arXiv subjects
Publications and source records attributed to Arkadiusz Jadczyk.
We propose a mathematical and a conceptual framework (called the `E-model' and the `event ontology' resp.) that encompasses and generalizes the `flash' ontology discussed in a recent paper by R. Tumulka (arXiv:quant-ph/0602208)
Simultaneous measurement of several noncommuting observables is modeled by using semigroups of completely positive maps on an algebra with a non-trivial center. The resulting piecewise-deterministic dynamics leads to chaos and to nonlinear iterated function systems (quantum fractals) on complex projective spaces.
It is shown that piecewise deterministic dissipative quantum dynamics in a vector space with indefinite metric can lead to well defined, positive probabilities. The case of quantum jumps on the Poincar'e disk is studied in details, including results of numerical simulations of quantum fractals. Keywords: iterated function systems, dynamical semigroups, EEQT, indefinite metric, quantum jumps, quantum measurement, non-commuting observables, fractals, Poincare disk
Quantum Iterated Function System on a complex projective space is defined by a family of linear operators on a complex Hilbert space. The operators define both the maps and their probabilities by one algebraic formula. Examples with conformal maps (relativistic boosts) on the Bloch sphere are discussed.
We discuss the problem of a degenerate vierbein in the framework of gauge theories of gravitation (thus including torsion). We discuss two examples: Hanson-Regge gravitational instanton and Einstein-Rose bridge.We argue that a region of space-time with vanishing vierbein but smooth principal connection can be, in principle, detected by scattering experiments.