Based on Robertson's formalism, a microscopic theory of the equations of motion for dilute magnetic alloys is derived in the relaxation process. Within the s-d model, the integral with memory kernel is calculated to the second order of the interaction.

The constitutive quantities in Mori's theory, the residual forces, are expanded in terms of time-dependent correlation functions and products of operators at t = 0, where it is assumed that the time derivatives of the observables are given by products of them. As a first consequence the...

It is pointed out that the Schwinger variational principle of scattering theory directly applies to the case of dynamic susceptibilities in statistical mechanics. The relation to other dynamic approximation schemes is discussed.

A response theory in quantum systems, which can discuss the stability of the total system and the appearance of subharmonics, is proposed. The propagator of the system in the Liouville space is decomposed into the periodic factor with the same frequency as the external field and the remaining...

Combined first and second order dynamic susceptibilities for a set of observables are expressed by a matrix resolvent operator in Liouville-space. A well-defined triangular projector is introduced to rewrite second order susceptibilities in terms of frequencies and memory functions. For these a...

A previously given formalism for the steady state statistical operator ϱη (t) is illustrated for the case of a periodically driven oscillator coupled to a bath of oscillators. The application to several types of observables is investigated. Explicit evaluation shows that ϱη (t) gives the...

We use FLUENT to calculate the wind profile over barchans and transverse dunes. The form of the streamlines of flow separation at the lee side of the dunes is determined for a symmetric barchan dune in three dimensions, and for the height profile of a measured transverse dune field in the...

The motion of dunes and their morphology is a fascinating, largely unexplored subject. Already the barchan, the simplest moving dune, poses many questions. We will present some results of field measurements on desert and costal dunes. Then we will present a model which consists of three coupled...