Comportamento assintótico e controlabilidade exata para a equação de Klein-Gordon

Pós-graduação em Matemática - IBILCE

Fonte escalar acoplada ao campo de Klein-Gordon orbitando um objeto estelar

Neste trabalho determinamos, utilizando Teoria Quântica de Campos em nível de árvore, a radiação escalar emitida por uma fonte em movimento circular uniforme no espaço-tempo plano de Minkowski, assumindo Gravitação Newtoniana, e no espaço-tempo curvo de um buraco negro sem carga e com momento angular nulo, assumindo Relatividade Geral. Efetuamos este cálculo analiticamente para o caso de Minkowski e numericamente no âmbito do espaço-tempo de Schwarzschild, sendo que neste espaço-tempo curvo obtivemos a forma analítica e a normalização dos modos nas regiões assintóticas. Verificamos que, para as órbitas circulares estáveis de acordo com a Relatividade Geral, a potência irradiada no caso de um buraco negro de Schwarzschild é menor do que a obtida no espaço-tempo de Minkowski assumindo a Gravitação Newtoniana. Obtemos também que apenas uma pequena parcela da radiação emitida é absorvida pelo buraco negro. Verificamos que a diferença entre as potências irradiadas em Schwarzschild e Minkowski diminui na medida em que aumentamos o valor da massa do campo. Em Schwarzschild, uma parcela cada vez maior da radiação emitida é absorvida pelo buraco negro na medida em que aumentamos o valor da massa do campo.

Scalar source in circular motion interacting with massive klein-gordon field in Minkowski spacetime

We analyze the scalar radiation emitted by a source in uniform circular motion in Minkowski spacetime interacting with a massive Klein-Gordon field. We assume the source rotating around a central object due to a Newtonian force. By considering the canonical quantization of this field, we use perturbation theory to compute the radiation emitted at the tree level. Regarding the initial state of the field as being the Minkowski vacuum, we compute the emission amplitude for the rotating source, assuming it as being minimally coupled to the massive Klein-Gordon field. We then compute the power emitted by the swirling source as a function of its angular velocity, as measured by asymptotic static observers.

Os códigos lingüísticos em Sinhá Secada

Apresentamos, neste trabalho, o resultado do levantamento de vocabulário e expressões para a interpretação da organização dos códigos lingüísticos presentes no conto Sinhá Secada de Guimarães Rosa. Utilizando o conceito de código (campos semânticos) de Barthes, analisam-se os códigos jurídico e religioso, que refletem, fundamentalmente, o universo cultural dos personagens, bem como os códigos do silêncio e do despojamento que funcionam, sobretudo, como elementos de caracterização da personagem. Acima deles, como supracódigo, analisamos o código da água, fundamental na estrutura narrativa.

Energy decay for the linear Klein-Gordon equation and boundary control

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Corroborating the equivalence between the Duffin-Kemmer-Petiau and the Klein-Gordon and Proca equations

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

New path integral simulation algorithms and their application to creep in the quantum sine-Gordon chain

A path integral simulation algorithm which includes a higher-order Trotter approximation (HOA)is analyzed and compared to an approach which includes the correct quantum mechanical pair interaction (effective Propagator (EPr)). It is found that the HOA algorithmconverges to the quantum limit with increasing Trotter number P as P^{-4}, while the EPr algorithm converges as P^{-2}.The convergence rate of the HOA algorithm is analyzed for various physical systemssuch as a harmonic chain,a particle in a double-well potential, gaseous argon, gaseous helium and crystalline argon. A new expression for the estimator for the pair correlation function in the HOA algorithm is derived. A new path integral algorithm, the hybrid algorithm, is developed.It combines an exact treatment of the quadratic part of the Hamiltonian and thehigher-order Trotter expansion techniques.For the discrete quantum sine-Gordon chain (DQSGC), it is shown that this algorithm works more efficiently than all other improved path integral algorithms discussed in this work. The new simulation techniques developed in this work allow the analysis of theDQSGC and disordered model systems in the highly quantum mechanical regime using path integral molecular dynamics (PIMD)and adiabatic centroid path integral molecular dynamics (ACPIMD).The ground state phonon dispersion relation is calculated for the DQSGC by the ACPIMD method.It is found that the excitation gap at zero wave vector is reduced by quantum fluctuations. Two different phases exist: One phase with a finite excitation gap at zero wave vector, and a gapless phase where the excitation gap vanishes.The reaction of the DQSGC to an external driving force is analyzed at T=0.In the gapless phase the system creeps if a small force is applied, and in the phase with a gap the system is pinned. At a critical force, the systems undergo a depinning transition in both phases and flow is induced. The analysis of the DQSGC is extended to models with disordered substrate potentials. Three different cases are analyzed: Disordered substrate potentials with roughness exponent H=0, H=1/2,and a model with disordered bond length. For all models, the ground state phonon dispersion relation is calculated.

