C*-dynamical systems that are asymptotically highly anticommutative

It is shown that with probability 1 on , resp. ongx the irrational rotation algebra with respect to the CAT map and the generalized Price-Powers shiftA _X are asymptotically highly anticommutative.     

Strong asymptotic abelianness for entropicK-systems

We prove that in entropicK-systems of type II₁ the automorphism is strongly asymptotically abelian.Supported in part by Fonds zur Förderung der wissenschaftlichen Forschung in Österreich, Project Nr. P7101-PHY     

The taming of the dipole ghost

A four-dimensional field theory satisfying a fourth-order differential equation is considered. It turns out that the theory has certain advantages regarding applications to gluons: the resolution of the ultraviolet catastrophe, a potential proportional tor and the requirement of colour neutrality. These features seem to make the theory worthy of further study. Some open problems are pointed out.Invited talk at the Symposium on Mathematical Methods in the Theory of Elementary Particles, Liblice castle, Czechoslovakia, June 18–23, 1978.Work supported in part by Fonds zur Förderung der wissenschaftlichen Forschung in Oesterreich, Project No. 3569.We are grateful to P. C.Aichelburg for helpful discussions and to H.Fritsch and W.Kummer for drawing our attention to some references.     

Negative specific heat, the thermodynamic limit, and ergodicity

Thermodynamic stability, in particular, the positivity of the specific heat in the microcanonical ensemble, is not an automatic consequence of the thermodynamic limit. But it holds under special circumstances such as for the most important case of quantum-mechanical Coulomb systems. Therefore, it is surprising that there are experimental indications to the contrary. In this Letter we study a simple model for which the microcanonical specific heat is positive, if the system is ergodic. However, if the system is not ergodic, the energy shell in phase space has some ergodic components with a negative specific heat. This provides another possible general pathway for a negative specific heat in addition to the commonly accepted, the small number of particles.     

The thermodynamic limit for jellium

The thermodynamic limit of the free energy, energy, pressure, and entropy is established for a neutral system of charged particles interacting with a fixed, uniformly charged background (jellium).     

Clustering for algebraicK-systems

We prove that for a von Neumann algebra that is an algebraicK system with respect to some automorphism, the invariant state isK-clustering andr-clustering. Further, we study by using examples how far the von Neumann algebra inherits theK property from the underlyingC ^* algebra.     

Transitivity and ergodicity of quantum systems

We generalize the notion of a topological transitive or a topologically mixing system for quantum mechanical systems in a consistent way. We compare these ergodic properties with the classical results. We deal with some aspects of nearly Abelian systems and investigate some relations between these notions.     

Thomas Fermi limit of Bose-jellium

The thermodynamic limit of charged bosons in a background that contracts according to Thomas-Fermi scaling is considered. The theory reduces to a mean field theory with the mean field determined by a “Thomas-Bose” equation. The Bose condensation of this system shows some special features.     

Local coexistence of different phases

Under intuitively reasonable assumptions it is shown that in two dimensions different phases cannot exist locally. In three dimensions we discuss the possibility of local coexistence of districts with different magnetization for the Heisenberg ferromagnet and show that an interaction that breaks rotational invariance is necessary for this phenomenon.