TASK Quarterly

Neural approach for rhyming word recommendations

Natalia Kosakowska — 2025-04-07

The research paper deals with the problem of rhyme generation. The project concerns words in the Polish language. Two methods have been proposed to determine whether two words rhyme. A proprietary algorithm was created and three types of neural networks were trained. The efficiency, the way each of the discussed methods works, was compared.

Systems of free particles and harmonic oscillators in rotationally-invariant noncommutative phase space

V. M. Tkachuk — 2025-04-07

In this paper, we introduce a rotationally-invariant noncommutative algebra that is equivalent to the canonical type. This algebra is built by extending the noncommutativity parameters to tensors. These tensors are defined with the help of additional coordinates and momenta corresponding to a rotationally-invariant system. In the frame of the rotationally-invariant noncommutative algebra we investigate a system of free particles, and systems of harmonic oscillators. The energy levels of these systems are found in noncommutative phase spave with preserved rotational symmetry.

Real time quantum tunneling through a double square barrier

George J. Papadopoulos — 2025-04-07

The propagator of a one-dimensional double square barrier is obtained analytically in terms of the relevant eigenfunctions. With the aid of the propagator the wavefunction evolution for a particle, initially in a state of wave packet, located on the left-hand side of the barrier, with ignorable overlap with the barrier, is obtained. There follows study of the probability and current densities stemming from the particle initial state. In particular, the space distributions at given times of the above densities are given. Furthermore, their evolution in time at the entrance and exit of the barrier is obtained. The numerical results show repeated reversal in the current density at the barrier entrance, while being unidirectional at the exit. However, the probability of entering the barrier over an extremely long time tends to equal the corresponding probability of exiting the barrier. Owing to the fact that the wave packet expands on both of its sides, as time goes by, it is possible to have transmission even if the particle’s initial momentum points away from the barrier. The effect, in question, becomes evident in diagrams for the transmitted probability beyond the barrier exit in terms of the particle initial momentum, over a region.