Semi-classical limit of large fermionic systems at positive temperature

We study a system of $N$ interacting fermions at positive temperature in a confining potential. In the regime where the intensity of the interaction scales as $1/N$ and with an effective semi-classical parameter $\hbar=N^{-1/d}$ where $d$ is the space dimension, we prove the convergence to the corresponding Thomas-Fermi model at positive temperature.Comment: Convergence of states rewritten. Some references adde

On the coupling between an ideal fluid and immersed particles

In this paper we use Lagrange-Poincare reduction to understand the coupling between a fluid and a set of Lagrangian particles that are supposed to simulate it. In particular, we reinterpret the work of Cendra et al. by substituting velocity interpolation from particle velocities for their principal connection. The consequence of writing evolution equations in terms of interpolation is two-fold. First, it gives estimates on the error incurred when interpolation is used to derive the evolution of the system. Second, this form of the equations of motion can inspire a family of particle and hybrid particle-spectral methods where the error analysis is "built-in". We also discuss the influence of other parameters attached to the particles, such as shape, orientation, or higher-order deformations, and how they can help with conservation of momenta in the sense of Kelvin's circulation theorem.Comment: to appear in Physica D, comments and questions welcom

Characters of graded parafermion conformal field theory

The graded parafermion conformal field theory at level k is a close cousin of the much-studied Z_k parafermion model. Three character formulas for the graded parafermion theory are presented, one bosonic, one fermionic (both previously known) and one of spinon type (which is new). The main result of this paper is a proof of the equivalence of these three forms using q-series methods combined with the combinatorics of lattice paths. The pivotal step in our approach is the observation that the graded parafermion theory -- which is equivalent to the coset osp(1,2)_k/ u(1) -- can be factored as (osp(1,2)_k/ su(2)_k) x (su(2)_k/ u(1)), with the two cosets on the right equivalent to the minimal model M(k+2,2k+3) and the Z_k parafermion model, respectively. This factorisation allows for a new combinatorial description of the graded parafermion characters in terms of the one-dimensional configuration sums of the (k+1)-state Andrews--Baxter--Forrester model.Comment: 36 page

The Painlev\'e analysis for N=2 super KdV equations

The Painlev\'e analysis of a generic multiparameter N=2 extension of the Korteweg-de Vries equation is presented. Unusual aspects of the analysis, pertaining to the presence of two fermionic fields, are emphasized. For the general class of models considered, we find that the only ones which manifestly pass the test are precisely the four known integrable supersymmetric KdV equations, including the SKdV$_1$ case.Comment: Harvmac (b mode : 29 p); various minor modifications -- to appear in J. Math Phy

A Discrete Geometric Optimal Control Framework for Systems with Symmetries

This paper studies the optimal motion control of mechanical systems through a discrete geometric approach. At the core of our formulation is a discrete Lagrange-d’Alembert- Pontryagin variational principle, from which are derived discrete equations of motion that serve as constraints in our optimization framework. We apply this discrete mechanical approach to holonomic systems with symmetries and, as a result, geometric structure and motion invariants are preserved. We illustrate our method by computing optimal trajectories for a simple model of an air vehicle flying through a digital terrain elevation map, and point out some of the numerical benefits that ensue

A Simple Cellular Automation that Solves the Density and Ordering Problems

Cellular automata (CA) are discrete, dynamical systems that perform computations in a distributed fashion on a spatially extended grid. The dynamical behavior of a CA may give rise to emergent computation, referring to the appearance of global information processing capabilities that are not explicitly represented in the system's elementary components nor in their local interconnections.1 As such, CAs o?er an austere yet versatile model for studying natural phenomena, as well as a powerful paradigm for attaining ?ne-grained, massively parallel computation. An example of such emergent computation is to use a CA to determine the global density of bits in an initial state con?guration. This problem, known as density classi?cation, has been studied quite intensively over the past few years. In this short communication we describe two previous versions of the problem along with their CA solutions, and then go on to show that there exists yet a third version | which admits a simple solution

The nanoscale phase separation in hole-doped manganites

A macroscopic phase separation, in which ferromagnetic clusters are observed in an insulating matrix, is sometimes observed, and believed to be essential to the colossal magnetoresistive (CMR) properties of manganese oxides. The application of a magnetic field may indeed trigger large magnetoresistance effects due to the percolation between clusters allowing the movement of the charge carriers. However, this macroscopic phase separation is mainly related to extrinsic defects or impurities, which hinder the long-ranged charge-orbital order of the system. We show in the present article that rather than the macroscopic phase separation, an homogeneous short-ranged charge-orbital order accompanied by a spin glass state occurs, as an intrinsic result of the uniformity of the random potential perturbation induced by the solid solution of the cations on the $A$-sites of the structure of these materials. Hence the phase separation does occur, but in a more subtle and interesting nanoscopic form, here referred as ``homogeneous''. Remarkably, this ``nanoscale phase separation'' alone is able to bring forth the colossal magnetoresistance in the perovskite manganites, and is potentially relevant to a wide variety of other magnetic and/or electrical properties of manganites, as well as many other transition metal oxides, in bulk or thin film form as we exemplify throughout the article.Comment: jpsj2 TeX style (J. Phys. Soc. Jpn); 18 pages, 7 figure