Some Inverse Problems in Analysis and Geometry

Thesis (Ph.D.)--University of Washington, 2016-08

Efeito do substituinte “-F” nas propriedades electrónicas e estruturais de fluoroquinolonas

Este estudo incide sobre as características que a presença do ião flúor em moléculas concede. Mais concretamente em fluoroquinolonas, antibióticos que cada vez são mais utilizados. Fez-se uma analise de vários parâmetros para obtermos informação sobre a interação fármaco-receptor nas fluoroquinolonas. Sendo para isso utilizadas técnicas de caracterização química computacional para conseguirmos caracterizar eletronicamente e estruturalmente (3D) as fluoroquinolonas em complemento aos métodos semi-empíricos utilizados inicialmente. Como é sabido, a especificidade e a afinidade para o sitio alvo, é essencial para eficácia de um fármaco. As fluoroquinolonas sofreram um grande desenvolvimento desde a primeira quinolona sintetizada em 1958, sendo que desde ai foram sintetizadas inúmeros derivados da mesma. Este facto deve-se a serem facilmente manipuladas, derivando fármacos altamente potentes, espectro alargado, factores farmacocinéticos optimizados e efeitos adversos reduzidos. A grande alteração farmacológica para o aumento do interesse neste grupo, foi a substituição em C6 de um átomo de flúor em vez de um de hidrogénio. Para obtermos as informações sobre a influência do ião flúor sobre as propriedades estruturais e electrónicas das fluoroquinolonas, foi feita uma comparação entre a fluoroquinolona com flúor em C6 e com hidrogénio em C6. As quatro fluoroquinolonas presentes neste estudo foram: ciprofloxacina, moxiflocacina, sparfloxacina e pefloxacina. As informações foram obtidas por programas informáticos de mecânica quântica e molecular. Concluiu-se que a presença de substituinte flúor não modificava de forma significativa a geometria das moléculas mas sim a distribuição da carga no carbono vicinal e nos átomos em posição alfa, beta e gama relativamente a este. Esta modificação da distribuição electrónica pode condicionar a ligação do fármaco ao receptor, modificando a sua actividade farmacológica.

A representation-free description of the Kasevich-Chu interferometer: a resolution of the redshift controversy

Motivated by a recent claim by Muller et al (2010 Nature 463 926-9) that an atom interferometer can serve as an atom clock to measure the gravitational redshift with an unprecedented accuracy, we provide a representation-free description of the Kasevich-Chu interferometer based on operator algebra. We use this framework to show that the operator product determining the number of atoms at the exit ports of the interferometer is a c-number phase factor whose phase is the sum of only two phases: one is due to the acceleration of the phases of the laser pulses and the other one is due to the acceleration of the atom. This formulation brings out most clearly that this interferometer is an accelerometer or a gravimeter. Moreover, we point out that in different representations of quantum mechanics such as the position or the momentum representation the phase shift appears as though it originates from different physical phenomena. Due to this representation dependence conclusions concerning an enhanced accuracy derived in a specific representation are unfounded.

Which-path problem for one and two particles with two degrees of freedom and a relation between transverse spatial structure and group velocity of light

Quantum mechanics, optics and indeed any wave theory exhibits the phenomenon of interference. In this thesis we present two problems investigating interference due to indistinguishable alternatives and a mostly unrelated investigation into the free space propagation speed of light pulses in particular spatial modes. In chapter 1 we introduce the basic properties of the electromagnetic field needed for the subsequent chapters. In chapter 2 we review the properties of interference using the beam splitter and the Mach-Zehnder interferometer. In particular we review what happens when one of the paths of the interferometer is marked in some way so that the particle having traversed it contains information as to which path it went down (to be followed up in chapter 3) and we review Hong-Ou-Mandel interference at a beam splitter (to be followed up in chapter 5). In chapter 3 we present the first of the interference problems. This consists of a nested Mach-Zehnder interferometer in which each of the free space propagation segments are weakly marked by mirrors vibrating at different frequencies [1]. The original experiment drew the conclusions that the photons followed disconnected paths. We partition the description of the light in the interferometer according to the number of paths it contains which-way information about and reinterpret the results reported in [1] in terms of the interference of paths spatially connected from source to detector. In chapter 4 we briefly review optical angular momentum, entanglement and spontaneous parametric down conversion. These concepts feed into chapter 5 in which we present the second of the interference problems namely Hong-Ou-Mandel interference with particles possessing two degrees of freedom. We analyse the problem in terms of exchange symmetry for both boson and fermion pairs and show that the particle statistics at a beam splitter can be controlled for suitably chosen states. We propose an experimental test of these ideas using orbital angular momentum entangled photons. In chapter 6 we look at the effect that the transverse spatial structure of the mode that a pulse of light is excited in has on its group velocity. We show that the resulting group velocity is slower than the speed of light in vacuum for plane waves and that this reduction in the group velocity is related to the spread in the wave vectors required to create the transverse spatial structure. We present experimental results of the measurement of this slowing down using Hong-Ou-Mandel interference.

