196 research outputs found
Estudo variacional do modelo de Moszkowski-q-deformado
No full textDissertação (Mestrado) - Universidade Federal de Santa Catarina, Centro de Ciências Físicas e Matemáticas.A validade da utilização do método variacional via estados coerentes q-deformados e aqui testada, no contexto das álgebras quânticas, para dois diferentes tipos de modelos, o de Lipkin e o de Moszkowski. O comportamento da transição de fase sob o efeito da deformação e também observado nos dois modelos acima. Há várias maneiras diferentes de se deformar quanticamente um sistema. Nessa dissertação duas dessas maneiras são estudadas em detalhe, e suas diferenças são apontadas
Extensions of a class of similarity solutions of Fokker-Planck equation with time-dependent coefficients and fixed/moving boundaries
No full textA general formula in closed form to obtain exact similarity solutions of the Fokker-Planck equation with both time-dependent drift and diffusion coefficients was recently presented by Lin and Ho [Ann. Phys.327, 386 (2012); Lin and Ho, J. Math. Phys.54, 041501 (2013)]. In this paper, we extend the class of exact solutions by exploiting certain properties of the general formula.補正完
Spherelike solutions in surface functional theory and Dirac’s membrane model
No full textA surface functional theory for p-dimensional extended objects, the p-branes, has been proposed in previous papers. The field equations for toroidal p-branes were exactly solved in d=p+2 dimensions, yielding an equally spaced mass-squared spectrum with massless states. In this paper, we obtain the asymptotic distribution of the mass spectrum in the point-particle limit of the theory with spherelike membranes (p=2) in d=4 dimensions. The similarity between this spectrum and that obtained in Dirac’s membrane model of the electron is discussed.國外SCI紙本US
Quantum Walk in Periodic Potential on a Line and a Model of Interacting Opinions
No full text紀要類（bulletin）departmental bulletin pape
Dirac(-Pauli), Fokker-Planck equations and exceptional Laguerre polynomials
No full textAn interesting discovery in the last two years in the field of mathematical physics has been the exceptional Laguerre and Jacobi polynomials. Unlike the well-known classical orthogonal polynomials which start with constant terms, these new polynomials have lowest degree , and yet they form complete set with respect to some positive-definite measure. While the mathematical properties of these new polynomials deserve further analysis, it is also of interest to see if they play any role in physical systems. In this paper we indicate some physical models in which these new polynomials appear as the main part of the eigenfunctions. The systems we consider include the Dirac equations coupled minimally and non-minimally with some external fields, and the Fokker-Planck equations. The systems presented here have enlarged the number of exactly solvable physical systems known so far.國外SCIY紙本US
Prepotential approach to quasinormal modes
No full textIn this paper we demonstrate how the recently reported exactly and quasi-exactly solvable models admitting quasinormal modes can be constructed and classified very simply and directly by the newly proposed prepotential approach. These new models were previously obtained within the Lie-algebraic approach. Unlike the Lie-algebraic approach, the prepotential approach does not require any knowledge of the underlying symmetry of the system. It treats both quasi-exact and exact solvabilities on the same footing, and gives the potential as well as the eigenfunctions and eigenvalues simultaneously. We also present three new models with quasinormal modes: a new exactly solvable Morse-like model, and two new quasi-exactly solvable models of the Scarf II and generalized Pöschl-Teller types.補正完畢國外SCIY紙本US
Shape invariance in prepotential approach to exactly solvable models
No full text100學年度研究獎補助論文In supersymmetric quantum mechanics, exact-solvability of one-dimensional quantum systems can be classified only with an additional assumption of integrability, the so-called shape invariance condition. In this paper we show that in the prepotential approach we proposed previously, shape invariance is automatically satisfied and needs not be assumed.國外SCI紙本US
Operator algebra in Chern-Simons theory on a torus
No full textWe consider Chern-Simons gauge theory on a torus with both nonrelativistic and relativistic matter. It is shown that the Hamiltonian and two total momenta commute among themselves only in the physical Hilbert space. We also discuss relations among degenerate physical states, degenerate vacua, and the existence of multicomponent Schrödinger wave functions.SCI紙本電子
Charged particles in external fields as physical examples of quasi-exactly-solvable models: A unified treatment
No full textWe present a unified treatment of three cases of quasi-exactly solvable problems, namely, charged particle moving in Coulomb and magnetic fields, for both the Schr\"odinger and the Klein-Gordon case, and the relative motion of two charged particles in an external oscillator potential. We show that all these cases are reducible to the same basic equation, which is quasi-exactly solvable owing to the existence of a hidden algebraic structure. A systematic and unified algebraic solution to the basic equation using the method of factorization is given. Analytic expressions of the energies and the allowed frequencies for the three cases are given in terms of the roots of one and the same set of Bethe ansatz equations.SCI紙
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