Title: Quantum Turbulence (QT)
Date: 2019-01-01 9:00
Category: Research
Slug: qthpc
Tags: bec,qt,gallery
Related_posts: qtbec
prev_article: qtbec
Summary: Quantum turbulence (QT) arises in superfluid systems (superfluid helium, Bose-Einstein condensates e.g.). We aim at developing new mathematical and numerical tools to investigate this phenomenon, at very low (but positive) temperature.
# Context
This topic is part of the new ANR project [QUTE-HPC](http://qute-hpc.math.cnrs.fr/). Using the home made software GPS (Gross Pitaevskii Simulator), we start simulating simple configurations for QT. This requires the implementation of suitable boundary conditions and diagnostics to study energy spectra.
> QT is modeled using the time-dependent Gross-Pitaevskii equation (in dimension less form): $$\begin{array}{rcl}
-i\partial_t \psi &=& \frac12\Delta\psi - V(x)\psi - \beta |\psi|^2\psi \\\\\\
\psi_{|t=0} &=& \psi_0. \end{array}$$
Different choices for $\psi_0$ are investigated to study the mechanisms of QT. A first choice is $\psi_0=e^{i\theta}$ where $\theta$ is a (smoothed) random phase field. A second choice is to introduce vortex rings pairs in a constant initial state. The last one is adapted from $`cite?`$
# Tools
We use our home made software GPS:
- written in Fortran,
- hybrid MPI/OpenMP code,
- spatial discretization: spectral or high order compact finite differences scheme,
- 2nd order time-splitting scheme.
# Results
![Final State]({attach}/images/VR_vortices_final.png)
*Final state for quantum turbulence: initial state contains 100 pairs of vortex rings. Click [here]({attach}/images/QT_ICVR_gnu.mpg) to see the time evolution of the vortices.*
![Kinetic Energy]({attach}/images/qt/VR_Ekin.png)
![Initial State]({attach}/images/qt/VR_Init.png)
![Final State]({attach}/images/qt/VR_Final.png)