Nonextensive Pesin identity. Exact renormalization group analytical results for the dynamics at the edge of chaos of the logistic map

We show that the dynamical and entropic properties at the chaos threshold of the logistic map are naturally linked through the nonextensive expressions for the sensitivity to initial conditions and for the entropy. We corroborate analytically, with the use of the Feigenbaum renormalization group(RG) transformation, the equality between the generalized Lyapunov coefficient $\lambda_{q}$ and the rate of entropy production $K_{q}$ given by the nonextensive statistical mechanics. Our results advocate the validity of the $q$-generalized Pesin identity at critical points of one-dimensional nonlinear dissipative maps.Comment: Revtex, 5 pages, 3 figure

Super Jackstraws and Super Waterwheels

We construct various new BPS states of D-branes preserving 8 supersymmetries. These include super Jackstraws (a bunch of scattered D- or (p,q)-strings preserving supersymmetries), and super waterwheels (a number of D2-branes intersecting at generic angles on parallel lines while preserving supersymmetries). Super D-Jackstraws are scattered in various dimensions but are dynamical with all their intersections following a common null direction. Meanwhile, super (p,q)-Jackstraws form a planar static configuration. We show that the SO(2) subgroup of SL(2,R), the group of classical S-duality transformations in IIB theory, can be used to generate this latter configuration of variously charged (p,q)-strings intersecting at various angles. The waterwheel configuration of D2-branes preserves 8 supersymmetries as long as the `critical' Born-Infeld electric fields are along the common direction.Comment: 23 pages, 10 figure

Lineal Trails of D2-D2bar Superstrings

We study the superstrings suspended between a D2- and an anti-D2-brane. We quantize the string in the presence of some general configuration of gauge fields over the (anti-)D-brane world volumes. The interstring can move only in a specific direction that is normal to the difference of the electric fields of each (anti-)D-branes. Especially when the electric fields are the same, the interstring cannot move. We obtain the condition for the tachyons to disappear from the spectrum.Comment: 15 pages with 4 figures, referenced added, Sec. 5 on the spectrum made cleare

Purification through Zeno-like Measurements

A series of frequent measurements on a quantum system (Zeno-like measurements) is shown to result in the ``purification'' of another quantum system in interaction with the former. Even though the measurements are performed on the former system, their effect drives the latter into a pure state, irrespectively of its initial (mixed) state, provided certain conditions are satisfied.Comment: REVTeX4, 4 pages, 1 figure; to be published in Phys. Rev. Lett. (2003

Blow-up behavior of collocation solutions to Hammerstein-type volterra integral equations

We analyze the blow-up behavior of one-parameter collocation solutions for Hammerstein-type Volterra integral equations (VIEs) whose solutions may blow up in finite time. To approximate such solutions (and the corresponding blow-up time), we will introduce an adaptive stepsize strategy that guarantees the existence of collocation solutions whose blow-up behavior is the same as the one for the exact solution. Based on the local convergence of the collocation methods for VIEs, we present the convergence analysis for the numerical blow-up time. Numerical experiments illustrate the analysis

Schwinger Effect in Non-parallel D1-branes: A Path Integral Approach

We study the Schwinger effect in a system of non-parallel D1-branes for the bosonic strings using the path integral formalism. We drive the string pair creation rate by calculating the one loop vacuum amplitude of the setup in presence of the background electric filed defined along one of the D1-branes. We find an angle dependent minimum value for the background field and show that the decaying of vacuum into string pairs takes place for the field above this value. It is shown that in $\theta\rightarrow\frac{\pi}{2}$ limit the vacuum becomes stable and thus no pair creation occurs

Gravitino fields in Schwarzschild black hole spacetimes

The analysis of gravitino fields in curved spacetimes is usually carried out using the Newman-Penrose formalism. In this paper we consider a more direct approach with eigenspinor-vectors on spheres, to separate out the angular parts of the fields in a Schwarzschild background. The radial equations of the corresponding gauge invariant variable obtained are shown to be the same as in the Newman-Penrose formalism. These equations are then applied to the evaluation of the quasinormal mode frequencies, as well as the absorption probabilities of the gravitino field scattering in this background.Comment: 21 pages, 2 figures. arXiv admin note: text overlap with arXiv:1006.3327 by other author

Holography with Gravitational Chern-Simons Term

The holographic description in the presence of gravitational Chern-Simons term is studied. The modified gravitational equations are integrated by using the Fefferman-Graham expansion and the holographic stress-energy tensor is identified. The stress-energy tensor has both conformal anomaly and gravitational or, if re-formulated in terms of the zweibein, Lorentz anomaly. We comment on the structure of anomalies in two dimensions and show that the two-dimensional stress-energy tensor can be reproduced by integrating the conformal and gravitational anomalies. We study the black hole entropy in theories with a gravitational Chern-Simons term and find that the usual Bekenstein-Hawking entropy is modified. For the BTZ black hole the modification is determined by area of the inner horizon. We show that the total entropy of the BTZ black hole is precisely reproduced in a boundary CFT calculation using the Cardy formula.Comment: 19 pages, Latex; v3: minor corrections, some clarification