215 research outputs found
Stabilization of causally and non-causally coupled map lattices
Two-dimensional coupled map lattices have global stability properties that
depend on the coupling between individual maps and their neighborhood. The
action of the neighborhood on individual maps can be implemented in terms of
"causal" coupling (to spatially distant past states) or "non-causal" coupling
(to spatially distant simultaneous states). In this contribution we show that
globally stable behavior of coupled map lattices is facilitated by causal
coupling, thus indicating a surprising relationship between stability and
causality. The influence of causal versus non-causal coupling for synchronous
and asynchronous updating as a function of coupling strength and for different
neighborhoods is analyzed in detail.Comment: 15 pages, 5 figures, accepted for publication in Physica
Inherent global stabilization of unstable local behavior in coupled map lattices
The behavior of two-dimensional coupled map lattices is studied with respect
to the global stabilization of unstable local fixed points without external
control. It is numerically shown under which circumstances such inherent global
stabilization can be achieved for both synchronous and asynchronous updating.
Two necessary conditions for inherent global stabilization are derived
analytically.Comment: 17 pages, 10 figures, accepted for publication in Int.J.Bif.Chao
Weak Quantum Theory: Complementarity and Entanglement in Physics and Beyond
The concepts of complementarity and entanglement are considered with respect
to their significance in and beyond physics. A formally generalized, weak
version of quantum theory, more general than ordinary quantum theory of
material systems, is outlined and tentatively applied to some examples.Comment: Revised version. Chapter 5.2 (old counting) omitted for separate
publication, chapter 5.2 (new counting) reformulate
Generalized Quantum Theory: Overview and Latest Developments
The main formal structures of Generalized Quantum Theory are summarized.
Recent progress has sharpened some of the concepts, in particular the notion of
an observable, the action of an observable on states (putting more emphasis on
the role of proposition observables), and the concept of generalized
entanglement. Furthermore, the active role of the observer in the structure of
observables and the partitioning of systems is emphasized.Comment: 14 pages, update in reference
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
Stability analysis of coupled map lattices at locally unstable fixed points
Numerical simulations of coupled map lattices (CMLs) and other complex model
systems show an enormous phenomenological variety that is difficult to classify
and understand. It is therefore desirable to establish analytical tools for
exploring fundamental features of CMLs, such as their stability properties.
Since CMLs can be considered as graphs, we apply methods of spectral graph
theory to analyze their stability at locally unstable fixed points for
different updating rules, different coupling scenarios, and different types of
neighborhoods. Numerical studies are found to be in excellent agreement with
our theoretical results.Comment: 22 pages, 6 figures, accepted for publication in European Physical
Journal
Sufficient conditions for the anti-Zeno effect
The ideal anti-Zeno effect means that a perpetual observation leads to an
immediate disappearance of the unstable system. We present a straightforward
way to derive sufficient conditions under which such a situation occurs
expressed in terms of the decaying states and spectral properties of the
Hamiltonian. They show, in particular, that the gap between Zeno and anti-Zeno
effects is in fact very narrow.Comment: LatEx2e, 9 pages; a revised text, to appear in J. Phys. A: Math. Ge
Epistemic Entanglement due to Non-Generating Partitions of Classical Dynamical Systems
Quantum entanglement relies on the fact that pure quantum states are
dispersive and often inseparable. Since pure classical states are
dispersion-free they are always separable and cannot be entangled. However,
entanglement is possible for epistemic, dispersive classical states. We show
how such epistemic entanglement arises for epistemic states of classical
dynamical systems based on phase space partitions that are not generating. We
compute epistemically entangled states for two coupled harmonic oscillators.Comment: 13 pages, no figures; International Journal of Theoretical Physics,
201
Complementarity in classical dynamical systems
The concept of complementarity, originally defined for non-commuting
observables of quantum systems with states of non-vanishing dispersion, is
extended to classical dynamical systems with a partitioned phase space.
Interpreting partitions in terms of ensembles of epistemic states (symbols)
with corresponding classical observables, it is shown that such observables are
complementary to each other with respect to particular partitions unless those
partitions are generating. This explains why symbolic descriptions based on an
\emph{ad hoc} partition of an underlying phase space description should
generally be expected to be incompatible. Related approaches with different
background and different objectives are discussed.Comment: 18 pages, no figure
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