Generalized finite differences

Quantum mechanics

Double slit experiment with Schrödinger equation

This double slit experiment was our first numerical experiment in quantum mechanics. The following figures illustrate particle probability density. For details, look at our short presentation.

Fig: Cross section of probability density at z=0. Particle approaches from left and collides wall in the middle. Part of the wave function passes through holes in the wall.

Fig: Cross section of probability density at x=1. This denotes interference pattern on the back wall.

Vortex splitting in Bose-Einstein condensates

To test our simulation scheme, we follow an article and reproduce its numerical simulations. For details, see our presentation and article:

Kuopanportti, P. & Möttönen, M. (2010). Splitting dynamics of giant vortices in dilute Bose-Einstein condensates. Physical Review A. 81(3) 033627.

Fig: Evolution of a 10-quantum vortex state.

Fig: Evolution of a 30-quantum vortex state.

We have studied the vortex splitting using 3-dimensional simulations. Now, we know the limitations of 2-dimensional models.

Following animations illustrate the evolution of two-, three-, and four-quantum vortices in cigar-shaped condensates.

cloudCigar2_5000.avi

cloudCigar3_5000.avi

cloudCigar5_5000.avi

You can find more details of our vortex splitting simulations in the following research article:

Räbinä, J., Kuopanportti, P., Kivoja, M., Möttönen, M., & Rossi, T. (2018). Three-dimensional splitting dynamics of giant vortices in Bose-Einstein condensates. Physical Review A 98 023624.

More details of simulations and a report of an early stage studies can be found here (in Finnish only).