Towards constructing one-particle representations of the deformed Poincar\'e algebra

We give a method for obtaining states of massive particle representations of the two-parameter deformation of the Poincar\'e algebra proposed in q-alg/9601010, q-alg/9505030 and q-alg/9501026. We discuss four procedures to generate eigenstates of a complete set of commuting operators starting from the rest state. One result of this work is the fact that upon deforming to the quantum Poincar\'e algebra the rest state is split into an infinite number of states. Another result is that the energy spectrum of these states is discrete. Some curious residual degeneracy remains: there are states constructed by applying different operators to the rest state which nevertheless are indistinguishable by eigenvalues of all the observables in the algebra.Comment: 23 pages. New interpretation of the results is given: upon the deformation the rest state of Poincar\'e algebra is split into an infinite number of states with discrete energy spectrum. Title, abstract and conclusion are change

Onset of Fokker-Planck dynamics within a Closed Finite Spin System

Relaxation according to Fokker-Planck equations is a standard scenario in classical statistical mechanics. It is however not obvious how such an equilibration may emerge within a closed, finite quantum system. We present an analytical and numerical analysis of a system comprising sixteen spins in which spatial inhomogeneities of the magnetization relax approximately in accord with a standard Fokker-Planck equation for a Brownian particle in a parabolic potential

A Two Parameter Deformation of the SU(1/1) Superalgebra and the XY Quantum Chain in a Magnetic Field

We show that the XY quantum chain in a magnetic field is invariant under a two parameter deformation of the SU(1/1) superalgebra. One is led to an extension of the braid group and the Hecke algebra which reduce to the known ones when the two parameter coincide. The physical significance of the two parameters is discussed.Comment:

Operator Representations on Quantum Spaces

In this article we present explicit formulae for q-differentiation on quantum spaces which could be of particular importance in physics, i.e., q-deformed Minkowski space and q-deformed Euclidean space in three or four dimensions. The calculations are based on the covariant differential calculus of these quantum spaces. Furthermore, our formulae can be regarded as a generalization of Jackson's q-derivative to three and four dimensions.Comment: 34 pages, Latex, major modifications to improve clarity, corrected typo

Tratamento de singularidades em estruturas condutoras para o metodo FETD /

Orientador: Wilson Arnaldo Artuzi JuniorInclui apendicesDissertacao (mestrado) - Universidade Federal do Parana, Setor de Tecnologia, Programa de Pos-Graduacao em Engenharia Eletrica. Defesa: Curitiba, 2006Inclui bibliografiaResumo: Nas proximidades de bordas ou extremidades de objetos metalicos e ao redor defios condutores, os campos eletromagneticos variam intensamente. A ocorrencia detais singularidades dos campos tem motivado muitas pesquisas cientificas nos ramos do calculo numerico aplicado a engenharia eletrica. Uma das ferramentasmais eficientes e precisas para a simulacao de problemas de eletromagnetismo tem sido o metodo FETD (Elementos Finitos no Domínio do Tempo). Para a aproximacao matematica do campo eletrico, este metodo emprega funcoes de base associadas a discretizacao espacial do dominio computacional, tais como funcoes de aresta e de face dos elementos tetraedricos. Mais amplamente tem sido utilizados os elementos de aresta baseados nas formas de Whitney. Estas funcoes vetoriais se caracterizampor serem solenoidais, com o divergente nulo, e sao apropriadas para a modelagemde fenomenos associados a eletrodinamica. Nas simulacoes de fenomenos que envolvem campos singulares, entretanto, nos quais os campos sao predominantemente irrotacionais, a precisao dos resultados obtidos com o metodo dos elementos finitos convencional a limitada. Com a finalidade de se aprimorar o metodo FETD no tratamento das singularidades presentes em estruturas condutoras, foi desenvolvida a tecnica de composicao de funcoes de base. Este metodo consiste na aplicacao combinada de funcoes dos tipos solenoidal eirrotacional. Para comprovar a eficiencia da tocnica proposta, e qual a melhor modalidade de aplicacao, foram realizados diversos experimentos numericos comlinhas de transmissao. Nestas simulacoes foram avaliadas a impedancia caracteristica e a frequencia de ressonancia das linhas. Os resultados obtidosmostram que para a primeira grandeza, a aplicacao do metodo sempre reduz os erros, e para a segunda tambem ocorre uma reducao dos erros mas que dependeda modalidade de aplicacao da tecnica

Bicovariant Differential Calculus on the Quantum D=2 Poincare Group

We present a bicovariant differential calculus on the quantum Poincare group in two dimensions. Gravity theories on quantum groups are discussed.Comment: 17 page

RHIC polarization for Runs 9-12

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On the Quantum Lorentz Group

The quantum analogues of Pauli matrices are introduced and investigated. From these matrices and an appropriate trace over spinorial indiceswe construct a quantum Minkowsky metric. In this framework, we show explicitely the correspondance between the SL(2,C) and Lorentz quantum groups.Comment: 17 page