Dispersive wave solutions of the klein-gordon equation in cosmology

L'equazione di Klein-Gordon descrive una ampia varietà di fenomeni fisici come la propagazione delle onde in Meccanica dei Continui ed il comportamento delle particelle spinless in Meccanica Quantistica Relativistica. Recentemente, la forma dissipativa di questa equazione si è rivelata essere una legge di evoluzione fondamentale in alcuni modelli cosmologici, in particolare nell'ambito dei cosiddetti modelli di k-inflazione in presenza di campi tachionici. L'obiettivo di questo lavoro consiste nell'analizzare gli effetti del parametro dissipativo sulla dispersione nelle soluzioni dell'equazione d'onda. Saranno inoltre studiati alcuni tipici problemi al contorno di particolare interesse cosmologico per mezzo di grafici corrispondenti alle soluzioni fondamentali (Funzioni di Green).

Lumbar spinal 'juxtaarticular' cyst in a Gordon setter

An 11-year-old Gordon setter bitch was presented with a history of progressive weakness in the right hind limb associated with pain in the lumbar spine. Neurological deficits consisted of ataxia, monoparesis, muscle atrophy and spontaneous over-knuckling of the affected limb. A large 'juxtaarticular' cyst located in a right dorsolateral position of the intervertebral foramen at L3-L4 was diagnosed by magnetic resonance imaging. The cyst was removed through a modified laminectomy. The dog recovered quickly and returned to the owners 4 days after surgery with slight neurological symptoms. During the follow-up examination 2 and 6 months later, the Setter showed normal gait and neurological examination.

Firing Up the Crucible with Senator Lee Metcalf & Governor Forrest Anderson -- Judge Gordon Bennett in “The Crucible of Change”

