__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).