Perfect Crystals for U_q(D_4^{(3)})

A perfect crystal of any level is constructed for the Kirillov-Reshetikhin module of $U_q(D_4^{(3)})$ corresponding to the middle vertex of the Dynkin diagram. The actions of Kashiwara operators are given explicitly. It is also shown that this family of perfect crystals is coherent. A uniqueness problem solved in this paper can be applied to other quantum affine algebras.Comment: 27 page

On multigraded generalizations of Kirillov-Reshetikhin modules

We study the category of Z^l-graded modules with finite-dimensional graded pieces for certain Z+^l-graded Lie algebras. We also consider certain Serre subcategories with finitely many isomorphism classes of simple objects. We construct projective resolutions for the simple modules in these categories and compute the Ext groups between simple modules. We show that the projective covers of the simple modules in these Serre subcategories can be regarded as multigraded generalizations of Kirillov-Reshetikhin modules and give a recursive formula for computing their graded characters

Anarchism, Utopianism and Hospitality: The Work of René Schérer

René Schérer (born 1922) is lamentably almost unknown to the Anglo-American world as his work has, as yet, not been translated . He is one of the main specialists of the French “utopian socialist”, Charles Fourier (1772-1837), and a major thinker in his own right. He is the author of more than twenty books and co-editor of the journal Chimères. Colleague and friend at Vincennes university (Paris 8) of Michel Foucault, Gilles Deleuze, Félix Guattari, Jacques Derrida, Jacques Rancière, Jean-François Lyotard, François Châletet, Alain Brossat, Georges Navet, Miguel Abensour, Pierre Macherey… he continues to host seminars at Paris 8 (now located at St. Denis). He is a living testimony to a radical past, and a continuing inspiration to a new generation of young thinkers. This article aims to convey the original specificity of his understanding of anarchism. By so doing, it will stress the importance of his work for any thinking concerned with a politicised resistance to social conformity and the supposed “state of things” today

Thermal conductivity through the nineteenth century

As a material property and as a metaphor, thermal conductivity occupies an important position in physical, biological and geological sciences. Yet, its precise measurement is dependent on using electricity as a proxy because flowing heat cannot directly be measured.Comment: Submitted to Physics Today. 4,500 words, 4 figure

Distribution of roots of random real generalized polynomials

The average density of zeros for monic generalized polynomials, $P_n(z)=\phi(z)+\sum_{k=1}^nc_kf_k(z)$, with real holomorphic $\phi ,f_k$ and real Gaussian coefficients is expressed in terms of correlation functions of the values of the polynomial and its derivative. We obtain compact expressions for both the regular component (generated by the complex roots) and the singular one (real roots) of the average density of roots. The density of the regular component goes to zero in the vicinity of the real axis like $|\hbox{\rm Im}\,z|$. We present the low and high disorder asymptotic behaviors. Then we particularize to the large $n$ limit of the average density of complex roots of monic algebraic polynomials of the form $P_n(z) = z^n +\sum_{k=1}^{n}c_kz^{n-k}$ with real independent, identically distributed Gaussian coefficients having zero mean and dispersion $\delta = \frac 1{\sqrt{n\lambda}}$. The average density tends to a simple, {\em universal} function of $\xi={2n}{\log |z|}$ and $\lambda$ in the domain $\xi\coth \frac{\xi}{2}\ll n|\sin \arg (z)|$ where nearly all the roots are located for large $n$.Comment: 17 pages, Revtex. To appear in J. Stat. Phys. Uuencoded gz-compresed tarfile (.66MB) containing 8 Postscript figures is available by e-mail from [email protected]

On minimal affinizations of representations of quantum groups

In this paper we study minimal affinizations of representations of quantum groups (generalizations of Kirillov-Reshetikhin modules of quantum affine algebras introduced by Chari). We prove that all minimal affinizations in types A, B, G are special in the sense of monomials. Although this property is not satisfied in general, we also prove an analog property for a large class of minimal affinization in types C, D, F. As an application, the Frenkel-Mukhin algorithm works for these modules. For minimal affinizations of type A, B we prove the thin property (the l-weight spaces are of dimension 1) and a conjecture of Nakai-Nakanishi (already known for type A). The proof of the special property is extended uniformly for more general quantum affinizations of quantum Kac-Moody algebras.Comment: 38 pages; references and additional results added. Accepted for publication in Communications in Mathematical Physic

