Relating a gluon mass scale to an infrared fixed point in pure gauge QCD

The condition for the global minimum of the vacuum energy for a non-Abelian gauge theory with a dynamically generated gauge boson mass scale which implies the existence of a nontrivial IR fixed point of the theory was shown. Thus, this vacuum energy depends on the dynamical masses through the nonperturbative propagators of the theory. The results show that the freezing of the QCD coupling constant observed in the calculations can be a natural consequence of the onset of a gluon mass scale, giving strong support to their claim.

Quantum entanglement and fixed point Hopf bifurcation

We present the qualitative differences in the phase transitions of the mono-mode Dicke model in its integrable and chaotic versions. These qualitative differences are shown to be connected to the degree of entanglement of the ground state correlations as measured by the linear entropy. We show that a first order phase transition occurs in the integrable case whereas a second order in the chaotic one. This difference is also reflected in the classical limit: for the integrable case the stable fixed point in phase space undergoes a Hopf type whereas the second one a pitchfork type bifurcation. The calculation of the atomic Wigner functions of the ground state follows the same trends. Moreover, strong correlations are evidenced by its negative parts. (c) 2006 Elsevier B.V. All rights reserved.

Vacuum energy and the fixed point of QED

The vacuum energy of QED, as a function of the coupling constant α, is shown to have an absolute minimum at the critical coupling αc=π/3. The effect of chiral symmetry breaking diminishes as the coupling is increased. We argue that these aspects of the vacuum energy shall remain unaltered beyond the ladder approximation.

Ponto fixo: uma introdução no ensino médio

Pós-graduação em Matemática em Rede Nacional - IBILCE

Renormalization in few-body nuclear physics

Renormalized fixed-point Hamiltonians are formulated for systems described by interactions that originally contain point-like singularities (as the Dirac-delta and/or its derivatives). They express the renormalization group invariance of quantum mechanics. The present approach for the renormalization scheme relies on a subtracted T-matrix equation.

Fixed points on torus fiber bundles over the circle

The main purpose of this work is to study fixed points of fiber-preserving maps over the circle S-1 for spaces which axe fibrations over S-1 and the fiber is the torus T. For the case where the fiber is a surface with nonpositive Euler characteristic, we establish general algebraic conditions, in terms of the fundamental group and the induced homomorphism, for the existence of a deformation of a map over S-1 to a fixed point, free map. For the case where the fiber is a torus, we classify all maps over S-1 which can be deformed fiberwise to a fixed point free map.

Coincidence points of fiber maps on S-n-bundles

In this note we study coincidence of pairs of fiber-preserving maps f, g : E-1 -> E-2 where E-1, E-2 are S-n-bundles over a space B. We will show that for each homotopy class vertical bar f vertical bar of fiber-preserving maps over B, there is only one homotopy class vertical bar g vertical bar such that the pair (f, g), where vertical bar g vertical bar = vertical bar tau circle f vertical bar can be deformed to a coincidence free pair. Here tau : E-2 -> E-2 is a fiber-preserving map which is fixed point free. In the case where the base is S-1 we classify the bundles, the homotopy classes of maps over S-1 and the pairs which can be deformed to coincidence free. At the end we discuss the self-coincidence problem. (C) 2010 Elsevier B.V. All rights reserved.

Abelianized obstruction for fixed points of fiber-preserving maps of surface bundles

Let f: M -> M be a fiber-preserving map where S -> M -> B is a bundle and S is a closed surface. We study the abelianized obstruction, which is a cohomology class in dimension 2, to deform f to a fixed point free map by a fiber-preserving homotopy. The vanishing of this obstruction is only a necessary condition in order to have such deformation, but in some cases it is sufficient. We describe this obstruction and we prove that the vanishing of this class is equivalent to the existence of solution of a system of equations over a certain group ring with coefficients given by Fox derivatives.

Fixed points on Klein bottle fiber bundles over the circle

The main purpose of this work is to study fixed points of fiber-preserving maps over the circle S(1) for spaces which are fiber bundles over S(1) and the fiber is the Klein bottle K. We classify all such maps which can be deformed fiberwise to a fixed point free map. The similar problem for torus fiber bundles over S(1) has been solved recently.

Absence of Cooper-type bound states in three- and few-electron systems

It is shown that the appearance of a fixed-point singularity in the kernel of the two-electron Cooper problem is responsible for the formation of the Cooper pair for an arbitrarily weak attractive interaction between two electrons. This singularity is absent in the problem of three and few superconducting electrons at zero temperature on the full Fermi sea. Consequently, such three- and few-electron systems on the full Fermi sea do not form Cooper-type bound states for an arbitrarily weak attractive pair interaction.

Some dynamical properties of a classical dissipative bouncing ball model with two nonlinearities

Some dynamical properties for a bouncing ball model are studied. We show that when dissipation is introduced the structure of the phase space is changed and attractors appear. Increasing the amount of dissipation, the edges of the basins of attraction of an attracting fixed point touch the chaotic attractor. Consequently the chaotic attractor and its basin of attraction are destroyed given place to a transient described by a power law with exponent -2. The parameter-space is also studied and we show that it presents a rich structure with infinite self-similar structures of shrimp-shape. © 2013 Elsevier B.V. All rights reserved.

Análise da dinâmica de um sistema vibrante não ideal de dois graus de liberdade

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Relaxation to Fixed Points in the Logistic and Cubic Maps: Analytical and Numerical Investigation

Convergence to a period one fixed point is investigated for both logistic and cubic maps. For the logistic map the relaxation to the fixed point is considered near a transcritical bifurcation while for the cubic map it is near a pitchfork bifurcation. We confirmed that the convergence to the fixed point in both logistic and cubic maps for a region close to the fixed point goes exponentially fast to the fixed point and with a relaxation time described by a power law of exponent -1. At the bifurcation point, the exponent is not universal and depends on the type of the bifurcation as well as on the nonlinearity of the map.

Non-perturbative fixed points and renormalization group improved effective potential

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Involutions whose fixed set has three or four components: a small codimension phenomenon

Let T : M → M be a smooth involution on a closed smooth manifold and F = n j=0 F j the fixed point set of T, where F j denotes the union of those components of F having dimension j and thus n is the dimension of the component of F of largest dimension. In this paper we prove the following result, which characterizes a small codimension phenomenon: suppose that n ≥ 4 is even and F has one of the following forms: 1) F = F n ∪ F 3 ∪ F 2 ∪ {point}; 2) F = F n ∪ F 3 ∪ F 2 ; 3) F = F n ∪ F 3 ∪ {point}; or 4) F = F n ∪ F 3 . Also, suppose that the normal bundles of F n, F 3 and F 2 in M do not bound. If k denote the codimension of F n, then k ≤ 4. Further, we construct involutions showing that this bound is best possible in the cases 2) and 4), and in the cases 1) and 3) when n is of the form n = 4t, with t ≥ 1.