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The Semiclassical Approximation and Strutinsky SmoothingJennings, Byron K. 11 1900 (has links)
<p> An expression for the semiclassical density of states for a particle in a smooth potential well is obtained from the Kirkwood expansion of the partition function. This expression for the semiclassical density of states is then shown to be essentially equivalent to the expression obtained from the Green's function method of Balian and Bloch.</p> <p> The Strutinsky shell correction to the nuclear binding energy is then analytically shown to be equivalent to the shell correction obtained from a consideration of the semiclassical partition function if certain restrictions on the Strutinsky smoothing parameter can be met.</p> / Thesis / Master of Science (MSc)
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Born-Oppenheimer Expansion for Diatomic Molecules with Large Angular MomentumHughes, Sharon Marie 14 November 2007 (has links)
Semiclassical and Born-Oppenheimer approximations are used to provide uniform error bounds for the energies of diatomic molecules for bounded vibrational quantum number n and large angular momentum quantum number l. Specifically, results are given when (l + 1) < κ𝛜⁻³/². Explicit formulas for the approximate energies are also given. Numerical comparisons for the H+₂ and HD+ molecules are presented. / Ph. D.
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The semiclassical theory of the de Haas-van Alphen oscillations in type-II superconductorsDuncan, Kevin P. January 1999 (has links)
No description available.
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Semiclassical monopole calculations in supersymmetric gauge theoriesDavies, N. Michael January 2000 (has links)
We investigate semiclassical contributions to correlation functions in N = 1 supersymmetric gauge theories. Our principal example is the gluino condensate, which signals the breaking of chiral symmetry, and should be exactly calculable, according to a persymmetric non-renormalisation theorem. However, the two calculational approaches previously employed, SCI and WCI methods, yield different values of the gluino condensate. We describe work undertaken to resolve this discrepancy, involving a new type of calculation in which the space is changed from R(^4) to the cylinder R(3) x S(1) This brings control over the coupling, and supersymmetry ensures that we are able to continue to large radii and extract answers relevant to R(^4). The dominant semiclassical configurations on the cylinder are all possible combinations of various types of fundamental monopoles. One specific combination is a periodic instanton, so monopoles are the analogue of the instanton partons that have been conjectured to be important at strong coupling. Other combinations provide significant contributions that are neglected in the SCI approach. Monopoles are shown to generate a superpotential that determines the quantum vacuum, where the theory is confining. The gluino condensate is calculated by summing the direct contributions from all fundamental monopoles. It is found to be in agreement with the WCI result for any classical gauge group, whereas the values for the exceptional groups have not been calculated before. The ADS superpotential, which describes the low energy dynamics of matter in a supersymmetric gauge theory, is derived using monopoles for all cases where instantons do not contribute. We report on progress made towards a two monopole calculation, in an attempt to quantify the missed contributions of the SCI method. Unfortunately, this eventually proved too complicated to be feasible.
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Developing a sorting code for Coulomb excitation data analysisMehl, Craig January 2015 (has links)
>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.
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Coulomb breakup of halo nuclei by a time-dependent methodCapel, Pierre 29 January 2004 (has links)
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: <sup>11</sup>Be, <sup>15</sup>C and <sup>8</sup>B.
<sup>11</sup>Be 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 <sup>10</sup>Be core in its
0<sup>+</sup> ground state.
However, the extraction of the corresponding spectroscopic factor
have to wait for the publication of these data.
<P>
<sup>15</sup>C 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
<sup>15</sup>C can be seen as a <sup>14</sup>C core in its 0<sup>+</sup>
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 <sup>8</sup>B.
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 <sup>8</sup>B 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.
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The semiclassical S-matrix theory of three body Coulomb break-upChocian, Peter January 1999 (has links)
No description available.
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High-frequency magneto-conductivity studies of low-dimensional organic conductorsSchrama, Judith Marije January 2000 (has links)
No description available.
