Two-dimensional background field gravity: A Hamilton-Jacobi analysis

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

Supersymmetry of Affine Toda Models as Fermionic Symmetry Flows of the Extended mKdV Hierarchy

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

Corrugated waveguide under scaling investigation

Some scaling properties for classical light ray dynamics inside a periodically corrugated waveguide are studied by use of a simplified two-dimensional nonlinear area-preserving map. It is shown that the phase space is mixed. The chaotic sea is characterized using scaling arguments revealing critical exponents connected by an analytic relationship. The formalism is widely applicable to systems with mixed phase space, and especially in studies of the transition from integrability to nonintegrability, including that in classical billiard problems.

Dynamical properties of a particle in a wave packet: Scaling invariance and boundary crisis

Some dynamical properties present in a problem concerning the acceleration of particles in a wave packet are studied. The dynamics of the model is described in terms of a two-dimensional area preserving map. We show that the phase space is mixed in the sense that there are regular and chaotic regions coexisting. We use a connection with the standard map in order to find the position of the first invariant spanning curve which borders the chaotic sea. We find that the position of the first invariant spanning curve increases as a power of the control parameter with the exponent 2/3. The standard deviation of the kinetic energy of an ensemble of initial conditions obeys a power law as a function of time, and saturates after some crossover. Scaling formalism is used in order to characterise the chaotic region close to the transition from integrability to nonintegrability and a relationship between the power law exponents is derived. The formalism can be applied in many different systems with mixed phase space. Then, dissipation is introduced into the model and therefore the property of area preservation is broken, and consequently attractors are observed. We show that after a small change of the dissipation, the chaotic attractor as well as its basin of attraction are destroyed, thus leading the system to experience a boundary crisis. The transient after the crisis follows a power law with exponent -2. (C) 2011 Elsevier Ltd. All rights reserved.

Phase Transition in Dynamical Systems: Defining Classes of Universality for Two-Dimensional Hamiltonian Mappings via Critical Exponents

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Finding critical exponents for two-dimensional Hamiltonian maps

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Loop scattering in two-dimensional QCD

Using the integrability conditions that we recently obtained in two-dimensional QCD with massless fermions we arrive at a sufficient number of conservation laws to fix the scattering amplitudes involving a local version of the Wilson loop operator.

Ladder operators for subtle hidden shape-invariant potentials

Ladder operators can be constructed for all potentials that present the integrability condition known as shape invariance, satisfied by most of the exactly solvable potentials. Using the superalgebra of supersymmetric quantum mechanics, we construct the ladder operators for two exactly solvable potentials that present a subtle hidden shape invariance.

Gravitational interactions of integrable models

We couple non-linear sigma-models to Liouville gravity, showing that integrability properties of symmetric space models still hold for the matter sector. Using similar arguments for the fermionic counterpart, namely Gross-Neveu-type models, we verify that such conclusions must also hold for them, as recently suggested.

On the dynamics of the Bianchi IX system

In this paper, we study the flow on three invariant sets of dimension five for the classical Bianchi IX system. In these invariant sets, using the Darboux theory of integrability, we prove the non-existence of periodic solutions and we study their dynamics. Moreover, we find three invariant sets of dimension four where the flow is integrable.

Centers on center manifolds in the Lu system

We confirm a conjecture of Mello and Coelho [Phys. Lett. A 373 (2009) 1116] concerning the existence of centers on local center manifolds at equilibria of the Lu system of differential equations on R(3). Our proof shows that the local center manifolds are algebraic ruled surfaces, and are unique. (C) 2011 Elsevier B.V. All rights reserved.

Kac-Moody construction of Toda type field theories

Using the coadjoint orbit method we derive a geometric WZWN action based on the extended two-loop Kac-Moody algebra. We show that under a hamiltonian reduction procedure, which respects conformal invariance, we obtain a hierarchy of Toda type field theories, which contain as submodels the Toda molecule and periodic Toda lattice theories. We also discuss the classical r-matrix and integrability properties.

Updating QCD2

We review two-dimensional QCD. We start with the field theory aspects since 't Hooft's 1/N expansion, arriving at the non-Abelian bosonization formula, coset construction and gauge-fixing procedure. Then we consider the string interpretation, phase structure and the collective coordinate approach. Adjoint matter is coupled to the theory, and the Landau-Ginzburg generalization is analysed. We end with considerations concerning higher algebras, integrability, constraint structure, and the relation of high-energy scattering of hadrons with two-dimensional (integrable) field theories.

Two-dimensional integrable generalization of the Camassa-Holm equation

In this letter we discuss the (2 + 1)-dimensional generalization of the Camassa-Holm equation. We require that this generalization be, at the same time, integrable and physically derivable under the same asymptotic analysis as the original Camassa-Holm equation. First, we find the equation in a perturbative calculation in shallow-water theory. We then demonstrate its integrability and find several particular solutions describing (2 + 1) solitary-wave like solutions. © 1999 Published by Elsevier Science B.V. All rights reserved.

Confinement, solitons and the equivalence between the sine-Gordon and massive Thirring models

We consider a two-dimensional integrable and conformally invariant field theory possessing two Dirac spinors and three scalar fields. The interaction couples bilinear terms in the spinors to exponentials of the scalars. Its integrability properties are based on the sl(2) affine Kac-Moody algebra, and it is a simple example of the so-called conformal affine Toda theories coupled to matter fields. We show, using bosonization techniques, that the classical equivalence between a U(1) Noether current and the topological current holds true at the quantum level, and then leads to a bag model like mechanism for the confinement of the spinor fields inside the solitons. By bosonizing the spinors we show that the theory decouples into a sine-Gordon model and free scalars. We construct the two-soliton solutions and show that their interactions lead to the same time delays as those for the sine-Gordon solitons. The model provides a good laboratory to test duality ideas in the context of the equivalence between the sine-Gordon and Thirring theories. © 2000 Elsevier Science B.V. All rights reserved.