Transition Specifications for Dynamic Abstract Data Types

Transition specifications extend algebraic specifications by a notion of states and state transitions, introducing a second dynamic layer on abstract data types. This makes possible a reduction of complex specifications by the introduction of an explicit system state, a formal comparison of algebraic specifications and imperative algorithms, and the specification of input/output and other communication features. States are modelled as partial algebras that extend a given algebra by an environment, that is, a partial function that assigns contents to references. State transitions are specified by conditional parallel assignments, analoguous to the conditional existence equations of partial equational specifications. A framework of transition specifications is developed, including initial model semantics, parameterization and general composition mechanisms, and a notion of model correctness. Examples from programming languages show the applicability of the approach.     

London field penetration in heavy fermion superconductors

We present results of a series of high resolution, low fielddc-magnetization measurements on the heavy fermion superconductors UPt₃, UBe₁₃, U_1–x Th _X Be₁₃ and CeCu₂Si₂, from which values of the magnetic penetration depth can be extracted. A study of the temperature variation reveals aT ² power law in all cases. This can not be reconciled with a BCS-like isotropic energy gap but may be explained by the presence of low energy quasiparticle states inside the gap. In the case of very pure superconductors, one such possibility is the assumption of point-nodes in the gap function. We argue, however, that an interpretation in terms of resonant impurity scattering in various anisotropic superconducting states is more likely to explain a broad range of experimental data. The results on differently oriented single crystals of UBe₁₃ and UPt₃ reveal no pronounced anisotropy related to the crystal lattice. Absolute values of atT=0 are deduced by a novel method in which the field is first screened out from the sample by means of an evaporated superconducting film (of lowerT _c ). Above this lowerT _c the sudden penetration of field into the sample can then be measured absolutely.     

Partial disorder in itinerant antiferromagnets—electronic density of states

We examine the behaviour of magnetically disordered, strong correlated electron systems for the case of antiferromagnetic arrangements of the electron-spins. Preceding calculations in earlier papers for homogeneous systems yielded a state, where localized magnetic moments at the atomic sites were built up. The moments showed a partial homogeneous magnetic order in the so called mixed state. In this contribution we realize equivalent conditions for antiferromagnetism: After a coordinate transformation in an approximated Hubbard-Hamiltonian, it is possible to use a CPA-like method for statistical distributions of the vectoral localized moments in the same way as for homogeneous systems. As an example we study at first the quasi-particle density of states for a Lorentz-distribution of the moments.Work supported by the Deutsche Forschungsgemeinschaft     

Numerically stable solution of coupled channel equations: The local reflection matrix

The second order linear Schrödinger equation is transformed to a first order nonlinear differential equation for a quantityp=(iq ^–1 –)/(iq ^–1 +). In a coupled channel problem all quantities occurring in this equation includingq (the WKB wave number) are matrices andp may be calledlocal reflection matrix. This quantity is closely related to the logarithmic derivative of the Schrödinger function but has no singularities in the classically allowed region. In the asymptotic region where the potential is constant the local reflection matrix approaches the physical reflection matrix. In a pure reflection problem (with an infinite potential on one side) this is the fullS-matrix, in a transmission problem (with an activation barrier of finite height) unitarity of theS-matrix can be used to determine most quantities of physical interest fromp. While standard logarithmic derivative methods can become instable for transmission problems the solution with the local reflection matrix is completely stable both for reflection and transmission problem.     

Single-laser light source for CARS microscopy based on soliton self-frequency shift in a microstructured fiber

A femtosecond light source comprising two high-intensity beams at different wavelengths is applied to coherent anti-Stokes Raman scattering microscopy. One wavelength is supplied by a Titanium?:?Sapphire oscillator, while the other is derived from that via soliton-self-frequency shift in a microstructured fiber. Clear CARS images are acquired with the frequency difference adjusted to resonances of polystyrene and lipids.