Radiation laws in the vicinity of metallic boundaries

Corrections to Planck's radiation law and to the Stefan Boltzmann law in the vicinity of a dissipative halfspacez<0 are studied. The dissipation is described by a frequency independent conductivity . The halfspacez0 is empty.For a perfectly reflecting wall (=) the proximity corrections of the thermal electric and magnetic energy mutually cancel out. Therefore the space-dependent corrections are only due to the finite conductivity of the wall.The dissipative properties of the system lead to divergencies in the limitz0. In the limitz all corrections vanish. In properly scaledz>0 ranges analytical expressions for the corrections to the radiation laws are calculated.As a by-product the density of states of surface polaritons in the passive medium (z>0) are derived.     

A derivation of the Broadwell equation

We consider a stochastic system of particles in a two dimensional lattice and prove that, under a suitable limit (i.e.N, 0,N²const, whereN is the number of particles and is the mesh of the lattice) the one-particle distribution function converges to a solution of the two-dimensional Broadwell equation for all times for which the solution (of this equation) exists. Propagation of chaos is also proven.Research partially supported by CNR-PS-MMAIT     

A two-dimensional Fokker-Planck equation degenerating on a straight line

By an example of a two-dimensional hydrodynamic system, second-order Langevin equations with two correlated noise sources are investigated. It is shown that the asymptotic expression (t) for the stationary distribution functionP depends on the order in which the limiting transitions;t andN ₂₂0 (N ₂₂ is the power of one of the noises) are made. Using the method of local expansions in trigonometric form, approximate expressions are written for the distribution functionP at small but finiteN ₂₂ tending atN ₂₂0 to the known exact solution.     

Euler–Poincaré Reduction on Principal Bundles

Let : P M be an arbitrary principal G-bundle. We give a full proof of the Euler–Poincaré reduction for a G-invariant Lagrangian L: J ¹ P R as well as the study of the second variation formula, the conservations laws, and study some of their properties.     

Studies on the microstructure of phase transitions in two kinds of liquid crystals by PAT and DSC

The positron lifetime and DSC measerments for EBBA and DOBAMBC have been made with heating and cooling clycles. The experimental results show that a shorter lifetime (₁) is essentially independent of temperature while the longer lifetime (₂) and the intensity (I ₂) change abruptly double or triple with temperature. Consequently, the EBBA has only nematic phases while the DOBAMBC has two liquid-crystalline phases (smectic C* and smectic A) with transition temperatures as follows: for EBBA, solid nematic (304.5 K), nematic isotropic (356.5 K), isotropic nematic (356.5 K), nematic solid (301 K); and for DOBAMBC, solid smectic C* (346 K), smectic C* smectic A (357.5 K), smectic A isotropic (389 K). These critical temperatures are in accordance with the transition temperatures measured by DSC. In addition, the difference in the solid-nematic transition temperature in the heating and cooling cycles was also observed. A discussion about the correlation of the observed changes in lifetime (₂) with the changes in molecular orientational order (S) and dielectric anisotropy () is presented.     

Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models. III. Triangular-Lattice Chromatic Polynomial

We study the chromatic polynomial P _G (q) for m×n triangular-lattice strips of widths m12_P,9_F (with periodic or free transverse boundary conditions, respectively) and arbitrary lengths n (with free longitudinal boundary conditions). The chromatic polynomial gives the zero-temperature limit of the partition function for the q-state Potts antiferromagnet. We compute the transfer matrix for such strips in the Fortuin–Kasteleyn representation and obtain the corresponding accumulation sets of chromatic zeros in the complex q-plane in the limit n. We recompute the limiting curve obtained by Baxter in the thermodynamic limit m,n and find new interesting features with possible physical consequences. Finally, we analyze the isolated limiting points and their relation with the Beraha numbers.     

Phase diagram and scattering intensity of binary amphiphilic systems

A Ginzburg-Landau model with a scalar and a vector order parameter, which describe the concentration and orientation of the amphiphile, respectively, is used to study the phase diagram and the scattering intensity of binary amphiphilic systems. With increasing amphiphile concentration, the calculated phase diagram shows the typical sequence of ordered phases observed experimentally, that is micellar liquid cubic micellar hexagonal lamellar cubic bicontinuous invers hexagonal. The scattering intensity in the homogeneous phase is calculated in the oneloop approximation. In the vicinity of a phase transition to an ordered phase, the intensity is found to show a 1/q behavior for not too small wave vectorsq, followed by a small peak, and a 1/q ² decay for large wave vectors, in agreement with experimental observations in theL ₃-(or sponge-)phase.Dedicated to Prof. H. Wagner on the occasion of his 60th birthday     

Thermodynamics of theSU(N) anderson impurity

The thermodynamic Bethe-ansatz equations of the degenerate Anderson model in theU limit with excluded multiple occupation of the localized level are solved numerically for the casesN=2, 3, 4, and 6. The f-level occupation, the entropy, the spin and charge susceptibilities and the specific heat are obtained as a function of temperature for variousf-level energies.Heisenberg-fellow of the Deutsche Forschungsgemeinschaft     

Uniform Infinite Planar Triangulations

The existence of the weak limit as n of the uniform measure on rooted triangulations of the sphere with n vertices is proved. Some properties of the limit are studied. In particular, the limit is a probability measure on random triangulations of the plane.     

The spherical-model limit in a random field

The spherical-model limitn of then-vector model in a random field, with either a statistically independent distribution or with long-range correlated random fields, is studied to demonstrate the correctness of the replica method in which then and replica limits limits are interchanged, provided the replica and thermodynamic limits are taken in the right order, in the case of long-range correlated random fields. A scaling form for the two-point correlation function relevant to the first-order phase transition below the lower critical dimensionality of the random system is also obtained.     