Satisfying the Einstein-Podolsky-Rosen criterion with massive particles

In 1935, Einstein, Podolsky and Rosen (EPR) questioned the completeness of quantum mechanics by devising a quantum state of two massive particles with maximally correlated space and momentum coordinates. The EPR criterion qualifies such continuous-variable entangled states, where a measurement of one subsystem seemingly allows for a prediction of the second subsystem beyond the Heisenberg uncertainty relation. Up to now, continuous-variable EPR correlations have only been created with photons, while the demonstration of such strongly correlated states with massive particles is still outstanding. Here we report on the creation of an EPR-correlated two-mode squeezed state in an ultracold atomic ensemble. The state shows an EPR entanglement parameter of 0.18(3), which is 2.4 s.d. below the threshold 1/4 of the EPR criterion. We also present a full tomographic reconstruction of the underlying many-particle quantum state. The state presents a resource for tests of quantum nonlocality and a wide variety of applications in the field of continuous-variable quantum information and metrology.

A interpretação de Copenhague e os estados relativos de Hugh Everett III : o problema do realismo científico

Dissertação (mestrado)—Universidade de Brasília,Instituto de Ciências Humanas, Programa de Pós-Graduação em Filosofia, 2015.

Atmospheric calibration for sub-millimeter radio astronomy

This thesis is focused on improving the calibration accuracy of sub-millimeter astronomical observations. The wavelength range covered by observational radio astronomy has been extended to sub-millimeter and far infrared with the advancement of receiver technology in recent years. Sub-millimeter observations carried out with airborne and ground-based telescopes typically suffer from 10% to 90% attenuation of the astronomical source signals by the terrestrial atmosphere. The amount of attenuation can be derived from the measured brightness of the atmospheric emission. In order to do this, the knowledge of the atmospheric temperature and chemical composition, as well as the frequency-dependent optical depth at each place along the line of sight is required. The altitude-dependent air temperature and composition are estimated using a parametrized static atmospheric model, which is described in Chapter 2, because direct measurements are technically and financially infeasible. The frequency dependent optical depth of the atmosphere is computed with a radiative transfer model based on the theories of quantum mechanics and, in addition, some empirical formulae. The choice, application, and improvement of third party radiative transfer models are discussed in Chapter 3. The application of the calibration procedure, which is described in Chapter 4, to the astronomical data observed with the SubMillimeter Array Receiver for Two Frequencies (SMART), and the German REceiver for Astronomy at Terahertz Frequencies (GREAT), is presented in Chapters 5 and 6. The brightnesses of atmospheric emission were fitted consistently to the simultaneous multi-band observation data from GREAT at 1.2 ∼ 1.4 and 1.8 ∼ 1.9 THz with a single set of parameters of the static atmospheric model. On the other hand, the cause of the inconsistency between the model parameters fitted from the 490 and 810 GHz data of SMART is found to be the lack of calibration of the effective cold load temperature. Besides the correctness of atmospheric modeling, the stability of the receiver is also important to achieving optimal calibration accuracy. The stabilities of SMART and GREAT are analyzed with a special calibration procedure, namely the “load calibration". The effects of the drift and fluctuation of the receiver gain and noise temperature on calibration accuracy are discussed in Chapters 5 and 6. Alternative observing strategies are proposed to combat receiver instability. The methods and conclusions presented in this thesis are applicable to the atmospheric calibration of sub-millimeter astronomical observations up to at least 4.7 THz (the H channel frequency of GREAT) for observations carried out from ∼ 4 to 14 km altitude. The procedures for receiver gain calibration and stability test are applicable to other instruments using the same calibration approach as that for SMART and GREAT. The structure of the high performance, modular, and extensible calibration program used and further developed for this thesis work is presented in the Appendix C.

