Andrzej Posiewnik

On some definition of physical state

We propose to describe physical systems (quantum or classical) with the aid of structures called information systems. We argue that in each theoretical description of the phenomenology of the preparation process one can identify the set of all (pure) states of a physical system with the set of (total) elements of some information system. Next we give some consequences of the above arguments.

Category Theoretical Construction of the Figure of States

We put Mielniks construction of the convex set of all states of a physical system in the general frame of category theory and give topological details lacking in previous papers on the subject.

How To Play Two-Player Restricted Quantum Games with 10 Cards

Abstract We show that it is possible to play ‘restricted’ two-player quantum games proposed originally by Marinatto and Weber (Phys. Lett. A 272:291–303, 2000) by purely macroscopic means, in the simplest case having as the only equipment a pack of 10 cards. Our example shows also that some apparently ‘genuine quantum’ results, even those that emerge as a consequence of dealing with entangled states, can be obtained by suitable application of Kolmogorovian probability calculus and secondary-school mathematics, without application of the ‘Hilbert space machinery’.

Beauty of financial time series

AIP qualitative method of discrimination of a dynamical system among stochastic noise, deterministic noise or deterministic function is applied to three stock market indices to identify similarities and discrepancies between developed and emergent markets when some expectations for extraordinary profits are present.

Dynamical Transformations and Information Systems

A description is given of dynamical transformations in the language of the theory of information systems. The dynamical transformations (morphisms) and sets of states (objects) form a Cartesian closed category, thus retaining the crucial consistency between structures and dynamics.

Interference in the double-slit experiment with only one slit open at a time

Abstract Analysis of an interference experiment employing single-photon states and a Mach-Zehnder interferometer with a shutter in each arm is given. The shutters operate in such a way that when one of them is open, the other one is closed and vice versa. Nevertheless, under special circumstances interference is possible.

Computability of physical operations

It is shown (for a very simplified model) that a number-theoretic function representing an experimental physical setup is general recursive.

Hilbert space representation of time evolution of pure states

Under a reasonable assumption it is shown that the set TotA of pure states of a physical system provided with the Scott information topology is homeomorphic to a subset of the Cantor discontinuum. Moreover, any “smooth” nonlinear time evolution with the set TotA as the phase space has a linear Hilber space representation.

Physical Experiments and Computation

A description is given of general (preparation-measurement) physical experiments in the language of Scotts mathematical theory of computation.

One property of dynamical semigroups

Abstract We give a proof that the elements of a dynamical semigroup cannot generate s -reflections.