Tomograms and other transforms. A unified view

A general framework is presented which unifies the treatment of wavelet-like, quasidistribution, and tomographic transforms. Explicit formulas relating the three types of transforms are obtained. The case of transforms associated to the symplectic and affine groups is treated in some detail. Special emphasis is given to the properties of the scale-time and scale-frequency tomograms. Tomograms are interpreted as a tool to sample the signal space by a family of curves or as the matrix element of a projector.Comment: 19 pages latex, submitted to J. Phys. A: Math and Ge

Falsification Of The Atmospheric CO2 Greenhouse Effects Within The Frame Of Physics

The atmospheric greenhouse effect, an idea that many authors trace back to the traditional works of Fourier (1824), Tyndall (1861), and Arrhenius (1896), and which is still supported in global climatology, essentially describes a fictitious mechanism, in which a planetary atmosphere acts as a heat pump driven by an environment that is radiatively interacting with but radiatively equilibrated to the atmospheric system. According to the second law of thermodynamics such a planetary machine can never exist. Nevertheless, in almost all texts of global climatology and in a widespread secondary literature it is taken for granted that such mechanism is real and stands on a firm scientific foundation. In this paper the popular conjecture is analyzed and the underlying physical principles are clarified. By showing that (a) there are no common physical laws between the warming phenomenon in glass houses and the fictitious atmospheric greenhouse effects, (b) there are no calculations to determine an average surface temperature of a planet, (c) the frequently mentioned difference of 33 degrees Celsius is a meaningless number calculated wrongly, (d) the formulas of cavity radiation are used inappropriately, (e) the assumption of a radiative balance is unphysical, (f) thermal conductivity and friction must not be set to zero, the atmospheric greenhouse conjecture is falsified.Comment: 115 pages, 32 figures, 13 tables (some typos corrected

Heat conduction and Fourier's law in a class of many particle dispersing billiards

We consider the motion of many confined billiard balls in interaction and discuss their transport and chaotic properties. In spite of the absence of mass transport, due to confinement, energy transport can take place through binary collisions between neighbouring particles. We explore the conditions under which relaxation to local equilibrium occurs on time scales much shorter than that of binary collisions, which characterize the transport of energy, and subsequent relaxation to local thermal equilibrium. Starting from the pseudo-Liouville equation for the time evolution of phase-space distributions, we derive a master equation which governs the energy exchange between the system constituents. We thus obtain analytical results relating the transport coefficient of thermal conductivity to the frequency of collision events and compute these quantities. We also provide estimates of the Lyapunov exponents and Kolmogorov-Sinai entropy under the assumption of scale separation. The validity of our results is confirmed by extensive numerical studies.Comment: fixed figs. 12 & 13. Version to appear in New J. Phy

Statistical Analysis and Molecular Dynamics Simulations of the Thermal Conductivity of Lennard–Jones Solids Including Their Pressure and Temperature Dependencies

© 2020 The Authors. Published by Wiley-VCH GmbH Aspects of the thermal conductivity, λ, of a Lennard–Jones (LJ) solid along an isotherm and the sublimation line are studied using equilibrium molecular dynamics (MD) simulations. A reformulation of the Green–Kubo time correlation function expression for λ in the form of a probability distribution function (PDF) of single trajectory contributions (STC) exhibits the same characteristic statistical trends as found previously for liquids, even at high pressures and low temperatures. The analysis reveals that for short periods of time the thermal conductivity can be negative. This feature is evident along the sublimation line isobar and a low-temperature isotherm going to high densities. Along the isobar and isotherm lines, λ is to a good approximation a power law in temperature and density, respectively. This behavior is used in a more general thermodynamics-based analysis description of the state point dependence of the thermal conductivity. The heat flux autocorrelation function increasingly develops a damped oscillatory appearance as pressure increases or temperature decreases, consistent with the phonon formulation of thermal conductivity.Engineering and Physical Sciences Research Council. Grant Number: EP/N025954/