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FRI: Friday Contributed Sessions

FRI 10: Foundational / Mathematical Aspects – Unconventional Approaches

FRI 10.7: Vortrag

Freitag, 12. September 2025, 12:15–12:30, ZHG103

Two quantum analogies — •Ryszard Wojnar and Andrzej Lissowski — Institute of Fundamental Technological Research PAS

In the first analogy, the diffusion equation with an imaginary coefficient D=ih/2m (it is Schrödinger equation) is considered. The solutions are harmonic functions decaying in time. The disappearance time of wave packet is proportional to m/h: for an electron of the order of seconds, for a mass of 1g of the order of 10^10 years.

The second analogy refers to the hexatic transformation. Hexatic is a phase between 2d liquid and 2d hexagonal crystal. Hexatic phase contains only 5-7 dislocatons aligned in grain boundaries. Quick movement of 5-7 dislocaton is an analogue of quantum wave. The analogue of a quantum particle is the slow local displacement of two grains by one hexagon diameter. The analogue of annihilation of elementary particles is the annihilation of two 5-7 dislocations moving on crystalic axes differing by 60 degrees. Then the third 5-7 dislocation is created moving on third axis. In the presentation we will also discuss the application of hexatic to 2d quantum gravity.

Keywords: quantum - classic analogy; diffusion; wave equation; creation; anihilation