Self-Similarity and Localization

The localized eigenstates of the Harper equation exhibit universal self-similar fluctuations once the exponentially decaying part of a wave function is factorized out. For a fixed quantum state, we show that the whole localized phase is characterized by a single strong coupling fixed point of the renormalization equations. This fixed point also describes the generalized Harper model with next nearest neighbor interaction below a certain threshold. Above the threshold, the fluctuations in the generalized Harper model are described by a strange invariant set of the renormalization equations.Comment: 4 pages, RevTeX, 2 figures include

Collision and symmetry-breaking in the transition to strange nonchaotic attractors

Strange nonchaotic attractors (SNAs) can be created due to the collision of an invariant curve with itself. This novel ``homoclinic'' transition to SNAs occurs in quasiperiodically driven maps which derive from the discrete Schr\"odinger equation for a particle in a quasiperiodic potential. In the classical dynamics, there is a transition from torus attractors to SNAs, which, in the quantum system is manifest as the localization transition. This equivalence provides new insights into a variety of properties of SNAs, including its fractal measure. Further, there is a {\it symmetry breaking} associated with the creation of SNAs which rigorously shows that the Lyapunov exponent is nonpositive. By considering other related driven iterative mappings, we show that these characteristics associated with the the appearance of SNA are robust and occur in a large class of systems.Comment: To be appear in Physical Review Letter

Binary Tree Approach to Scaling in Unimodal Maps

Ge, Rusjan, and Zweifel (J. Stat. Phys. 59, 1265 (1990)) introduced a binary tree which represents all the periodic windows in the chaotic regime of iterated one-dimensional unimodal maps. We consider the scaling behavior in a modified tree which takes into account the self-similarity of the window structure. A non-universal geometric convergence of the associated superstable parameter values towards a Misiurewicz point is observed for almost all binary sequences with periodic tails. There are an infinite number of exceptional sequences, however, which lead to superexponential scaling. The origin of such sequences is explained.Comment: 25 pages, plain Te

Phosphorus in manure and sewage sludge more recyclable than in soluble inorganic fertilizer

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Universal criterion for the breakup of invariant tori in dissipative systems

The transition from quasiperiodicity to chaos is studied in a two-dimensional dissipative map with the inverse golden mean rotation number. On the basis of a decimation scheme, it is argued that the (minimal) slope of the critical iterated circle map is proportional to the effective Jacobian determinant. Approaching the zero-Jacobian-determinant limit, the factor of proportion becomes a universal constant. Numerical investigation on the dissipative standard map suggests that this universal number could become observable in experiments. The decimation technique introduced in this paper is readily applicable also to the discrete quasiperiodic Schrodinger equation.Comment: 13 page

Mutaciones y tensiones de la escuela contemporánea: miradas críticas

A fines de la década de los años 70 del siglo XX, se percibieron los primeros síntomas de las mudanzas a las que fue sometida la escuela de la modernidad. Estas variaciones fueron usadas como pretexto para exponer un profundo cambio que la época develada, la educación de masas, explosión demográfica, entre otras. La reforma estatal más importante, omnipresente, amplia y extendida de todas las épocas es la vinculación a la escuela de las dificultades propias de la economía, el Estado y las organizaciones. En los últimos treinta años se han configurado las subjetividades más complejas presentes en la historia de la escuela, donde el más crudo de los individualismos colonizó este espacio. Las anteriores mutaciones parecieran pertenecer al género de obviedades que no es preciso explicar, pues “los cambios son porque están”. De ahí que se requiera, desde miradas históricas y pedagógicas, comprender la génesis de estos cambios que determinaron el formato de la escuela contemporánea. Desde miradas genealógicas arqueológicas para futuras revisiones, este documento dará algunas pistas sobre el giro de la escuela dentro del consenso transcultural adherido a la educación de masas y sobre la creación de un dispositivo de control social del mundo escolar a través de las disciplinas escolares.Palabras clave: escuela, cambios, historia, crítica.AbstractIn the late 70s of the twentieth century, the first signs of the changes to which the School of modernity was brought under are perceived. These variations were used as a pretext to expose an existing deep change that stood out above others: education to the masses. The most important, pervasive, widespread and extensive state reform of all ages is the link to the school of the own difficulties of the economy, the State and organizations. In the last thirty years, the most complex subjectivities present in the history of the school have been set up, the crudest model of individualism colonized this space. The previous mutations seem to belong to the genre of truism that is not necessary to explain: “The changes are because they are”. Hence, it is required from historical and pedagogical understanding the genesis of these changes that determined the format of the contemporary school. From archaeological genealogical looks for future reviews, this document will give some clues about the shift of the school in the transcultural consensus adhered to the education to the masses, and the creation of a device for social control of the school system through school subjects.Keywords: school, changes, history, criticism

Dimer Decimation and Intricately Nested Localized-Ballistic Phases of Kicked Harper

Dimer decimation scheme is introduced in order to study the kicked quantum systems exhibiting localization transition. The tight-binding representation of the model is mapped to a vectorized dimer where an asymptotic dissociation of the dimer is shown to correspond to the vanishing of the transmission coefficient thru the system. The method unveils an intricate nesting of extended and localized phases in two-dimensional parameter space. In addition to computing transport characteristics with extremely high precision, the renormalization tools also provide a new method to compute quasienergy spectrum.Comment: There are five postscript figures. Only half of the figure (3) is shown to reduce file size. However, missing part is the mirror image of the part show