Speaker
Description
Numerically simulating partial differential equations can be a challenging task. Often one requires huge simulation grids to be able to correctly resolve all physical length scales, leading to huge memory and CPU time requirements. Recently, there has been a focus in extending the applications of Tensor Networks (TNs) into simulations of challenging non-linear partial differential equations [1,2,3]. TNs have been widely successful, in the study of quantum many-body physics and strongly correlated systems [4], providing a framework to obtain physically motivated data compression. In this work, we extend the application of TNs to simulate quantum fluids and turbulence through the Gross-Pitaevskii Equation (GPE). We introduce a procedure to implement the split-step Fourier method for time evolution [5], and use this to demonstrate vortex formation in the GPE and dipolar condensates. We show that by encoding our problem in a TN format, one can perform simulations on large spatial grids in 2D and 3D, which would be unfeasible with standard direct numerical simulations.
References
[1] - N.Gourianov et.al, Nat Comput Sci 2, 30–37 (2022), https://doi.org/10.1038/s43588-021-00181-1
[2] - E. Ye and N. F. G. Loureiro, Physical Review E 106,
10.1103, https://link.aps.org/doi/10.1103/PhysRevE.106.035208
[3] - M.Kiffner and D.Jaksch, Preprint, arXiv:2303.03010, https://doi.org/10.48550/arXiv.2303.03010
[4] - U.Schollwoeck, Annals of Physics 326, 96 (2011), https://doi.org/10.1016/j.aop.2010.09.012
[5] - M.D Feit et.al, Journal of Computational Physics,Volume 47, Issue 3 (1982), https://doi.org/10.1016/0021-9991(82)90091-2
Short bio (50 words) or link to website
I am a second year PhD student at the University of Strathclyde, within a quantum many body physics group led by Prof Andrew Daley. Within this group, I am focused on quantum inspired methods and quantum algorithms for solving partial differential equations and strongly correlated systems.
| Career stage | Student |
|---|
