scattering, with corrections for branching ratios and cascading from higher states to deduce the total level excitation cross sections. Results are also presented for the first studies of the 399 nm line emission from laser-excited ytterbium, yielding an upper limit on the apparent cross section for the (6s6p)3P1→(6s6p)1P1 transition. Results are compared with the latest theoretical models and previous data, where available. / October 2015

This thesis presents an implementation of path integral molecular dynamics (PIMD) for sampling equilibrium and dynamical properties within the molecular modelling toolkit (MMTK) [J. Comp. Chem. 21, 79 (2000)], an open source Python package. Rigorous simulation using this code serves to benchmark this implementation as well as the robust- ness of the path integral Langevin equation as a thermostat [J. Chem. Phys. 133, 124104 (2010)]. PIMD is used to calculate equilibrium properties for clusters of HeN-CO2 at low- temperatures, with comparison to experimental and exact results. We characterize the convergence of structural and energetic properties as a function of path-integral discretiza- tion error. The radial and angular distribution of these clusters is studied as a function of size in the absence of rotation and bosonic exchange. These distributions are subsequently used to calculate vibrational shifts of CO2. This result is compared to high-accuracy path integral Monte Carlo simulations which include rotational and exchange effects. These sim- ulations indicate that the neglect of rotational degrees of freedom leads to an unphysical localization of helium atoms and incorrect vibrational shifts when compared to experiment. Approximate real-time quantum dynamics is presented for doped helium clusters using the ring-polymer molecular dynamics (RPMD) method. The accuracy of RPMD is tested iii for low-temperature simulations and compared to exact results. Preliminary calculation of the dynamics of the helium solvated CO2 dopant with respect to the center of mass of the cluster is presented. The effect of a cartesian integrator versus a normal-mode integrator for quantum dynamics is addressed. The path integral ground-state method is applied in order to calculate T = 0 properties. A convergence study of the ground-state energy of the quantum harmonic oscillator with respect to sampling time and path discretization is shown. As a final application of this implementation, a sugar in a periodic water box is simulated at T = 300K. The calculation of rotamer populations and a dipole autocorrelation indicate negligible change with the inclusion of quantum effects. This work offers a comprehensive foundation from which to base future PIMD centered research.

xi, 125 p. : ill. (some col.) A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number. / This dissertation presents experimental and theoretical studies of radiation pressure cooling in silica optomechanical microresonators where whispering gallery modes (WGMs) are coupled to thermal mechanical vibrations. In an optomechanical system, circulating optical fields couple to mechanical vibrations via radiation pressure, inducing Stokes and anti-Stokes scattering of photons. In analogy to laser cooling of trapped ions, the mechanical motion can in principle be cooled to its ground state via the anti-Stokes process in the resolved-sideband limit, in which the cavity photon lifetime far exceeds the mechanical oscillation period. Our optomechanical system is a slightly deformed silica microsphere (with a diameter 25-30 μm ), featuring extremely high Q -factors for both optical ( Q o ∼ 10 8 ) and mechanical ( Q m ∼ 10 4 ) systems. Exploiting the unique property of directional evanescent escape in the deformed resonator, we have developed a free-space configuration for the excitation of WGMs and for the interferometric detection of mechanical displacement, for which the part of input laser that is not coupled into the microsphere serves as a local oscillator. Measurement sensitivity better than 5 × 10 -18 m /[Special characters omitted.] has been achieved. The three optically active mechanical modes observed in the displacement power spectrum are well described by finite element analysis. Both radiation pressure cooling and parametric instabilities have been observed in our experiments. The dependence of the mechanical resonator frequency and linewidth on the detuning as well as the intensity of the input laser show excellent agreement with theoretical calculations with no adjustable parameters. The free-space excitation technique has enabled us to combine resolved sideband cooling with cryogenic cooling. At a cryogenic temperature of 1.4 K, the sideband cooling leads to an effective temperature as low as 210 m K for a 110 MHz mechanical oscillator, corresponding to an average phonon occupation of 37, which is one of the three lowest phonon occupations achieved thus far for optomechanical systems. The cooling process is limited by ultrasonic attenuation in fused silica, which should diminish when bath temperature is further lowered, with a 3 He cryostat, to a few hundred millikelvin. Our experimental studies thus indicate that we are tantalizingly close to realizing the ground-state cooling for the exploration of quantum effects in an otherwise macroscopic mechanical system. / Committee in charge: Michael Raymer, Chairperson, Physics; Jens Noeckel, Member, Physics; Hailin Wang, Member, Physics; Paul Csonka, Member, Physics; Jeffrey Cina, Outside Member, Chemistry