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Propagação semiclássica na representação de estados coerentes / Semiclassical propagation in the coherent-state representationViscondi, Thiago de Freitas, 1985- 22 August 2018 (has links)
Orientador: Marcus Aloizio Martinez de Aguiar / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin / Made available in DSpace on 2018-08-22T04:47:13Z (GMT). No. of bitstreams: 1
Viscondi_ThiagodeFreitas_D.pdf: 5908171 bytes, checksum: 62e83e5e2d7f988db884e3964fd40971 (MD5)
Previous issue date: 2013 / Resumo: A propagação semiclássica consiste na elaboração e aplicação de métodos para a resolução aproximada da equação de Schrödinger dependente do tempo, assumindo como hipótese que a ação clássica do sistema possui valor bastante superior à constante de Planck. Dentro deste contexto, o propagador quântico representa um elemento de interesse central, uma vez que esta grandeza corresponde à amplitude de probabilidade para a transição entre dois estados do sistema físico. Em um estágio preliminar de nosso trabalho, empregamos o conceito generalizado de estados coerentes para reformular o propagador quântico em termos de uma integral de caminho. Em seguida, com a utilização do método do ponto de sela, realizamos uma dedução detalhada para a aproximação semiclássica do propagador correspondente a uma ampla classe de grupos dinâmicos. A aplicação deste resultado formal está subordinada à resolução de equações clássicas de movimento sob condições de contorno, considerando um espaço de fase com dimensão duplicada. De maneira geral, a busca por trajetórias clássicas sujeitas a valores de contorno demonstra elevado custo computacional e complexidade técnica. Por esta razão, desenvolvemos três diferentes aproximações semiclássicas determinadas exclusivamente por condições iniciais. Em uma primeira situação, elaboramos um método de propagação constituído por uma integral sobre soluções clássicas no espaço de fase duplicado. No segundo caso, com a formulação do operador semiclássico de evolução temporal, eliminamos a necessidade pela duplicação dos graus de liberdade clássicos. A terceira abordagem, designada por propagador clássico corrigido, está definida pela contribuição de uma única trajetória. Com o propósito de avaliar a precisão e eficiência das expressões semiclássicas adquiridas, exemplificamos a aplicação destas ferramentas teóricas para os estados coerentes de SU(2) e SU(3). Por fim, apresentamos uma extensa discussão sobre as vantagens introduzidas pelo espaço de fase duplicado na implementação de uma aproximação semiclássica. Deste modo, verificamos que soluções clássicas tunelantes possuem uma importante participação na descrição precisa da penetração parcial de um pacote de onda em uma barreira de potencial finita. Além disto, mostramos que o fenômeno quântico de reflexão por um potencial atrativo está diretamente associado à ocorrência de trajetórias com comportamento não-clássico. / Abstract: The semiclassical propagation comprises the development and application of methods for obtaining approximate solutions to the time-dependent Schrödinger equation, assuming the hypothesis that the classical action of the system is much greater than the Planck constant. In this context, the quantum propagator represents an element of central interest, since this quantity corresponds to the probability amplitude for the transition between two states of thephysical system. In a preliminary stage of our work, we employ the generalized concept of coherent states to reformulate the quantum propagator in terms of a path integral. Then, with use of the saddlepoint method, we conduct a detailed derivation of the semiclassical approximation for the propagator corresponding to a wide class of dynamical groups. The application of this formal result depends on the resolution of classical equations of motion under boundary conditions, considering a phase space with doubled dimension. Generally, the search for classical trajectories subject to boundary values demonstrates high computational cost and technical complexity. For this reason, we have developed three distinct semiclassical approximations exclusively determined by initial conditions. In a first situation, we elaborate a propagation method composed of an integral over classical solutions in the doubled phase space. In the second case, with the formulation of the semiclassical time-evolution operator, we eliminate the need for the duplication of the classical degrees of freedom. The third approach, designated as corrected classical propagator, is defined by the contribution of a single trajectory. In order to evaluate the accuracy and efficiency of the obtained semiclassical expressions, we exemplify the application of these theoretical tools for the coherent states of SU(2) and SU(3). At last, we present an extensive discussion on the advantages introduced by the doubled phase space in implementing a semiclassical approximation. In this way, we find that tunneling classical solutions have an important participation in the accurate description of the partial penetration of a wave packet in a finite potential barrier. Furthermore, we show that the quantum phenomenon of reflection by an attractive potential is directly associated to the occurrence of trajectories with non-classical behavior. / Doutorado / Física / Doutor em Ciências
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The transport properties of two dimensional electron gases in spatially random magnetic fieldsRushforth, Andrew William January 2000 (has links)
No description available.
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