Tabulating families of functions with symmetries

We propose a general algorithm which aims at optimizing the usage of computer resources fortabulating families of functions possessing known symmetries. The approach is based on the grouptheoretical description of symmetry relations among the functions and their parameters, whereorbits play a crucial role

A review of some scientific papers by Prof. Stanisław Szpikowski

A short review of the most important (arbitrary choice) papers published by Prof. Stanisław Szpikowski (1926-2014) is presented

Projection evolution of quantum states

We discuss the problem of time in quantum mechanics. In the traditional formulation time enters the model as a parameter, not an observable, which follows from the famous Pauli theorem. It is now known, that Pauli's assumptions were too strong and that by removing some of them time can be represented as a quantum observable. In this case, instead of the unitary time evolution, other operators which map the space of initial states into the space of final states at each step of the evolution can be used. This allows to treat time as a quantum observable in a consistent way. We present the projection evolution model and show how the traditional Schroedinger evolution can be obtained from it. We propose the form of the time operator which satisfies the energy-time uncertainty relation. As an example, we discuss the temporal version of the double-slit experiment.Comment: Merged with arxiv:1910.1315

Linux based Live CD on optical disks

We present an introduction to LiveCD system remastering based on a prospective UnionFS filesystem

Quantum gates and projection evolution

A new model of quantum objects time evolution called the projection evolution is analyzed against a possibility of constructing the basic quantumgates following the Nielsen's scheme

Quantum Belinski-Khalatnikov-Lifshitz scenario

We present the quantum model of the asymptotic dynamics underlying the Belinski-Khalatnikov-Lifshitz (BKL) scenario. The symmetry of the physical phase space enables making use of the affine coherent states quantization. Our results show that quantum dynamics is regular in the sense that during quantum evolution the expectation values of all considered observables are finite. The classical singularity of the BKL scenario is replaced by the quantum bounce that presents a unitary evolution of considered gravitational system. Our results suggest that quantum general relativity is free from singularities.Comment: 33 pages, 4 figures, version accepted for publication in European Physical Journal C. arXiv admin note: substantial text overlap with arXiv:1705.0402