Made available in DSpace on 2015-05-14T13:21:20Z (GMT). No. of bitstreams: 1 ArquivoTotal.pdf: 4842604 bytes, checksum: 4468b46dc88edcbb8cca74341b5e5b91 (MD5) Previous issue date: 2013-03-05 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / A research of nitrosamines has attracted attention, because its complexation with the heme group of cytochrome P450 may be associated with its carcinogenic potential. To characterize this problem is realized quantum-chemical treatment of some molecules from the class of metalloporphyrins, more specifically porphyrins Iron III, similar to the heme group mentioned above, with two nitrosamines ligand in axial positions. In literature it is reported that, experimentally these ferroporfirinas containing nitrosamines ligand, have been synthesized and structurally characterized and properly paramagneticamente (sextet spin state). As the Fe (III), this complex presents three possible spin state (doublet, quartet and sextet) the motivation of this dissertation is to know theoretically what spin state most likely to be the ground state, with the goal of describing the relative energy difference between these spin states of Fe (III), as well as characterize the order of energy d orbitals belonging to unpaired electrons alpha iron, these three electronic states. Thus, we performed single-point calculations analyzing guess in control from the beginning of SCF calculation using the program Gaussian09, using ab initio methods at the Hartree-Fock version restricted and unrestricted layer to open with charges calculations NBO, with a set base 6-31 + g *, 6-311 + g * and cc-pVDZ. The method UHF / cc-pVDZ, with Harris and guess Rdscale, showed the best results, providing the lowest energies and contamination in spin states. For the method using the ROHF wave function generated by calculating the spin state in the method sextet UHF wave function as initial results showed parallel to the UHF method. The Mulliken population analysis and NBO, the shape of the spin density and the electrostatic potential map show the location of the positive charge on the iron. The d orbitals, the unpaired electrons, show no overlap with the orbitals of dimetilnitrosaminas. The main contribution of the theoretical results are in agreement with the experimental results available in the literature about the spin state of Fe (III) heme group in the interaction with the dimetilnitrosaminas. / A pesquisa envolvendo nitrosaminas tem despertado interesse, pois a sua complexação com o Fe do grupo heme do Citocromo P450 pode estar associada ao seu potencial carcinogênico. Para caracterização deste problema, realiza-se o tratamento químico-quântico de algumas moléculas da classe das metaloporfirinas, mais especificamente porfirinas de Ferro III, similares às do grupo heme citado acima, com duas nitrosaminas ligadas nas posições axiais. Na literatura é relatado que, experimentalmente, estas ferroporfirinas contendo ligantes nitrosaminas, já foram sintetizadas e devidamente caracterizadas estruturalmente e paramagneticamente (estado de spin sexteto). Como o Fe(III), neste complexo, apresenta três possibilidades de estado de spin (dubleto, quarteto e sexteto) a motivação desta dissertação é saber teoricamente qual o estado de spin mais provável para ser o estado fundamental, com o objetivo de descrever a diferença de energia relativa entre esses estados de spin do Fe(III), assim como caracterizar a ordem de energia dos orbitais d, pertencentes aos elétrons alfa desemparelhados do ferro, nesses três estados eletrônicos. Para isso, foram realizados cálculos single-point analisando os chutes iniciais no controle do início do cálculo SCF utilizando o programa Gaussian09, empregando métodos ab initio a nível Hartree-Fock na versão restrita e irrestrita para camada aberta com cálculos de carga NBO, com um conjunto de base 6-31+G*, 6-311+G* e cc-pVDZ. O método UHF/cc-pVDZ, com o chute inicial para função de onda Harris e Rdscale, apresentaram os melhores resultados, fornecendo as menores energias e contaminações nos estados de spin. Para o método ROHF utilizando a função de onda gerada pelo cálculo no estado de spin sexteto no método UHF, como função de onda inicial, mostrou resultados paralelos ao do método UHF. A análise populacional de Mulliken e NBO, a forma da densidade de spin e o mapa do potencial eletrostático evidenciam a localização da carga positiva no ferro. Os orbitais d, dos elétrons desemparelhados, mostram nenhuma sobreposição com os orbitais das dimetilnitrosaminas. A principal contribuição dos resultados teóricos, está na concordância com o resultado experimental disponível na literatura, sobre o estado de spin do Fe(III) do grupo Heme na interação com as dimetilnitrosaminas.