[en] An order-of-magnitude elaboration and a more mathematical derivation results both in an entropy of 10⁷⁶ for a black hole of the mass of the sun. (G.Q.)

[en] After a brief survey of Hamiltonian theory and of relevant notions of set theory and manifolds, these lecture notes present some general properties of orbits, paying special attention to integrable systems. This is followed by a discussion of the Kolmogorov-Arnol'd-Moser theorem, dealing with the stability of orbits under small perturbations, and its importance for ergodic theory. Ergodicity and mixing are then treated in detail. In particular, the ergodic theorem of von Neumann is derived, and a specific example is given of a (strongly) mixing system. (author)

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[en] We generalize the classical notion of a K-system to a non-commutative dynamical system by requiring that an invariantly defined memory loss be 100%. We give some examples of quantum K-systems and show that they cannot contain any quasi-periodic subsystem. 13 refs. (Author)

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[en] Some thoughts are given to the antropic principle and its traces in physics. (Author)

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[en] Basing on quantum mechanics and the simple Hamiltonian consisting of kinetic energy and Coulomb potential, heuristic arguments and estimates are used to guess the essential stability properties of many-particle systems. In view of applications in astrophysics, gravitation as a second potential and thermodynamic arguments are added. The guesses thus obtained are confronted with known exact results. The connection between the stabilities against explosion and against implosion, and thermodynamic stability is considered. In systems with a particle number larger than approx= 10⁵⁴ (corresponding to the Jupiter mass) gravitational energy prevails over the electrostatic energy and determines the history of a star. Negative specific heat accompanies life and death of a star. Finally the role of stability and instability in the universe for life is outlined. (G.Q.)

[en] We exhibit a class of quantum field theories where particles interact with pair potentials and for which the time evolution exists in the Heisenberg representation. The essential condition for existence is the stability in the thermodynamic sense and this is achieved by having the interaction fall off with the relative momenta of the particles. This can be done in a Galilei-invariant manner. We show that these systems have some mixing behaviour which one postulates in ergodic theory but difficult to prove for classical systems. (Authors) 59 refs

[en] Andre Martin is the master of the Schroedinger equation. Where others may do with cheap approximations he would not buy anything but a conclusive result proved by hard analysis. In recent years he applied his skill to meson spectroscopy where one deals with confining potentials. As a birthday present we will offer him a charged medium which gives such a potential purely in the framework of electrodynamics. We realize that this is just a toy and not the mechanism realized in nature. There it is supposed to emerge from QCD where also nonlinear and quantum effects are important. But our model may provide a formal basis to the heuristic discussions one finds in textbooks [1,2]. 6 refs. (Author)