Course: Phenomena and Theoretical Methods of Bose-Einstein Condensates

(Full course on BEC in summer 2011 Heidelberg) by Dr. Alexej I. Streltsov

Brief description of the course

Duration : SS2011 semester

When : Each Thursday from 11.15-13.45 (2,5 hours)

Where: CIP-Pools: KIP INF227

When it starts: 12 of May 2011

When if finishes?: End of the Summer Semester

Credit points ( 4 pt)

Working languages: English + Fortran.

Supporting languages: Russian, German, C.

Operation system: Unix

Course format: Lecture (get a knowledge) → PC-pool (apply the knowledge)

Phenomena: Condensation, Fragmentation, Statics and Dynamics in a real space

Theoretical methods: BEC from the perspective of Many-Body physics.

Full Many-Body → Simple Mean-Field → Clever Mean-Field

Brutforce Many-Body → Clever Many-body

 

Vocabulary : BEC, MB, MF, BMF, GP, MCTDHB, TDSE, NLSE, BH, BdG, SIL, ABM, BLAS, LAPACK, MKL, ACML, DVR



Scientific Cycle:

→  ”Real” physical system or process → Our model of it → Governing equation(s) →

→  Numerical solution of  this equation → Analysis of the numbers obtained →

→  Connection to the “original” physical system → Can we do better?

 

Computational experience (mathematical) gained:

Numerical solution of time-(in)dependent  (non-)linear integro-differential equations

DVR

Integrators: SIL (we’ll code it),  ABM ( as an external subroutine)

 

Additional software involved:

blas + lapack→ If we can simplify the life – let us do it.

gnuplot → Data plotting *.ps, *.jpg – cool for a “single figure”, but dynamics means changes in time.

mencoder → How to make a movie out of a collection of the “single figures”.

scripts → Once it was written, push a button and get the results

Some examples:



1) Scattering of an attractive Bose-Einstein condensate from a barrier:
Formation of quantum superposition states Phys. Rev. A 80, 043616 (2009). arXiv:0812.3573





2) Efficient generation and properties of mesoscopic quantum superposition states

in an attractive Bose–Einstein condensate threaded by a potential barrier   J. Phys. B: At. Mol. Opt. Phys. 42 091004 (2009).

Hlf-scattering