Expoentes de escala para mapeamentos discretos bidimensionais

Pós-graduação em Física - IGCE

Type-II super-Backlund transformation and integrable defects for the N=1 super sinh-Gordon model

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

N=1 super sinh-Gordon model with defects revisited

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Normal Forms for Polynomial Differential Systems in R-3 Having an Invariant Quadric and a Darboux Invariant

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Integrable deformations of strings on symmetric spaces

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Toroidal solitons in 3+1 dimensional integrable theories

We analyze the integrability properties of models defined on the symmetric space SU(2)/U(1) in 3 + 1 dimensions, using a recently proposed approach for integrable theories in any dimension. We point out the key ingredients for a theory to possess an infinite number of local conservation laws, and discuss classes of models with such property, We propose a 3 + 1-dimensional, relativistic invariant field theory possessing a toroidal soliton solution carrying a unit of topological charge given by the Hopf map. Construction of the action is guided by the requirement that the energy of static configuration should be scale invariant. The solution is constructed exactly. The model possesses an infinite number of local conserved currents. The method is also applied to the Skyrme-Faddeev model, and integrable submodels are proposed. (C) 1999 Elsevier B.V. B.V. All rights reserved.

Estudo sobre a teoria de vínculos de Hamilton-Jacobi

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Iniciação ao estudo da dinâmica de rotação de um satélite em variáves de Andoyer

The dynamics of the rotation of a satellite is an old and classical problem, specially in the Euler formalism. However, with these variables, even in torque free motion problem, the integrability of the system is far from trivial, mainly when the three moments of the inertia are not equal. Another disadvantage occurs when the inclinations between some plans are null or close to zero, so the nodes become undetermined. In this work, we propose the use of modern Andoyer's variables. These are a set of canonical variables and therefore some significant advantages can be obtained when dealing with perturbation methods. On other the hand, the integrability of the torque free motion becomes very clear, as the system is reduced to a problem of one degree of freedom. The elimination of the singularities mentioned above, can be solved very easily, with Pincaré-type variables. In this work we give the background concepts of the Andoyer's variables and the disturbing potential is obtained for the rotational dynamics of a satellite perturbed by a planet. In the case when A = B (moments of inertia) and due to the current variables, the averaged system is trivially obtained through very simple integrations

Fluxo do grupo de renormalização dos modelos-'alfa' e as álgebras de Lie contínuas

Pós-graduação em Física - IFT

Integrable Models: from Dynamical Solutions to String Theory

We review the status of integrable models from the point of view of their dynamics and integrability conditions. A few integrable models are discussed in detail. We comment on the use it is made of them in string theory. We also discuss the SO(6) symmetric Hamiltonian with SO(6) boundary. This work is especially prepared for the 70th anniversaries of Andr, Swieca (in memoriam) and Roland Koberle.

Charge dynamics in half-filled Hubbard chains with finite on-site interaction

We study the charge dynamic structure factor of the one-dimensional Hubbard model with finite on-site repulsion U at half-filling. Numerical results from the time-dependent density matrix renormalization group are analyzed by comparison with the exact spectrum of the model. The evolution of the line shape as a function of U is explained in terms of a relative transfer of spectral weight between the two-holon continuum that dominates in the limit U -> infinity and a subset of the two-holon-two-spinon continuum that reconstructs the electron-hole continuum in the limit U -> 0. Power-law singularities along boundary lines of the spectrum are described by effective impurity models that are explicitly invariant under spin and eta-spin SU(2) rotations. The Mott-Hubbard metal-insulator transition is reflected in a discontinuous change of the exponents of edge singularities at U = 0. The sharp feature observed in the spectrum for momenta near the zone boundary is attributed to a van Hove singularity that persists as a consequence of integrability.

Spectral fluctuation and 1/f(alpha) noise in the energy level statistics of interacting trapped bosons

It has been recently shown numerically that the transition from integrability to chaos in quantum systems and the corresponding spectral fluctuations are characterized by 1/f(alpha) noise with 1 <= alpha <= 2. The system of interacting trapped bosons is inhomogeneous and complex. The presence of an external harmonic trap makes it more interesting as, in the atomic trap, the bosons occupy partly degenerate single-particle states. Earlier theoretical and experimental results show that at zero temperature the low-lying levels are of a collective nature and high-lying excitations are of a single-particle nature. We observe that for few bosons, the P(s) distribution shows the Shnirelman peak, which exhibits a large number of quasidegenerate states. For a large number of bosons the low-lying levels are strongly affected by the interatomic interaction, and the corresponding level fluctuation shows a transition to a Wigner distribution with an increase in particle number. It does not follow Gaussian orthogonal ensemble random matrix predictions. For high-lying levels we observe the uncorrelated Poisson distribution. Thus it may be a very realistic system to prove that 1/f(alpha) noise is ubiquitous in nature.

Hirota method for oblique solitons in two-dimensional supersonic nonlinear Schrodinger flow

In a previous work El et al. (2006) [1] exact stable oblique soliton solutions were revealed in two-dimensional nonlinear Schrodinger flow. In this work we show that single soliton solution can be expressed within the Hirota bilinear formalism. An attempt to build two-soliton solutions shows that the system is "close" to integrability provided that the angle between the solitons is small and/or we are in the hypersonic limit. (C) 2012 Elsevier B.V. All rights reserved.

The r-matrix of the Alday-Arutyunov-Frolov model

We investigate the classical integrability of the Alday-Arutyunov-Frolov model, and show that the Lax connection can be reduced to a simpler 2 x 2 representation. Based on this result, we calculate the algebra between the L-operators and find that it has a highly non-ultralocal form. We then employ and make a suitable generalization of the regularization technique proposed by Mail let for a simpler class of non-ultralocal models, and find the corresponding r- and s-matrices. We also make a connection between the operator-regularization method proposed earlier for the quantum case, and the Mail let's symmetric limit regularization prescription used for non-ultralocal algebras in the classical theory.

Examples of PDEs all whose points are characteristic

Let π : FM ! M be the bundle of linear frames of a manifold M. A basis Lijk , j < k, of diffeomorphism invariant Lagrangians on J1 (FM) was determined in [J. Muñoz Masqué, M. E. Rosado, Invariant variational problems on linear frame bundles, J. Phys. A35 (2002) 2013-2036]. The notion of a characteristic hypersurface for an arbitrary first-order PDE system on an ar- bitrary bred manifold π : P → M, is introduced and for the systems dened by the Euler-Lagrange equations of Lijk every hypersurface is shown to be characteristic. The Euler-Lagrange equations of the natural basis of Lagrangian densities Lijk on the bundle of linear frames of a manifold M which are invariant under diffeomorphisms, are shown to be an underdetermined PDEs systems such that every hypersurface of M is characteristic for such equations. This explains why these systems cannot be written in the Cauchy-Kowaleska form, although they are known to be formally integrable by using the tools of geometric theory of partial differential equations, see [J. Muñoz Masqué, M. E. Rosado, Integrability of the eld equations of invariant variational problems on linear frame bundles, J. Geom. Phys. 49 (2004), 119-155]