Multiparticle fractal aggregation

Kinetic fractal aggregation in a particle bath where a fractionf of the sites are initially occupied is studied withd=2 computer simulations. Independent particles diffusing to a fixed cluster produce an aggregate with fractal dimensionD 1.7 up to a correlation length(f). At larger lengthsD2.(f) asf 0. When the particles remain fixed but the cluster undergoes a rigid random walkD appears constant at larger scales but varies withf. D 1.95 at largef andD 1.7 asf 0. In both cases, the aggregate sizeN(t) grows with timet ^(f) . Aggregation on a surface by independently diffusing particles produces shapes reminiscent of electrochemical dendritic growth. The dependence of growth rate and geometry is studied as a function of particle concentration and sticking probability.     

Comparison of (π− d→nn withdσ(π+ d→pp) to test charge symmetry in the Δ-region

First results on ^– d are reported. The measurements were made using 8 specially designed neutron counters, which were carefully calibratedin situ. The differential cross sections atT =142, 180, 217, and 254 MeV were obtained at four angles between 0° and 90°, they are compared to ⁺ d pp data measured at the same energies and angles with the same setup. At every beam energy, the shape of the angular distributions of ^– d nn and ⁺ d pp is the same to ±2%. The absolute cross sections differ by 1 to 10%. The error in this comparison is ±4% implying a small violation of charge symmetry.Dedicated to Prof. I. laus on the occasion of his 60th birthdayDeceased     

A complementary thermodynamic limit for classical Coulomb matter

The canonical equilibrium measure of classical two-component Coulomb matter with regularized interactions is analyzed in a finite volume. It is shown that, in the mean-field regime, the one-particle density is inhomogeneous on a new characteristic length scale _inh. For a system ofN positive andN negative particles, _inh and the characteristic length scale of correlations _corr (=Debye screening length) are related via _inh=(2N)^1/2 _corr. The major conceptual conclusion that is drawn from this is that one needs two nontrivial complementary thermodynamic limits to define the equilibrium thermodynamics of two-component Coulomb systems. One of them is the standard thermodynamic limit (infinite volume), where one takesN, _corr fixed. Its complementary limit is characterized byN, _inh fixed, and is a finite-volume inhomogeneous mean-field limit. The most prominent new feature in the mean-field thermodynamic limit, which is absent in the standard thermodynamic limit, is an anomalous first-order phase transition where the Coulomb system explodes or implodes, respectively. The phase transition is connected with the existence of a metastable plasma phase far below the ionization temperature.     

On a class of exact geodesics of the erez-rosen metric

In a previous paper, a class of exact geodesics for the motion of a particle in a gravitational-monopole-prolate-quadrupole field was investigated, both in Newtonian mechanics and in general relativity. This paper consists of both an amplification of the analysis contained in the previous paper and an extension of the analysis to the case for negative quadrupole moment, which was not treated previously. The relativistic results are based on the monopole-quadrupole metric of Erez and Rosen, the Newtonian results on the monopole-quadrupole potential of Laplace. In the limit of vanishing quadrupole parameter (q 0), the relativistic results reduce to those of the familiar Schwarzschild case; in the weak-field limit (r/m ), the relativistic results reduce to those of the Newtonian case. The existence and stability thresholds in the relativistic case yield values that uniquely characterize the Erez-Rosen metric.     

On the distribution of zeros of a Ruelle zeta-function

We study the limit distribution of zeros of a Ruelle -function for the dynamical systemzz ²+c whenc is real andc–2–0 and apply the results to the correlation functions of this dynamical system.Supported by NSF grant DMS-9101798     

The induced action ofW 3 gravity

We obtain the induced action [h, b] for chiralW ₃ gravity in thec± limit from the induced action of a gaugedSl(3,R) Wess-Zumino-Witten model by imposing constraints on the currents of the latter. In the process we find a closed gauge algebra for the gauge sector ofW ₃ gravity in which the currentsT andW become auxiliary fields. An explicit realization ofT andW in terms of the gauge fields is given. In terms of new fieldsr ands, which are a generalization of Polyakov'sf variable for ordinary gravity, the complete induced action [h, b; c±] becomes local.Work supported in part by NSF grant No. PHYS 89-08495Address after September 1, 1991: Physics Department, U.C. Berkeley, Berkeley, CA 94720, USA     

Thermodynamics of a spin 1/2 Anderson impurity in theU→∞ limit

The Bethe-ansatz equations describing the thermodynamics of the non-degenerate Anderson model are derived in theU limit (double occupation of the localized level is excluded). The set of Bethe-ansatz equations for theU limit is considerably different from the one for the finiteU case. The Kondo limit, the Fermi liquid behavior at lowT and the highT perturbation expansion for the thermodynamic potential are extracted from these equations.Heisenberg-fellow of the Deutsche Forschungsgemeinschaft     

The quasi-classical limit of quantum scattering theory

We study the quasi-classical limit of the quantum mechanical scattering operator for non-relativistic simple scattering system. The connection between the quantum mechanical and classical mechanical scattering theories is obtained by considering the asymptotic behavior as 0 of the quantum mechanical scattering operator on the state exp(—ip·a/)f(p) in the momentum representation.Partially supported by Fûjû-kai Foundation and Sakkô-kai Foundation     

Thermodynamic behaviour of a collective atomic system driven by a classical field

Exact analytical expressions for the expectation values of collective atomic polarization and population-inversion operators in the thermodynamic limit (N) are derived for a model describing a collection of N identical two-level atoms driven by an external field.