Temperature Profiles in Hamiltonian Heat Conduction

We study heat transport in the context of Hamiltonian and related stochastic models with nearest-neighbor coupling, and derive a universal law for the temperature profiles of a large class of such models. This law contains a parameter $\alpha$, and is linear only when $\alpha=1$. The value of $\alpha$ depends on energy-exchange mechanisms, including the range of motion of tracer particles and their times of flight.Comment: Revised text, same results Second revisio

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

Crystal energy functions via the charge in types A and C

The Ram-Yip formula for Macdonald polynomials (at t=0) provides a statistic which we call charge. In types A and C it can be defined on tensor products of Kashiwara-Nakashima single column crystals. In this paper we prove that the charge is equal to the (negative of the) energy function on affine crystals. The algorithm for computing charge is much simpler and can be more efficiently computed than the recursive definition of energy in terms of the combinatorial R-matrix.Comment: 25 pages; 1 figur

Equivariant map superalgebras

Suppose a group $\Gamma$ acts on a scheme $X$ and a Lie superalgebra $\mathfrak{g}$. The corresponding equivariant map superalgebra is the Lie superalgebra of equivariant regular maps from $X$ to $\mathfrak{g}$. We classify the irreducible finite dimensional modules for these superalgebras under the assumptions that the coordinate ring of $X$ is finitely generated, $\Gamma$ is finite abelian and acts freely on the rational points of $X$, and $\mathfrak{g}$ is a basic classical Lie superalgebra (or $\mathfrak{sl}(n,n)$, $n > 0$, if $\Gamma$ is trivial). We show that they are all (tensor products of) generalized evaluation modules and are parameterized by a certain set of equivariant finitely supported maps defined on $X$. Furthermore, in the case that the even part of $\mathfrak{g}$ is semisimple, we show that all such modules are in fact (tensor products of) evaluation modules. On the other hand, if the even part of $\mathfrak{g}$ is not semisimple (more generally, if $\mathfrak{g}$ is of type I), we introduce a natural generalization of Kac modules and show that all irreducible finite dimensional modules are quotients of these. As a special case, our results give the first classification of the irreducible finite dimensional modules for twisted loop superalgebras.Comment: 27 pages. v2: Section numbering changed to match published version. Other minor corrections. v3: Minor corrections (see change log at end of introduction

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

Electronic thermal transport in strongly correlated multilayered nanostructures

The formalism for a linear-response many-body treatment of the electronic contributions to thermal transport is developed for multilayered nanostructures. By properly determining the local heat-current operator, it is possible to show that the Jonson-Mahan theorem for the bulk can be extended to inhomogeneous problems, so the various thermal-transport coefficient integrands are related by powers of frequency (including all effects of vertex corrections when appropriate). We illustrate how to use this formalism by showing how it applies to measurements of the Peltier effect, the Seebeck effect, and the thermal conductance.Comment: 17 pages, 4 figures, submitted to Phys. Rev.

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]

Affine crystal structure on rigged configurations of type D_n^(1)

Extending the work arXiv:math/0508107, we introduce the affine crystal action on rigged configurations which is isomorphic to the Kirillov-Reshetikhin crystal B^{r,s} of type D_n^(1) for any r,s. We also introduce a representation of B^{r,s} (r not equal to n-1,n) in terms of tableaux of rectangular shape r x s, which we coin Kirillov-Reshetikhin tableaux (using a non-trivial analogue of the type A column splitting procedure) to construct a bijection between elements of a tensor product of Kirillov-Reshetikhin crystals and rigged configurations.Comment: 26 pages, 3 figures. (v3) corrections in the proof reading. (v2) 26 pages; examples added; introduction revised; final version. (v1) 24 page

Self-similarity and Reynolds number invariance in Froude modelling

This review aims to improve the reliability of Froude modelling in fluid flows where both the Froude number and Reynolds number are a priori relevant. Two concepts may help to exclude significant Reynolds number scale effects under these conditions: (i) self-similarity and (ii) Reynolds number invariance. Both concepts relate herein to turbulent flows, thereby excluding self-similarity observed in laminar flows and in non-fluid phenomena. These two concepts are illustrated with a wide range of examples: (i) irrotational vortices, wakes, jets and plumes, shear-driven entrainment, high-velocity open channel flows, sediment transport and homogeneous isotropic turbulence and (ii) tidal energy converters, complete mixing in contact tanks and gravity currents. The limitations of self-similarity and Reynolds number invariance are also highlighted. Many fluid phenomena with the limitations under which self-similarity and Reynolds number invariance are observed are summarised in tables, aimed at excluding significant Reynolds number scale effects in physical Froude-based models

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