- back to listing
Past Events
Public Seminar of PhD Candidate:
Fast Algorithms for Large Scale Quantum Transport Simulations with Application
| Speaker: | Mr. King Tai CHEUNG |
| Affiliation: | The University of Hong Kong |
| Date: | December 4, 2017 (Monday) |
| Time: | 2:30 p.m. |
| Venue: | Rm 518, 5/F, Chong Yuet Ming Physics Building, HKU |
Abstract
Time is limited. While sophisticated quantum formalism like non-equilibrium Green's function (NEGF) exists for solving complicated quantum transport problems, it is useful only if we can calculate it within a reasonable time scale. This is indeed the problem for many systems covered in the physical length scale that is small enough to crave for quantum description but not large enough to be described solely by the classical one. In general, computational complexity grows with time T, system size N=NxNyNz, basis Nb and k-points Nk, while a simple matrix inversion would require O(T Nk NbN3) so that required computational cost is easily beyond reach.
In this talk, fast algorithms for large scale quantum transport simulations are purposed. Here, the scale refers to two cases, temporal and spatial length scale. In the first part, fast algorithms for larger temporal scale simulation are purposed based on the NEGF-CAP method for transient current calculation which is suitable to combine with the first principles density functional theory (DFT) calculation. That is made possible with the four key ingredients 1) exact solution based on NEGF that goes beyond wide band limit, 2) complex absorbing potential, 3) possibility of the separation of space and time domains and 4) the fast multipole method. The construction and benchmarking of the algorithm which is O(1) with respect to time T will be discussed and applied leading to the discovery of all-electrical generated spin polarized current.
In the second part, fast and memory efficient algorithms for large spatial scale quantum transport simulation called Hierarchical self-energization (HSE) that based on nested dissection methods will be discussed. The computation is first reduced by mean of hierarchical divide and conquer technique for two-dimensional (2D) and the three-dimensional (3D) case and done under the Nautilus-shell-growth model. Finally, I will give a summary and discuss the perspective of the developed algorithms.
Anyone interested is welcome to attend.