On the centralizer of vector fields: criteria of triviality and genericity results

In this paper, we investigate the question of whether a typical vector field on a compact connected Riemannian manifold $M^d$ has a `small' centralizer. In the $C^1$ case, we give two criteria, one of which is $C^1$-generic, which guarantees that the centralizer of a $C^1$-generic vector field is indeed small, namely \textit{collinear}. The other criterion states that a $C^1$ \textit{separating} flow has a collinear $C^1$-centralizer. When all the singularities are hyperbolic, we prove that the collinearity property can actually be promoted to a stronger one, refered as \textit{quasi-triviality}. In particular, the $C^1$-centralizer of a $C^1$-generic vector field is quasi-trivial. In certain cases, we obtain the triviality of the centralizer of a $C^1$-generic vector field, which includes $C^1$-generic Axiom A (or sectional Axiom A) vector fields and $C^1$-generic vector fields with countably many chain recurrent classes. For sufficiently regular vector fields, we also obtain various criteria which ensure that the centralizer is \textit{trivial} (as small as it can be), and we show that in higher regularity, collinearity and triviality of the $C^d$-centralizer are equivalent properties for a generic vector field in the $C^d$ topology. We also obtain that in the non-uniformly hyperbolic scenario, with regularity $C^2$, the $C^1$-centralizer is trivial.Comment: This is the final version, accepted in Mathematische Zeitschrift. New introduction and some proofs where rewritten and/or expanded, according to referee's suggestion. Also, a new appendix was adde

Dynamics of non-convolution operators and holomorphy types

In this article we study the hypercyclic behavior of non-convolution operators defined on spaces of analytic functions of different holomorphy types over Banach spaces. The operators in the family we analyze are a composition of differentiation and composition operators, and are extensions of operators in H(C) studied by Aron and Markose in 2004. The dynamics of this class of operators, in the context of one and several complex variables, was further investigated by many authors. It turns out that the situation is somewhat different and that some purely infinite dimensional difficulties appear. For example, in contrast to the several complex variable case, it may happen that the symbol of the composition operator has no fixed points and still, the operator is not hypercyclic. We also prove a Runge type theorem for holomorphy types on Banach spaces.Fil: Muro, Luis Santiago Miguel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaFil: Pinasco, Damian. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Torcuato Di Tella. Departamento de Matemáticas y Estadística; ArgentinaFil: Savransky, Martin. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentin

Localization and oscillations of Majorana fermions in a two-dimensional electron gas coupled with dd-wave superconductors

We study the localization and oscillation properties of the Majorana fermions that arise in a two-dimensional electron gas (2DEG) with spin-orbit coupling (SOC) and a Zeeman field coupled with a d-wave superconductor. Despite the angular dependence of the d-wave pairing, localization and oscillation properties are found to be similar to the ones seen in conventional s-wave superconductors. In addition, we study a microscopic lattice version of the previous system that can be characterized by a topological invariant. We derive its real space representation that involves nearest and next-to-nearest-neighbors pairing. Finally, we show that the emerging chiral Majorana fermions are indeed robust against static disorder. This analysis has potential applications to quantum simulations and experiments in high-$T_c$ superconductors.Comment: revtex4 file, color figure

Quantum Error Correction with the Semion Code

We present a full quantum error correcting procedure with the semion code: an off-shell extension of the double semion model. We construct open strings operators that recover the quantum memory from arbitrary errors and closed string operators that implement the basic logical operations for information processing. Physically, the new open string operators provide a detailed microscopic description of the creation of semions at their endpoints. Remarkably, topological properties of the string operators are determined using fundamental properties of the Hamiltonian, namely the fact that it is composed of commuting local terms squaring to the identity. In all, the semion code is a topological code that, unlike previously studied topological codes, it is of non-CSS type and fits into the stabilizer formalism. This is in sharp contrast with previous attempts yielding non-commutative codes.Comment: REVTeX 4 file, color figure

Ionized gas outflows and global kinematics of low-z luminous star forming galaxies

