We present a time-dependent mixed quantum/semiclassical approach to calculating linear absorption spectra. Applying Variational Fixed Vibrational Basis/Gaussian Bath theory (FVB/GB) to the treatment of small molecules isolated in an extended cryogenic medium, an assumed time-scale separation between the few rapid, largely intramolecular modes of the guest and the several slower extended modes of the medium is utilized to partition a system from the surrounding bath. The system dynamics are handled with basis set methods, while the bath degrees of freedom are subject to a semiclasscial thawed Gaussian ansatz. The linear absorption spectrum for a realistic model system is calculated using FVB/GB results and then compared with a numerically exact calculation. Also contained in this dissertation are previously published theoretical works on Transient Absorption and Femtosecond Stimulated Raman Spectroscopy. Both encompass a rebuilding of the theory and elucidate the information content of the respective spectroscopic signals. This dissertation includes previously published co-authored material.

Orientador: Marcus Aloizio Martinez de Aguiar / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin / Made available in DSpace on 2018-08-24T22:36:15Z (GMT). No. of bitstreams: 1 Barreto_WendellPereira_M.pdf: 1811207 bytes, checksum: 0f8c73a79029cd1792710999b0f258a0 (MD5) Previous issue date: 2014 / Resumo: A evolução temporal de estados quânticos é estudada do ponto de vista semiclássico usando o propagador na representação de estados coerentes. No limite semiclássico o propagador pode ser calculado em termos de soluções complexas das equações de Hamilton que devem satisfazer condições de contorno apropriadas. No entanto, nem todas as soluções podem ser utilizadas no cálculo do propagador. Certas trajetórias, denominadas não contribuintes devem ser descartadas, pois dão contribuições incorretas ao propagador. Aqui, exploramos a questão das trajetórias não contribuintes, que é um dos problemas mais sérios na aplicação sistemática das expressões semiclássicas envolvendo órbitas complexas. Para isso consideramos uma classe de problemas unidimensionais não-lineares onde as soluções clássicas e quânticas poder ser obtidas analiticamente. Dessa forma, o propagador semiclássico pode ser escrito de forma explícita, o que permite uma análise detalhada da contribuição de cada trajetória. Definimos então um critério mais preciso para a exclusão de soluções espúrias e, enfim, melhorar o cálculo semiclássico. O sistema foco neste estudo foi o oscilador harmônico ao quadrado, cuja dinâmica tem solução analítica e está presente em problemas de óptica não linear / Abstract: The time evolution of quantum states is studied in the semiclassical limit using the semiclassical propagator in the coherent-state representation. In the semiclassical limit the quantum propagator can be calculated with complex solutions of Hamilton's equations satisfying appropriate boundary conditions. However, not all these solutions can be used in the expression for the propagator. Some trajectories, called non contributing trajectories, give incorrect contributions to the propagator and should be excluded. In this work the issue of non-contributing trajectories, which is one of the most serious problems in the systematic application of semiclassical expression involving complex orbits, is studied. We explore a class of nonlinear one-dimensional problems for which classical and quantum solutions can be analytically obtained. For these problems, the semiclassical propagator can be written explicitty allowing a detailed analisys of the contribution of each trajectory. In this work we will focus on the ''squared harmonic oscillator'', it can be solved analytically and it is present in problems of nonlinear optics / Mestrado / Física / Mestre em Física

>Magister Scientiae - MSc / This thesis aims at developing a sorting code for Coulomb excitation studies at iThemba LABS. In Coulomb excitation reactions, the inelastic scattering of the projectile transfers energy to the partner nucleus (and vice-versa) through a time-dependent electromagnetic field. At energies well below the Coulomb barrier, the particles interact solely through the well known electromagnetic interaction, thereby excluding nuclear excitations from the process . The data can therefore be analyzed using a semiclassical approximation. The sorting code was used to process and analyze data acquired from the Coulomb excitation of 20Ne beams at 73 and 96 MeV, onto a 194Pt target. The detection of gamma rays was done using the AFRODITE HPGe clover detector array, which consists of nine clover detectors, in coincidence with the 20Ne particles detected with an S3 double-sided silicon detector. The new sorting code includes Doppler-correction effects, charge-sharing, energy and time conditions, kinematics and stopping powers, among others, and can be used for any particle-γ coincidence measurements at iThemba LABS. Results from other Coulomb excitation measurements at iThemba LABS will also be presented.

