Non-Hermitian robust edge states in one-dimension: Anomalous localization and eigenspace condensation at exceptional points

Capital to topological insulators, the bulk-boundary correspondence ties a topological invariant computed from the bulk (extended) states with those at the boundary, which are hence robust to disorder. Here we put forward an ordering unique to non-Hermitian lattices, whereby a pristine system becomes devoid of extended states, a property which turns out to be robust to disorder. This is enabled by a peculiar type of non-Hermitian degeneracy where a macroscopic fraction of the states coalesce at a single point with geometrical multiplicity of $1$, that we call a phenomenal point.Comment: 6 pages, 4 figure

Homological Epimorphisms and Hochschild-Mitchell Cohomology

In this work, we study the Hochschild-Mitchell Cohomology of triangular matrix categories. Given a triangular matrix category $\Lambda=\left[ \begin{smallmatrix} \mathcal{T} & 0 \\ M & \mathcal{U} \end{smallmatrix}\right]$, we investigate the relationship of the Hochschild-Mitchell cohomologies $H^{i}(\Lambda)$ and $H^{i}(\mathcal{U})$ of $\Lambda$ and $\mathcal{U}$ respectively; and we show that they can be connected by a long exact sequence. This result extend the well-known result of Michelana-Platzeck given in [S. Michelena, M. I. Platzeck. {\it{Hochschild cohomology of triangular matrix algebras}}. J. Algebra 233, (2000) 502-525].Comment: In this new version, the title of the article has been changed and a new section has been adde

Stretched Polymers in Random Environment

We survey recent results and open questions on the ballistic phase of stretched polymers in both annealed and quenched random environments.Comment: Dedicated to Erwin Bolthausen on the occasion of his 65th birthda

Evaluación briológica de los efectos de la contaminación atmosférica en la Ciudad de México

The Index of Atmospheric Purity (IAP) was used to make a preliminary evaluation of epiphytic moss response to atmospheric pollution in the urban area of Mexico City. Areal analysis indicates that there is a significant negative correlation (p < 0.5) between IAP values and SO2, NO2, NOx, Pb and temperature values of -0.45, -0.90, -0.80, -0.80, -0.90. Significant positive correlation (p < 0.05) between IAP values and O3, rainfall and relative atmospheric humidity with values of 0.70, 0.80, 0.90. Increase in atmospheric pollutants in Mexico City have promoted a gradual decrease in frequency and cover of epiphytic mosses even though some ecological factors may show the oposite effect.Se hace una evaluación preliminar de la respuesta de los musgos epífitos a la contaminación atmosférica usando el Indice de Pureza Atmosférica (IPA) en el área urbana de la Ciudad de México. El análisis por zonas indica que hay una relación inversa y significativa (p < 0.5) entre el IPA y SO2, NO2, NOx, Pb y la temperatura con valores de -0.45, -0.90, -0.80, -0.80, -0.90. También se encontró una relación directa y significativa (p < 0.05) entre el IPA y el O3, la precipitación pluvial y la humedad relativa con valores de 0.70, 0.80, 0.90. Los incrementos en los niveles de algunos contaminantes atmosféricos en la Ciudad de México han promovido la disminución gradual en la frecuencia de aparición y cobertura de musgos epífitos, aunque algunas variables ambientales pueden tener el efecto opuesto

Diverse routes to oscillation death in a coupled-oscillator system.

We study oscillation death (OD) in a well-known coupled-oscillator system that has been used to model cardiovascular phenomena. We derive exact analytic conditions that allow the prediction of OD through the two known bifurcation routes, in the same model, and for different numbers of coupled oscillators. Our exact analytic results enable us to generalize OD as a multiparameter-sensitive phenomenon. It can be induced, not only by changes in couplings, but also by changes in the oscillator frequencies or amplitudes. We observe synchronization transitions as a function of coupling and confirm the robustness of the phenomena in the presence of noise. Numerical and analogue simulations are in good agreement with the theory

SIGMA and XTE observations of the soft X-ray transient XTEJ1755-324

We present observations of the X-ray transient XTEJ1755-324 performed during summer 1997 with the XTE satellite and with the SIGMA hard X-ray telescope onboard the GRANAT observatory. The source was first detected in soft X-rays with XTE on July 25 1997 with a rather soft X-ray spectrum and its outburst was monitored in soft X-rays up to November 1997. On September 16 it was first detected in hard X-rays by the French soft gamma ray telescope SIGMA during a Galactic Center observation. The flux was stronger on September 16 and 17 reaching a level of about 110 mCrab in the 40-80 keV energy band. On the same days the photon index of the spectrum was determined to be alpha =-2.3 +/- 0.9 (1 sigma error) while the 40-150 keV luminosity was about 8 x 10^{36} erg/s for a distance of 8.5 kpc. SIGMA and XTE results on this source indicate that this source had an ultrasoft-like state during its main outburst and a harder secondary outburst in September. These characteristics make the source similar to X-Nova Muscae 1991, a well known black hole candidate.Comment: 19 pages LaTeX, 6 Postscript figures included, Accepted by Astrophysical Journa

Pre-freezing of multifractal exponents in Random Energy Models with logarithmically correlated potential

Boltzmann-Gibbs measures generated by logarithmically correlated random potentials are multifractal. We investigate the abrupt change ("pre-freezing") of multifractality exponents extracted from the averaged moments of the measure - the so-called inverse participation ratios. The pre-freezing can be identified with termination of the disorder-averaged multifractality spectrum. Naive replica limit employed to study a one-dimensional variant of the model is shown to break down at the pre-freezing point. Further insights are possible when employing zero-dimensional and infinite-dimensional versions of the problem. In particular, the latter version allows one to identify the pattern of the replica symmetry breaking responsible for the pre-freezing phenomenon.Comment: This is published version, 11 pages, 1 figur