Quantum Zeno Features of Bistable Perception

A generalized quantum theoretical framework, not restricted to the validity domain of standard quantum physics, is used to model the dynamics of the bistable perception of ambiguous visual stimuli. The central idea is to treat the perception process in terms of the evolution of an unstable two-state quantum system, yielding a quantum Zeno type of effect. A quantitative relation between the involved time scales is theoretically derived. This relation is found to be satisfied by empirically obtained cognitive time scales relevant for bistable perception.Comment: 19 pages, 1 figur

Dimension Theory of Graphs and Networks

Starting from the working hypothesis that both physics and the corresponding mathematics have to be described by means of discrete concepts on the Planck-scale, one of the many problems one has to face in this enterprise is to find the discrete protoforms of the building blocks of continuum physics and mathematics. A core concept is the notion of dimension. In the following we develop such a notion for irregular structures like (large) graphs and networks and derive a number of its properties. Among other things we show its stability under a wide class of perturbations which is important if one has 'dimensional phase transitions' in mind. Furthermore we systematically construct graphs with almost arbitrary 'fractal dimension' which may be of some use in the context of 'dimensional renormalization' or statistical mechanics on irregular sets.Comment: 20 pages, 7 figures, LaTex2e, uses amsmath, amsfonts, amssymb, latexsym, epsfi

A methodological call for a quantum econophysics

Econophysics is an emerging field dealing with complex systems. A deeper analysis of themes studied by econophysicists shows that research conducted in this field can be decomposed into two different computational techniques: statistical econophysics and agent-based econophysics. Both perspectives import the classical idea of randomness coming from statistical physics. This methodological paper calls for the development of a more quantum-oriented econophysics which could complete the approach provided by classical econophysics by enlarging our way of thinking randomness and, therefore, economic uncertainty