Berry curvature appears in the semi-classical theory of Bloch electrons already to first order in electromagnetic fields, resulting in profound modification of the carrier velocity and phase space density of states. Here we derive the equations of motion for the physical position and crystal momentum to second order in the fields. The dynamics still has a Hamiltonian structure, albeit with noncanonical Poisson brackets between the physical variables. We are able to expand both the carrier energy and the Poisson brackets to second order in the fields with terms of clear physical meaning. To demonstrate the utility of our theory, we obtain with much ease the electromagnetic response and orbital magnetic susceptibility. / text

Halo nuclei are among the strangest nuclear structures. They are viewed as a core containing most of the nucleons surrounded by one or two loosely bound nucleons. These have a high probability of presence at a large distance from the core. Therefore, they constitute a sort of halo surrounding the other nucleons. The core, remaining almost unperturbed by the presence of the halo is seen as a usual nucleus. <P> The Coulomb breakup reaction is one of the most useful tools to study these nuclei. It corresponds to the dissociation of the halo from the core during a collision with a heavy (high <I>Z</I>) target. In order to correctly extract information about the structure of these nuclei from experimental cross sections, an accurate theoretical description of this mechanism is necessary. <P> In this work, we present a theoretical method for studying the Coulomb breakup of one-nucleon halo nuclei. This method is based on a semiclassical approximation in which the projectile is assumed to follow a classical trajectory. In this approximation, the projectile is seen as evolving in a time-varying potential simulating its interaction with the target. This leads to the resolution of a time-dependent Schrödinger equation for the projectile wave function. <P> In our method, the halo nucleus is described with a two-body structure: a pointlike nucleon linked to a pointlike core. In the present state of our model, the interaction between the two clusters is modelled by a local potential. <P> The main idea of our method is to expand the projectile wave function on a three-dimensional spherical mesh. With this mesh, the representation of the time-dependent potential is fully diagonal. Furthermore, it leads to a simple representation of the Hamiltonian modelling the halo nucleus. This expansion is used to derive an accurate evolution algorithm. <P> With this method, we study the Coulomb breakup of three nuclei: ¹¹Be, ¹⁵C and ⁸B. ¹¹Be is the best known one-neutron halo nucleus. Its Coulomb breakup has been extensively studied both experimentally and theoretically. Nevertheless, some uncertainty remains about its structure. The good agreement between our calculations and recent experimental data suggests that it can be seen as a <I>s1/2</I> neutron loosely bound to a ¹⁰Be core in its 0⁺ ground state. However, the extraction of the corresponding spectroscopic factor have to wait for the publication of these data. <P> ¹⁵C is a candidate one-neutron halo nucleus whose Coulomb breakup has just been studied experimentally. The results of our model are in good agreement with the preliminary experimental data. It seems therefore that ¹⁵C can be seen as a ¹⁴C core in its 0⁺ ground state surrounded by a <I>s1/2</I> neutron. Our analysis suggests that the spectroscopic factor corresponding to this configuration should be slightly lower than unity. <P> We have also used our method to study the Coulomb breakup of the candidate one-proton halo nucleus ⁸B. Unfortunately, no quantitative agreement could be obtained between our results and the experimental data. This is mainly due to an inaccuracy in the treatment of the results of our calculations. Accordingly, no conclusion can be drawn about the pertinence of the two-body model of ⁸B before an accurate reanalysis of these results. <P> In the future, we plan to improve our method in two ways. The first concerns the modelling of the halo nuclei. It would be indeed of particular interest to test other models of halo nuclei than the simple two-body structure used up to now. The second is the extension of this semiclassical model to two-neutron halo nuclei. However, this cannot be achieved without improving significantly the time-evolution algorithm so as to reach affordable computational times.

