Heide Narnhofer

Dynamical Entropy of C* Algebras and von Neumann Algebras

The definition of the dynamical entropy is extended for automorphism groups ofC* algebras. As an example, the dynamical entropy of the shift of a lattice algebra is studied, and it is shown that in some cases it coincides with the entropy density.

Vlasov hydrodynamics of a quantum mechanical model

We derive the Vlasov hydrodynamics from the microscopic equations of a quantum mechanical model, which simulates that of an assembly of gravitating particles. In addition we show that the local microscopic dynamics of the model corresponds, on a suitable time-scale, to that of an ideal Fermi gas.

QUASIPARTICLES AT FINITE TEMPERATURES

We study the consequences of the KMS-condition on the properties of quasi-particles, assuming their existence. We establish(i)If the correlation functions decay sufficiently, we can create them by quasi-free field operators.(ii)The outgoing and incoming quasi-free fields coincide, there is no scattering.(iii)There are may age-operatorsT conjugate toH. For special forms of the dispersion law ε(k) of the quasi-particles there is aT commuting with the number of quasi-particles and its time-monotonicity describes how the quasi-particles travel to infinity.

A Geometric picture of entanglement and Bell inequalities

We work in the real Hilbert space

Anosov actions on noncommutative algebras

{\mathcal{H}}_{s}

Thermodynamic functions for fermions with gravostatic and electrostatic interactions

of Hermitian Hilbert-Schmidt operators and show that the entanglement witness which shows the maximal violation of a generalized Bell inequality (GBI) is a tangent functional to the convex set

A non-commutative version of the Arnold cat map

S\ensuremath{\subset}{\mathcal{H}}_{s}

Analysis of quantum semigroups with GKS-Lindblad generators: II. General

of separable states. This violation equals the Euclidean distance in

THE STRUCTURES OF STATE SPACE CONCERNING QUANTUM DYNAMICAL SEMIGROUPS

{\mathcal{H}}_{s}

The taming of the dipole ghost

of the entangled state to S and thus entanglement, GBI, and tangent functional are only different aspects of the same geometric picture. This is explicitly illustrated in the example of two spins, where also a comparison with familiar Bell inequalities is presented.