Robustness of equilibrium in the Kyle model of informed speculation

We analyze a static Kyle (1983) model in which a risk-neutral informed trader can use arbitrary (linear or non-linear) deterministic strategies, and a nite number of market makers can use arbitrary pricing rules. We establish a strong sense in which the linear Kyle equilibrium is robust: the rst variation in any agent's expected payo with respect to a small variation in his conjecture about the strategies of others vanishes at equilibrium. Thus, small errors in a market maker's beliefs about the informed speculator's trading strategy do not reduce his expected payo s. Therefore, the original equilibrium strategies remain optimal and still constitute an equilibrium (neglecting the higher-order terms.) We also establish that if a non-linear equilibrium exists, then it is not robust

Double butterfly spectrum for two interacting particles in the Harper model

We study the effect of interparticle interaction $U$ on the spectrum of the Harper model and show that it leads to a pure-point component arising from the multifractal spectrum of non interacting problem. Our numerical studies allow to understand the global structure of the spectrum. Analytical approach developed permits to understand the origin of localized states in the limit of strong interaction $U$ and fine spectral structure for small $U$.Comment: revtex, 4 pages, 5 figure

Two interacting Hofstadter butterflies

The problem of two interacting particles in a quasiperiodic potential is addressed. Using analytical and numerical methods, we explore the spectral properties and eigenstates structure from the weak to the strong interaction case. More precisely, a semiclassical approach based on non commutative geometry techniques permits to understand the intricate structure of such a spectrum. An interaction induced localization effect is furthermore emphasized. We discuss the application of our results on a two-dimensional model of two particles in a uniform magnetic field with on-site interaction.Comment: revtex, 12 pages, 11 figure

Exact Random Walk Distributions using Noncommutative Geometry

Using the results obtained by the non commutative geometry techniques applied to the Harper equation, we derive the areas distribution of random walks of length $N$ on a two-dimensional square lattice for large $N$, taking into account finite size contributions.Comment: Latex, 3 pages, 1 figure, to be published in J. Phys. A : Math. Ge

Exploring the boundaries in an interdisciplinary context through the Family Resemblance Approach: The Dialogue Between Physics and Mathematics

Among the relevant aspects of the family resemblance approach (FRA), our study focuses on the potential of the approach to elaborate on disciplinary identities in an interdisciplinary context, specifically regarding the interplay between physics and mathematics. We present and discuss how the FRA wheel can be used and intertwined with the framework of boundary objects and boundary crossing mechanisms (Akkerman & Bakker, Review of Educational Research, 81, 132–169, 2011), which is well-known in STEM education for dealing with interdisciplinarity. The role of the FRA discussed in the article is dual: both practical and theoretical. It is practical in that we show how its use, in combination with the Akkerman and Bakker framework, appears effective in fostering productive discussions among prospective teachers on disciplinary identities and interdisciplinarity in historical cases. It is theoretical in that the combination of the two frameworks provides the vocabulary to characterise the ‘ambiguous nature’ of interdisciplinarity: like boundaries, interdisciplinarity both separates disciplines, making their identities emerge, and connects them, fostering mechanisms of crossing and transgressing the boundaries. This empirical study reveals how the theoretical elaboration took advantage of the prospective teachers’ contributions. We initially presented the FRA to characterise disciplinary identities, but the prospective teachers highlighted its potential to characterise also the boundary zone and the dialogue between physics and mathematics. The data analysis showed that the combination of the two frameworks shaped a complex learning space where there was room for very different epistemic demands of the prospective teachers: from those who feel better within the identity cores of the disciplines, to those who like to inhabit the boundary zone and others who like to re-shape boundary spaces and move dynamically across them

Interaction induced delocalisation for two particles in a periodic potential

We consider two interacting particles evolving in a one-dimensional periodic structure embedded in a magnetic field. We show that the strong localization induced by the magnetic field for particular values of the flux per unit cell is destroyed as soon as the particles interact. We study the spectral and the dynamical aspects of this transition.Comment: 4 pages, 5 EPS figures, minor misprints correcte

Reactive Metals as Energy Storage and Carrier Media: Use of Aluminum for Power Generation in Fuel Cell-Based Power Plants

In recent years, the energy production sector has experienced a growing interest in new energy vectors enabling energy storage and, at the same time, intersectoral energy applications among users. Hydrogen is one of the most promising energy storage and carrier media featuring a very high gravimetric energy density, but a rather low volumetric energy density. To this regard, this study focuses on the use of aluminum as energy storage and carrier medium, offering high volumetric energy density (23.5 kWh L$^{-1}$), ease to transport and stock (e.g., as ingots), and is neither toxic nor dangerous when stored. In addition, mature production and recycling technologies exist for aluminum. Herein, the performance of power systems driven by aluminum powder in terms of electrical efficiency (η$_{(I)}$) and round‐trip efficiency (RTE) is analyzed. Along with the additional advantages relating to high volumetric energy density, and safety and management aspects, the aluminum‐based technology appears to outperform the power‐to‐power systems based on hydrogen and liquid fuels

Bloch Electrons in a Magnetic Field - Why Does Chaos Send Electrons the Hard Way?

We find that a 2D periodic potential with different modulation amplitudes in x- and y-direction and a perpendicular magnetic field may lead to a transition to electron transport along the direction of stronger modulation and to localization in the direction of weaker modulation. In the experimentally accessible regime we relate this new quantum transport phenomenon to avoided band crossing due to classical chaos.Comment: 4 pages, 3 figures, minor modifications, PRL to appea

Metal-insulator transitions in cyclotron resonance of periodic nanostructures due to avoided band crossings

A recently found metal-insulator transition in a model for cyclotron resonance in a two-dimensional periodic potential is investigated by means of spectral properties of the time evolution operator. The previously found dynamical signatures of the transition are explained in terms of avoided band crossings due to the change of the external electric field. The occurrence of a cross-like transport is predicted and numerically confirmed