# Honours/MPT/311/PhD projects

### Energy, momentum, and angular momentum transfer in electron systems

This project aims to derive an exact formula for the transmission of angular momentum in topological materials
(such as the Haldane model). The students are expected to have a good knowledge of quantum mechanics,
statistical mechanics, and electrodynamics. Earlier, a formula has been derived in a paper by
Y.-M. Zhang and J.-S. Wang, "Far-field heat and angular momentum radiation of the Haldane model,"
J. Phys.:Condens. Matter 33, 055301 (2021). However, the result presented there is an approximate one.
This project aims to correct the result represented there using the nonequilibrium Greenâ€™s function method.
The exact results for energy and force from a 2D surface have already been worked out by this supervisor.
This is a good starting point, and the students are expected to repeat this derivation; after this,
we hope a new result for the angular momentum transfer to the far field can be worked out. The technique
needed for this work can be obtained by studying our recent review from J.-S. Wang, J. Peng, Z.-Q. Zhang,
Y.-M. Zhang, and T. Zhu, "Transport in electron-photon systems," Frontiers of Physics, {18}, 43602 (2023).
If possible, we also perform some numerical calculations. I hope this is an interesting but also challenging
project for the students.
A related topic is the computation of Casimir forces in equilibrium and non-equilibrium situations, which can
be tailored for Honours/MPT students.

For more information, contact Prof. Wang Jian-Sheng, phywjs@nus.edu.sg.