Scaling the energy and width of small-particle systems in 2D

Univerzalnost povezuje fenomene među raznim područjima fizike i omogućuje razaznavanje svojstava u teško dostupnom području proučavanjem nekih lakših problema. Tako je Efimov efekt u nuklearnoj fizici otvorio raspravu o univerzalnosti osnovnog halo stanja, tj. vezanog sustava koji preferira biti u klasično zabranjenom području. Temeljita analiza napravljena je u lakše dostupnom području - atomskoj fizici, gdje su proučavani slabo vezani atomski dimeri, trimeri i tetrameri. Pokazano je da se univerzalno skaliranje širine i energije proteže čak i ispod halo-područja. U ovom je radu preispitana univerzalnost skaliranja energije i širine dimera i trimera u 2D prostoru, a koji interagiraju Lennard-Jonesovim 12-6 potencijalom. Schrödingerova jednadžba riješena je koristeći Numerov algoritam i varijacijski Monte Carlo.Universality connects phenomena in various fields of physics and enables to discern properties in a hardly accessible field by studying some easier model problems. This way the search of the Efimov effect in nuclear physics opened discussions about the ground-state universality of few-body halo states, i.e., of few-body systems which prefer to be in classically forbidden regions of space. A thorough analysis have been done in an easily accessible field – atomic physics, where weakly-bound atomic dimers, trimers and tetramers were studied. It was shown that universal size-energy scaling extends even below the halo area. In this work energy-size scaling is examined for few-body systems in 2D, interacting with Lennard-Jones 12-6 potential. Schrödinger equation is solved using Numerov’s method and variational Monte Carlo