Magneto - Transport of electron symmetric and antisymmrtric states in highly doped InGaAs/InAlAs single quantum well

Beating patterns in longitudinal resistance caused by the symmetric and antisymmetric states were observed in a heavily doped InGaAs/InAlAs quantum well by using variable temperature Hall measurement. The energy gap of symmetric and antisymmetric states is estimated to be 4meV from the analysis of beating node positions. In addition, the temperature dependences of the subband electron mobility and concentration were also studied from the mobility spectrum and multicarrier fitting procedure.

Suppression of exciton recombination in symmetric GaAs0.7Sb0.3/GaAs/GaAs0.7P0.3 coupled quantum wells induced by an in-plane magnetic field

Suppression of the exciton recombination in GaAs0.7Sb0.3/GaAs/GaAs0.7P0.3 coupled quantum well (CQW) induced by an external magnetic field is investigated theoretically. Unlike the usual electro-Stark effect, the exciton energy dispersion of an exciton is modified by an external in-plane magnetic field, the ground state of the magnetoexciton shifts from a zero in-plane center of mass (CM) momentum to a finite CM momentum, and the Lorentz force induces the spatial separation of electron and hole. Consequently, this effect renders the ground state of magnetoexciton stable against radiative recombination due to momentum conservation. This effect depends sensitively on the thickness and height of GaAs0.7Sb0.3 layer, therefore it could provide us useful infometion about the band alignment of CQW. (C) 2004 American Institute of Physics.

In-plane optical anisotropy of symmetric and asymmetric (001) GaAs/Al(Ga)As superlattices and quantum wells

Two sensitive polarized spectroscopies, reflectance difference spectroscopy and photocurrent difference spectroscopy, are used to study the characteristic of the in-plane optical anisotropy in the symmetric and the asymmetric (001) GaAs/Al(Ga)As superlattices (SLs). The anisotropy spectra of the symmetric and the asymmetric SLs show significant difference: for symmetric ones, the anisotropies of the 1HH-->1E transition (1H1E) and 1L1E are dominant, and they are always approximately equal and opposite; while for asymmetric ones, the anisotropy of 1H1E is much less than that of 1L1E and 2H1E, and the anisotropy of 3H2E is very strong. The calculated anisotropy spectra within the envelope function model agree with the experimental results, and a perturbation approach is used to understand the role of the electric field and the interface potential in the anisotropy. (C) 2001 American Institute of Physics.

CONSTRUCTING QUANTUM OBSERVABLES AND SELF-ADJOINT EXTENSIONS OF SYMMETRIC OPERATORS. III. SELF-ADJOINT BOUNDARY CONDITIONS

This paper completes the review of the theory of self-adjoint extensions of symmetric operators for physicists as a basis for constructing quantum-mechanical observables. It contains a comparative presentation of the well-known methods and a newly proposed method for constructing ordinary self-adjoint differential operators associated with self-adjoint differential expressions in terms of self-adjoint boundary conditions. The new method has the advantage that it does not require explicitly evaluating deficient subspaces and deficiency indices (these latter are determined in passing) and that boundary conditions are of explicit character irrespective of the singularity of a differential expression. General assertions and constructions are illustrated by examples of well-known quantum-mechanical operators like momentum and Hamiltonian.

Quantum spin tunneling in a soluble quasi-spin model: an angle-based potential description

We propose an approach which allows one to construct and use a potential function written in terms of an angle variable to describe interacting spin systems. We show how this can be implemented in the Lipkin-Meshkov-Glick, here considered a paradigmatic spin model. It is shown how some features of the energy gap can be interpreted in terms of a spin tunneling. A discrete Wigner function is constructed for a symmetric combination of two states of the model and its time evolution is obtained. The physical information extracted from that function reinforces our description of phase oscillations in a potential. (c) 2004 Elsevier B.V. All rights reserved.

Quantum exchange interaction of spherically symmetric plasmoids

We study nano-sized spherically symmetric plasma structures which are radial nonlinear oscillations of electrons in plasma. The effective interaction of these plasmoids via quantum exchange forces between ions is described. We calculate the energy of this interaction for the case of a dense plasma. The conditions when the exchange interaction is attractive are examined and it is shown that separate plasmoids can form a single object. The application of our results to the theoretical description of stable atmospheric plasma structures is considered. (C) 2012 Elsevier Ltd. All rights reserved.