No description available.

No description available.

O objetivo desta Tese foi a aplicação da teoria dos estados coerentes para sistemas quânticos não-triviais. A partir da definição de estados coerentes para grupos de Lie compactos em geral, nos dedicamos a uma investigação detalhada da construção de tais estados e de suas propriedades no caso do grupo simplético unitário Sp(4), que é extremamente importante tanto em mecânica quântica quanto em mecânica clássica. Esse grupo possui uma complexidade intermediária, que permite um tratamento analítico ainda que apresente propriedades não-triviais do ponto de vista de teoria de representação de álgebras de Lie. Os estados coerentes obtidos nos permitiram uma investigação do limite clássico para sistemas com simetria Sp(4) e uma conexão com a teoria do caos em mecânica quântica. Além disso, tratamos uma proposta recente de generalização do conceito de estados coerentes para sistemas de espectro discreto não-degenerado, os estados de Gazeau-Klauder. Esses estados foram aplicados a um problema de magnetização bidimensional e também ao potencial unidimensional de mínimos duplos, onde observamos o aparecimento dos estados chamados \"Gatos de Schrödinger\", que consistem na superposição de dois estados de mínima incerteza. / The subject of the Thesis was the aplication of the coherent states theory to non-trivial quantum systems. Starting from the general definition of coherent states for compact Lie groups, we made a detailed investigation of the construction of these states and its properties in the case of the unitary symplectic group Sp(4), which is extremely important in both quantum and classical mechanics. This group has an intermediate complexity, allowing an analytic treatment while presenting non-trivial properties from the point of view of represention theory of Lie algebras. The coherent states so obtained allowed us an investigation of the classical limit of systems with Sp(4) symmetry and a conection with the theory of chaos in quantum mechanics. Besides that, we have treated a recent generalization of the concept of coherent states for systems with discrete and nondegenerate spectrum, the Gazeau-Klauder states. These states were applied to a twodimensional magnetization problem and also to the onedimensional double-well potential, where we have observed the appearence of the so-called \"Schrödinger cats\", which consist in the superposition of two minimum-uncertainty states.

