20.500.12556/RUL-187898 Simulacija superfluidnega helija s popotnointegralsko molekularno dinamiko Path integral molecular dynamics simulation of superfluid Helium Popotnointegralska molekularna dinamika (PIMD) preslika ravnovesni kvantni večdelčni sistem na klasičen ansambel obročastih polimerov. V magistrskem delu smo uporabili bozonsko različico (PIMD-B) za simulacijo tekočega helija 4 pri nasičenem parnem tlaku v temperaturnem območju $T\in[1,3]\,\mathrm{K}$, ki vključuje superfluidni prehod. Simulirali smo $N=64$ atomov in rezultate primerjali z metodo PIMC ter eksperimentalnimi meritvami. Pokazali smo, da različne opazljivke konvergirajo na zelo različnih časovnih skalah. Izračunane energije kvalitativno sledijo referenčnim rezultatom, parska korelacijska funkcija in statični strukturni faktor pa dobro reproducirata izmerjeno prostorsko strukturo tekočine. Pri superfluidnem prehodu ne opazimo izrazite spremembe prostorske strukture, izrazito pa se povečajo korelacije gibalnih količin. Delež superfluida smo ocenili na dva načina: iz ovojnega števila polimernih poti in iz korelacijske funkcije gostote gibalne količine. Oba pristopa reproducirata splošno temperaturno odvisnost superfluidnega deleža in dajeta vrednosti, primerljive z rezultati PIMC in eksperimentom. Rezultati kažejo, da je mogoče superfluidne lastnosti bozonskih sistemov preučevati tudi z deterministično dinamiko PIMD-B. Path integral molecular dynamics (PIMD) maps an equilibrium quantum many-body problem onto a classical system of ring polymers. In this thesis, we apply its bosonic extension (PIMD-B) to liquid helium-4 at saturated vapour pressure in the temperature range $T\in[1,3]\,\mathrm{K}$, which includes the superfluid transition. We simulate $N=64$ atoms and compare the results with PIMC calculations and experimental measurements. We show that different observables converge on very different time scales. The calculated energies reproduce the qualitative behaviour of the reference data, while the pair correlation function and static structure factor agree well with the measured spatial structure of the liquid. No pronounced change in spatial structure is observed at the superfluid transition, whereas momentum correlations become significantly stronger at low temperatures. We estimate the superfluid fraction in two ways: from the winding number of the polymer paths and from the momentum-density correlation function. Both approaches reproduce the overall temperature dependence of the superfluid fraction and yield values comparable with PIMC and experiment. These results show that superfluid properties of bosonic systems can also be studied using deterministic PIMD-B dynamics. Popotni integral molekularna dinamika bozoni superfluidnost Path integrals molecular dynamics bosons superfluidity true false false Slovenski jezik Angleški jezik Magistrsko delo/naloga 2026-09-16 08:15:48 2026-09-16 08:15:51 2026-09-21 11:14:41 0000-00-00 00:00:00 2026 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 164161 291777795 24469.pdf 24469.pdf 1 C3A440D3D0AEC5B3DDAFC761003724AC 69b2776825d905c32bd3873a11b3946d6155912055f5c5eaacbe17c182eaa420 08128d67-b196-11f1-8bc5-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=247727 Fakulteta za matematiko in fiziko 0 0 0