We study the kinematic properties of the ambient ionized ISM and ionized gas outflows in a large and representative sample of local luminous and ultraluminous infrared galaxies (U/LIRGs) (58 systems, 75 galaxies), on the basis of integral field spectroscopy (IFS)-based high S/N integrated spectra at galactic and sub-galactic, i.e. star forming (SF) clumps, scales. Ambient ionized gas. The velocity dispersion of the ionized ISM in U/LIRGs ( ~ 70 kms-1) is larger than in lower luminosity local star forming galaxies ( ~ 25 kms-1). While for isolated disc LIRGs star formation appears to sustain turbulence, gravitational energy release associated to interactions and mergers plays an important role driving sigma in the U/LIRG range. We also find that the impact of an AGN in ULIRGs is strong, increasing sigma by a factor 1.5 on average. The observed weak dependency of sigma with SFR surface density for local U/LIRGs is in very good agreement with that measured in some high-z samples. Ionized outflows. The presence of ionized gas outflows in U/LIRGs seems universal based on the detection of a broad, usually blueshifted, Halpha line. AGNs in U/LIRGs are able to generate faster (x2) and more massive (x1.4) ionized gas outflows than pure starbursts. The derived ionized mass loading factors are in general below one, with only a few AGNs above this limit. Only a small fraction of the ionized material from low mass LIRGs (log(Mdyn/Msun) < 10.4) could reach the intergalactic medium, with more massive galaxies retaining the gas. The observed average outflow properties in U/LIRGs are similar to high-z galaxies of comparable SFR. In the bright SF clumps found in LIRGs, ionized gas outflows appear to be very common. For a given SFR surface density, outflows in LIRG clumps would be about one to two orders of magnitude less energetic than those launched by clumps in high-z SF galaxies.Comment: 36 pages, 20 figures, 6 tables. Accepted for publication in A&

Human Frataxin Folds Via an Intermediate State. Role of the C-Terminal Region

The aim of this study is to investigate the folding reaction of human frataxin, whose deficiency causes the neurodegenerative disease Friedreich’s Ataxia (FRDA). The characterization of different conformational states would provide knowledge about how frataxin can be stabilized without altering its functionality. Wild-type human frataxin and a set of mutants, including two highly destabilized FRDA-associated variants were studied by urea-induced folding/unfolding in a rapid mixing device and followed by circular dichroism. The analysis clearly indicates the existence of an intermediate state (I) in the folding route with significant secondary structure content but relatively low compactness, compared with the native ensemble. However, at high NaCl concentrations I-state gains substantial compaction, and the unfolding barrier is strongly affected, revealing the importance of electrostatics in the folding mechanism. The role of the C-terminal region (CTR), the key determinant of frataxin stability, was also studied. Simulations consistently with experiments revealed that this stretch is essentially unstructured, in the most compact transition state ensemble (TSE2). The complete truncation of the CTR drastically destabilizes the native state without altering TSE2. Results presented here shed light on the folding mechanism of frataxin, opening the possibility of mutating it to generate hyperstable variants without altering their folding kinetics.Fil: Faraj, Santiago Enrique. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Houssay. Instituto de Química y Físico-Química Biológicas "Prof. Alejandro C. Paladini". Universidad de Buenos Aires. Facultad de Farmacia y Bioquímica. Instituto de Química y Físico-Química Biológicas; ArgentinaFil: Gonzalez-Lebrero, Rodolfo Martin. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Houssay. Instituto de Química y Físico-Química Biológicas "Prof. Alejandro C. Paladini". Universidad de Buenos Aires. Facultad de Farmacia y Bioquímica. Instituto de Química y Físico-Química Biológicas; ArgentinaFil: Roman, Ernesto Andres. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Houssay. Instituto de Química y Físico-Química Biológicas "Prof. Alejandro C. Paladini". Universidad de Buenos Aires. Facultad de Farmacia y Bioquímica. Instituto de Química y Físico-Química Biológicas; ArgentinaFil: Santos, Javier. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Houssay. Instituto de Química y Físico-Química Biológicas "Prof. Alejandro C. Paladini". Universidad de Buenos Aires. Facultad de Farmacia y Bioquímica. Instituto de Química y Físico-Química Biológicas; Argentin