Nesta tese, obtemos estados quânticos que satisfazem a equação de Schrödinger, para Hamiltonianos quadráticos de forma geral e, ao mesmo tempo, permitem de maneira natural obter a correspondência com a descrição clássica. Usamos o método de integrais de movimento para construir operadores de criação e aniquilação, que satisfazem a álgebra de Weyl-Heisenberg. Dessa forma, construímos os estados de número generalizados (ENG) de maneira análoga ao que é feito para os estados de Fock. Obtemos diferentes famílias de estados coerentes (EC), através de uma superposição dos ENG, que chamamos de estados coerentes generalizados (ECG). Esses estados são rotulados pela constante complexa z escrita em termos do valor esperado inicial da coordenada e do momento. Escrevemos os ECG em função do desvio padrão inicial na coordenada, $\\sigma_q$, de modo a minimizar a relação de incerteza de Heisenberg no instante de tempo inicial. Obtemos, de forma pioneira, os ECG para partícula livre e discutimos em detalhes suas propriedades, tal como a relação de completeza, a minimização das relações de incerteza e a evolução da correspondente densidade de probabilidade. Mostramos que o valor esperado da coordenada e do momento segue ao longo da trajetória clássica no espaço de fase. Mostramos que, quando o comprimento de onda da partícula livre é muito menor que $\\sigma_q$, os EC se comportam como estados semiclássicos. Além da partícula livre, construímos pela primeira vez, os ECG para o oscilador invertido e discutimos em detalhes suas propriedades. Mostramos que os ECG de sistemas diferentes podem ser relacionados, impondo condições sobre os parâmetros do Hamiltoniano. Por fim, consideramos Hamiltonianos dependentes do tempo, em particular, construímos os ECG, de forma exata, para um oscilador harmônico cuja frequência varia explicitamente no tempo. Mostramos ainda modelos úteis para obter solução exata de sistemas dependentes do tempo, fazendo analogia com a equação de spin ou equação de Schrödinger unidimensional independente do tempo. Além disso, desenvolvemos um método próprio, que fixa a solução e em seguida determinamos a forma da frequência. / In this thesis we obtain quantum states that satisfy the Schrödinger equation for quadratic Hamiltonians in the general form and at the same time allow, naturally, to obtain the correspondence with the classical description. For this, we use the method of integrals of motion to construct creation and annihilation operators, which satisfy the algebra of Weyl-Heisenberg. Thus, we obtain the generalized number states (GNS) in the same way that is done for the Fock states. We obtain diferent families of coherent states (CS) that we call generalized CS (GCS), by a superposition of GNS. These states are labeled by a complex constant z which is written in terms of the initial expected values of the coordinate and momentum. We write the GCS in terms of the initial standard deviation of the coordinate, $\\sigma_q$, which provides the minimization of Heisenberg uncertainty relation at the initial instant time. In particular, we obtain for the first time the GCS for the free particle and discuss in detail their properties, such as the completeness relation, the minimization of uncertainty relations, and the evolution of the corresponding probability density. We show that the expected values of coordinated and momentum propagate along the classical trajectory in phas espace. When the Compton wavelength is much smaller than $\\sigma_q$, the CS can be considered a semiclassical state. In addition to the free particle, we obtain for the first time the GCS for the inverted oscillator and discuss in detail their properties. We show that the GCS of diferent systems can be related by imposing conditions on the parameters of the Hamiltonian. Finally, we consider the time-dependent Hamiltonian, especially to obtain the GCS for a harmonic oscillator whose frequency varies explicitly in time. We also show useful models to obtain exact solution for time-dependent systems, by analogy with the spin equation or one-dimensionaltime-independent Schrödinger equation, as well as a method which consists first to find the solution and then determine the shape of the frequency.

Orientador: Marcus Aloizio Martinez de Aguiar / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin / Made available in DSpace on 2018-09-02T17:51:39Z (GMT). No. of bitstreams: 1 Grigolo_Adriano_D.pdf: 6040981 bytes, checksum: 874a21109be77dc3f306ac9ce74f90b5 (MD5) Previous issue date: 2017 / Resumo: Uma versão generalizada do método 'coupled coherent states' é desenvolvida para estados coerentes associados a grupos de Lie arbitrários. Em contraste com a abordagem original, restrita a funções de base gaussianas, o método estendido é adequado para propagação de estados quânticos de sistemas exibindo propriedades físicas destituídas de análogo clássico, tais como graus de liberdade de spin ou indistinguibilidade de partículas. A formulação para o caso de sistemas com um número fixo de partículas idênticas interagentes é examinada em detalhe, sendo este um caso relevante descrito em termos de estados coerentes do grupo especial unitário. A técnica é ilustrada com aplicações simples, envolvendo modelos de Hubbard bosônicos e fermiônicos. Diversos aspectos da implementação numérica são discutidos / Abstract: A generalized version of the coupled coherent states method for coherent states of arbitrary Lie groups is developed. In contrast to the original approach, which is restricted to frozen-Gaussian basis sets, the extended method is suitable for propagating quantum states of systems featuring non-classical physical properties, such as spin degrees of freedom or particle interchange symmetry. The formulation for the relevant case of number-conserving systems of interacting identical particles, most adequately described in terms of coherent states of the special unitary group, is studied in detail. The technique is illustrated with applications to simple Hubbard-like models for both bosons and fermions. Several aspects of the numerical implementation are discussed / Doutorado / Física / Doutor em Ciências / 2011/20065-4 / 141338/2011-3 / FAPESP / CNPQ