On the Lattice Distortion Problem

We introduce and study the \emph{Lattice Distortion Problem} (LDP). LDP asks how "similar" two lattices are. I.e., what is the minimal distortion of a linear bijection between the two lattices? LDP generalizes the Lattice Isomorphism Problem (the lattice analogue of Graph Isomorphism), which simply asks whether the minimal distortion is one. As our first contribution, we show that the distortion between any two lattices is approximated up to a $n^{O(\log n)}$ factor by a simple function of their successive minima. Our methods are constructive, allowing us to compute low-distortion mappings that are within a $2^{O(n \log \log n/\log n)}$ factor of optimal in polynomial time and within a $n^{O(\log n)}$ factor of optimal in singly exponential time. Our algorithms rely on a notion of basis reduction introduced by Seysen (Combinatorica 1993), which we show is intimately related to lattice distortion. Lastly, we show that LDP is NP-hard to approximate to within any constant factor (under randomized reductions), by a reduction from the Shortest Vector Problem.Comment: This is the full version of a paper that appeared in ESA 201

Illuminating Dark Matter at the ILC

The WIMP (weakly interacting massive particle) paradigm for dark matter is currently being probed via many different experiments. Direct detection, indirect detection and collider searches are all hoping to catch a glimpse of these elusive particles. Here, we examine the potential of the ILC (International Linear Collider) to shed light on the origin of dark matter. By using an effective field theory approach we are also able to compare the reach of the ILC with that of the other searches. We find that for low mass dark matter (< 10 GeV), the ILC offers a unique opportunity to search for WIMPS beyond any other experiment. In addition, if dark matter happens to only couple to leptons or via a spin dependent interaction, the ILC can give an unrivalled window to these models. We improve on previous ILC studies by constructing a comprehensive list of effective theories that allows us to move beyond the non-relativistic approximation.Comment: 26 page

On Percolation and NP-Hardness

The edge-percolation and vertex-percolation random graph models start with an arbitrary graph G, and randomly delete edges or vertices of G with some fixed probability. We study the computational hardness of problems whose inputs are obtained by applying percolation to worst-case instances. Specifically, we show that a number of classical N P-hard graph problems remain essentially as hard on percolated instances as they are in the worst-case (assuming NP !subseteq BPP). We also prove hardness results for other NP-hard problems such as Constraint Satisfaction Problems, where random deletions are applied to clauses or variables. We focus on proving the hardness of the Maximum Independent Set problem and the Graph Coloring problem on percolated instances. To show this we establish the robustness of the corresponding parameters alpha(.) and Chi(.) to percolation, which may be of independent interest. Given a graph G, let G\u27 be the graph obtained by randomly deleting edges of G. We show that if alpha(G) is small, then alpha(G\u27) remains small with probability at least 0.99. Similarly, we show that if Chi(G) is large, then Chi(G\u27) remains large with probability at least 0.99

Dynamical Coulomb blockade and spin-entangled electrons

We consider the production of mobile and nonlocal pairwise spin-entangled electrons from tunneling of a BCS-superconductor (SC) to two normal Fermi liquid leads. The necessary mechanism to separate the two electrons coming from the same Cooper pair (spin-singlet) is achieved by coupling the SC to leads with a finite resistance. The resulting dynamical Coulomb blockade effect, which we describe phenomenologically in terms of an electromagnetic environment, is shown to be enhanced for tunneling of two spin-entangled electrons into the same lead compared to the process where the pair splits and each electron tunnels into a different lead. On the other hand in the pair-split process, the spatial correlation of a Cooper pair leads to a current suppression as a function of distance between the two tunnel junctions which is weaker for effectively lower dimensional SCs.Comment: 5 pages, 2 figure

In situ study of the endotaxial growth of hexagonal CoSi2 nanoplatelets in Si(001)

This investigation aims at studying-by in situ grazing-incidence small-angle x-ray scattering-the process of growth of hexagonal CoSi2 nanoplatelets endotaxially buried in a Si(001) wafer. The early formation of spherical Co nanoparticles with bimodal size distribution in the deposited silica thin film during a pretreatment at 500 °C and their subsequent growth at 700 °C were also characterized. Isothermal annealing at 700 °C promotes a drastic reduction in the number of the smallest Co nanoparticles and a continuous decrease in their volume fraction in the silica thin film. At the same time, Co atoms diffuse across the SiO2/Si(001) interface into the silicon wafer, react with Si, and build up thin hexagonal CoSi2 nanoplatelets, all of them with their main surfaces parallel to Si{111} crystallographic planes. The observed progressive growths in thickness and lateral size of the hexagonal CoSi2 nanoplatelets occur at the expense of the dissolution of the small Co nanoparticles that are formed during the pretreatment at 500 °C and become unstable at the annealing temperature (700 °C). The kinetics of growth of the volume fraction of hexagonal platelets is well described by the classical Avrami equation.Fil: Costa, Daniel Da Silva. Universidade Federal do Paraná; BrasilFil: Huck Iriart, Cristián. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas; ArgentinaFil: Kellermann, Guinther. Universidade Federal do Paraná; BrasilFil: Giovanetti, Lisandro Jose. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas; ArgentinaFil: Craievich, Aldo F.. Universidade de Sao Paulo; BrasilFil: Requejo, Felix Gregorio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas; Argentin