During the lead-up to Montana second progressive era, Lee Metcalf and Forrest Anderson, along with others, kept the progressive flame lit in Montana. Metcalf’s political history is replete with close electoral wins because of his commitment to progressive ideals when the times were not always politically favorable for that. As State Legislator, MT Supreme Court Justice, Congressman and eventually as US Senator, Lee won races by as little as 55 votes because he stuck to his guns as a progressive. In Forrest Anderson’s career as a County Attorney, State Legislator, MT Supreme Court Justice and 12 years as MT Attorney General he was respected as a pragmatic practitioner of politics. But during that entire career leading up to his election as Governor, Forrest Anderson was also a stalwart supporter of the progressive agenda exemplified by FDR and the New Deal, which brought folks out of the Great Depression that was brought on by the bad policies of the GOP and big business. As MT’s second progressive period began in 1965, the first important election was Senator Metcalf’s successful re-election battle in 1966 with the sitting MT Governor, Tim Babcock. And the progressive express was really ignited by the election of Forrest Anderson as Governor in 1968 after 16 years of Republican Governors in MT. Gordon Bennett played a rather unique role, being a confidant of Metcalf and Anderson, both who respected his wide and varied experience, his intellect, and his roots in progressivism beginning with his formative years in the Red Corner of NE Montana. Working with Senator Metcalf and his team, including Brit Englund, Vic Reinemer, Peggy McLaughlin, Betty Davis and Jack Condon among others, Bennett helped shape the progressive message both in Washington DC and MT. Progressive labor and farm organizations, part of the progressive coalition, benefitted from Bennett’s advice and counsel and aided the Senator in his career including the huge challenge of having a sitting popular governor run against him for the Senate in 1966. Metcalf’s noted intern program produced a cadre of progressive leaders in Montana over the years. Most notably, Ron Richards transitioned from Metcalf Intern to Executive Secretary of the Montana Democratic Party (MDP) and assisted, along with Bennett, in the 1966 Metcalf-Babcock race in a big way. As Executive Secretary Richards was critical to the success of the MDP as a platform for Forrest Anderson’s general election run and win in 1968. After Forrest’s gubernatorial election, Richards became Executive Assistant (now called Chief of Staff) for Governor Anderson and also for Governor Thomas Judge. The Metcalf progressive strain, exemplified by many including Richards and Bennett, permeated Democratic politics during the second progressive era. So, too, did the coalition that supported Metcalf and his policies. The progressivism of the period of “In the Crucible of Change” was fired up by Lee Metcalf, Forrest Anderson and their supporters and coalitions, and Gordon Bennett was in the center of all of that, helping fire up the crucible, setting the stage for many policy advancements in both Washington DC and Montana. Gordon Bennett’s important role in the 1966 re-election of Senator Lee Metcalf and the 1968 election of Governor Forrest Anderson, as well as his wide experience in government and politics of that time allows him to provide us with an insider’s personal perspective of those races and other events at the beginning of the period of progressive change being documented “In the Crucible of Change,” as well as his personal insights into the larger political/policy picture of Montana. Gordon Bennett, a major and formative player “In the Crucible of Change,” was born in the far northeast town of Scobey, MT in 1922. He attended school in Scobey through the eighth grade and graduated from Helena High School. After attending Carroll College for two years, he received his BA in economics from Carleton College in Northfield, MN. During a brief stint on the east coast, his daily reading of the New York Times (“best newspaper in the world at that time … and now”) inspired him to pursue a career in journalism. He received his MA in Journalism from the University of Missouri and entered the field. As a reporter for the Great Falls Tribune under the ownership and management of the Warden Family, he observed and competed with the rigid control of Montana’s press by the Anaconda Company (the Great Falls Tribune was the only large newspaper in Montana NOT owned by ACM). Following his intellectual curiosity and his philosophical bend, he attended a number of Farm-Labor Institutes which he credits with motivating him to pursue solutions to economic and social woes through the law. In 1956, at the age of 34, he received his Juris Doctorate degree from the Georgetown University Law Center in Washington, DC. Bennett’s varied career included eighteen years as a farmer, four years in the US Army during WWII (1942-46), two years as Assistant MT Attorney General (1957-59) with Forrest Anderson, three years in private practice in Glasgow (1959-61), two years as Associate Solicitor in the Department of Interior in Washington, DC (1961-62), and private law practice in Helena from 1962 to 1969. While in Helena he was an unsuccessful candidate for the Montana Supreme Court (1962) and cemented his previous relationships with Attorney General Forrest Anderson and US Senator Lee Metcalf. Bennett modestly refuses to accept the title of Campaign Manager for either Lee Metcalf (1966 re-election over the challenger, MT Republican Governor Tim Babcock) or Forrest Anderson (his 1968 election as Governor), saying that “they ran their campaigns … we were only there to help.” But he has been generally recognized as having filled that critical role in both of those critical elections. After Governor Anderson’s election in 1968, Bennett was appointed Director of the MT Unemployment Compensation Commission, a position from where he could be a close advisor and confidant of the new Governor. In 1971, Governor Anderson appointed him Judge in the most important jurisdiction in Montana, the 1st Judicial District in Helena, a position he held for seventeen years (1971-88). Upon stepping down from his judgeship, for twenty years (1988-2008) he was a law instructor, mediator and arbitrator. He currently resides in Helena with his wife, Norma Tirrell, former newspaper reporter and researcher/writer. Bennett has two adult children and four grandchildren.