Izbrane teme sodobne fizike in matematike
Bose-Einsteinov kondenzat hladnih atomov je faza snovi, v kateri večina atomov zasede osnovno enodelčno kvantnomehansko stanje. Članek se ukvarja s simulacijo Bose-Einsteinovih kondenzatov za eksperimentalno pomembne primere. Najprej je opisana metoda laserskega hlajenja atomov, ki v eksperimentu omogoča doseganje Bose-Einsteinovega kondenzata, sledi pregled teoretičnega modela plina hladnih atomov, zatem je nakazana izpeljava enačbe Grossa in Pitaevskega. V drugem delu članka so predstavljene spektralne metode kot učinkovit način za numerično reševanje nelinearne Schrödingerjeve enačbe. Na koncu članek analizira dva konkretna primera nelinearne Schrödingerjeve enačbe v eni dimenziji.
Bose-Einstein condensate is a state of matter of a dilute gas of bosons, where a macroscopic fraction of bosons occupies the lowest quantum state. This article discusses simulation of Bose-Einstein condensates and its relevance to experimental work with Bose-Einstein condensates. It starts with a description of laser cooling which enables condensation in experiments with cold atoms. An overview of the theoretical model for describing cold atom gas is then made and derivation of the Gross-Pitaevski equation briefly summarized. In the second part of the article an efficient algorithm based on spectral methods is presented as an efficient way of numerically solving nonlinear Schrödinger equation. An implementation of the algorithm is then applied to two specific one-dimensional examples and the results are compared to experiments.