Limit Theorems for Individual-Based Models in Economics and Finance

There is a widespread recent interest in using ideas from statistical physics to model certain types of problems in economics and finance. The main idea is to derive the macroscopic behavior of the market from the random local interactions between agents. Our purpose is to present a general framework that encompasses a broad range of models, by proving a law of large numbers and a central limit theorem for certain interacting particle systems with very general state spaces. To do this we draw inspiration from some work done in mathematical ecology and mathematical physics. The first result is proved for the system seen as a measure-valued process, while to prove the second one we will need to introduce a chain of embeddings of some abstract Banach and Hilbert spaces of test functions and prove that the fluctuations converge to the solution of a certain generalized Gaussian stochastic differential equation taking values in the dual of one of these spaces.Comment: To appear in Stochastic Processes and their Application

Electro-Optical Design for Efficient Visual Communication

Visual communication, in the form of telephotography and television, for example, can be regarded as efficient only if the amount of information that it conveys about the scene to the observer approaches the maximum possible and the associated cost approaches the minimum possible. Elsewhere we have addressed the problem of assessing the end to end performance of visual communication systems in terms of their efficiency in this sense by integrating the critical limiting factors that constrain image gathering into classical communications theory. We use this approach to assess the electro-optical design of image gathering devices as a function of the f number and apodization of the objective lens and the aperture size and sampling geometry of the phot-detection mechanism. Results show that an image gathering device that is designed to optimize information capacity performs similarly to the human eye. For both, the performance approaches the maximum possible, in terms of the efficiency with which the acquired information can be transmitted as decorrelated data, and the fidelity, sharpness, and clearity with which fine detail can be restored

Supramolecular organogels based on mesogenic 2,7-difunctionalized triphenylenes as a simple system for water content assessment in light alcohols

A series of three triphenylene compounds-denoted 2,7-THTP-DiCnOH-bearing four hexyloxy ancillary chains and two variable-length alkoxy chains terminally functionalized with hydroxyl groups have been synthesized and characterized. The studied compounds exhibited thermotropic mesomorphism; the detailed nature of the mesophases was found to depend on the relative positions of the terminal functional groups relative to the crown formed by the ancillary chains. All the studied compounds were able to act as supramolecular gelators in a variety of alcohols; their organogelating ability has been rationalized in terms of physicochemical parameters like the dielectric constant, which allowed us to establish very precise predictive "solvent gelation windows" for each compound. Remarkably stable gels have been detected for 2,7-THTP-DiC6OH in methanol. As a proof of principle, we present the water sensing performance as a rapid method for the assessment of water content in alcohol samples based on the influence that the water content exerts on the gels' thermostability.Fil: Vadra, Nahir. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Química, Física de los Materiales, Medioambiente y Energía. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Química, Física de los Materiales, Medioambiente y Energía; ArgentinaFil: Huck Iriart, Cristián. Universidad Nacional de San Martín. Escuela de Ciencia y Tecnología; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Giovanetti, Lisandro Jose. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas; ArgentinaFil: Di Chenna, Pablo Hector. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Unidad de Microanálisis y Métodos Físicos en Química Orgánica. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Unidad de Microanálisis y Métodos Físicos en Química Orgánica; ArgentinaFil: Cukiernik, Fabio Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Química, Física de los Materiales, Medioambiente y Energía. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Química, Física de los Materiales, Medioambiente y Energía; Argentin

Narrow-bandwidth sensing of high-frequency fields with continuous dynamical decoupling

State-of-the-art methods for sensing weak AC fields are only efficient in the low frequency domain. Here, Stark et al. demonstrate a sensing scheme that is capable of probing high frequencies through continuous dynamical coupling by applying it to a nitrogen-vacancy centre in diamond

In situ study of the endotaxial growth of hexagonal CoSi2 nanoplatelets in Si(001)

This investigation aims at studying-by in situ grazing-incidence small-angle x-ray scattering-the process of growth of hexagonal CoSi2 nanoplatelets endotaxially buried in a Si(001) wafer. The early formation of spherical Co nanoparticles with bimodal size distribution in the deposited silica thin film during a pretreatment at 500 °C and their subsequent growth at 700 °C were also characterized. Isothermal annealing at 700 °C promotes a drastic reduction in the number of the smallest Co nanoparticles and a continuous decrease in their volume fraction in the silica thin film. At the same time, Co atoms diffuse across the SiO2/Si(001) interface into the silicon wafer, react with Si, and build up thin hexagonal CoSi2 nanoplatelets, all of them with their main surfaces parallel to Si{111} crystallographic planes. The observed progressive growths in thickness and lateral size of the hexagonal CoSi2 nanoplatelets occur at the expense of the dissolution of the small Co nanoparticles that are formed during the pretreatment at 500 °C and become unstable at the annealing temperature (700 °C). The kinetics of growth of the volume fraction of hexagonal platelets is well described by the classical Avrami equation.Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicada