Theory of Non-Equilibrium Stationary States as a Theory of Resonances

We study a small quantum system (e.g., a simplified model for an atom or molecule) interacting with two bosonic or fermionic reservoirs (say, photon or phonon fields). We show that the combined system has a family of stationary states parametrized by two numbers, T ₁ and T ₂ (‘reservoir temperatures’). If T ₁ ≠ T ₂, then these states are non-equilibrium stationary states (NESS). In the latter case we show that they have nonvanishing heat fluxes and positive entropy production and are dynamically asymptotically stable. The latter means that the evolution with an initial condition, normal with respect to any state where the reservoirs are in equilibria at temperatures T ₁ and T ₂, converges to the corresponding NESS. Our results are valid for the temperatures satisfying the bound min (T ₁,T ₂) > g ^{2 + α}, where g is the coupling constant and 0 < α < 1 is a power related to the infra-red behaviour of the coupling functions. Submitted: March 20, 2006. Revised: March 19, 2007. Accepted: May 11, 2007. Marco Merkli: Partly supported by an NSERC PDF, the Institute of Theoretical Physics of ETH Zürich, Switzerland, the Departments of Mathematics of McGill University and the University of Toronto, Canada. Matthias Mück: Supported by DAAD under grant HSP III. Israel Michael Sigal: Supported by NSERC under grant NA7901.     

Intermixing during epitaxial growth and Mössbauer spectroscopy with probe layers

Mössbauer spectroscopy with ⁵⁷Fe (¹¹⁹Sn) probe layers is a useful method to study the local magnetic structures at buried interfaces. However interface alloying, which always exists in the real samples, have to be taken into account for accurate interpretation of experimental data. We developed an algorithm, which describes the interface intermixing in the multilayers. Substituting deposited atoms by atoms of substrate and floating of deposited atoms in the upper layers during epitaxial growth leads to the formation of asymmetric chemical and magnetic interfaces. This asymmetry in the M₁/M₂ superlattices can explain the difference between magnetic responses from M₁ on M₂ and M₂ on M₁ interfaces which were observed in experiments. Applying this intermixing model to the systems with probe layers located at different distances from the interfaces gives the natural explanation of hyperfine fields distributions on probe atoms and helps us clarify some discrepancies reported in the literature.     

Characteristics of soft magnetic composite material under rotating magnetic fluxes

This paper reports the measurement of magnetic properties of the soft magnetic composite material SOMALOY^TM 500 in a square sample under different patterns of flux density with 2D magnetic excitations. The test system, principle of measurement, magnetic power loss calculation, and methods of correction for misalignment of H surface sensing coils are presented. The experimental results show that although nominally isotropic, the SOMALOY^TM 500 sample exhibits some anisotropy. The results are useful in the design and performance analysis of rotating electrical machines.     

Intercalated smectic-A structures in a new class of laterally branched substances

X-ray, DSC and optical studies of a new class of substances with aromatic rings in the lateral branches are reported. The thermal behaviour of the substances is discussed. The X-ray measurements lead to a structural model of the SA phases consisting of layer structures with intercalating molecules.     

The first <Emphasis Type="Italic">L</Emphasis><Superscript><Emphasis Type="Italic">p</Emphasis></Superscript>-cohomology of some groups with one end

Let p be a real number greater than one. In this paper we study the vanishing and nonvanishing of the first L ^p -cohomology space of some groups that have one end. We also make a connection between the first L ^p -cohomolgy space and the Floyd boundary of the Cayley graph of a group. We apply the result about Floyd boundaries to show that there exists a real number p such that the first L ^p -cohomology space of a nonelementary hyperbolic group does not vanish. Received: 4 August 2006 Revised: 2 November 2006     

Time Asymptotic Behaviour for a One-Velocity Transport Operator with Maxwell Boundary Condition

This paper is concerned with the spectral analysis of a one-velocity transport operator with Maxwell boundary condition in L ₁-space. After a detailed spectral analysis it is shown that the associated Cauchy problem is governed by a C ₀-semigroup. Next, we discuss the irreducibility of the transport semigroup. In particular, we show that the transport semigroup is irreducible. Finally, a spectral decomposition of the solutions into an asymptotic term and a transient one which will be estimated for smooth initial data is given.     

Raman spectroscopy of carbon fibres

Investigations of coated carbon fibres are reported using Raman spectroscopy. Relationships between different process parameters (for example precursor concentration, reactor temperature and various precursors) and the resulting types of carbon fibres are discussed.     

Comparison of four quantification methods for the determination of PCB in transformer oils

The analysis of PCB in transformer oils has been achieved with three HRGC/ECD based methods, proposed by the International Electrotechnical Commission (IEC/TC 10), by the Comité Européen de Normalisation (CEN/TC 19/WG 22) and by the Deutsches Institut für Normung (DIN 51 527). The same clean-up, described in the CEN/TC 19/WG 22, has been used for all the samples, allowing a comparison of the quantification procedure only. The total chlorine content has also been determined with X-ray fluorescence. These different methods of quantification are compared and their application for legislative purposes is discussed.Dedicated to Professor Dr Dieter Klockow on the occasion of his 60th birthday