Diffusion induced by grain boundaries: a SHE model
Naoufel Ben Abdallah, Hédia Chaker · Communications in Mathematical Sciences · 2004
Classical motion of electrons in a two dimensional superlattice is considered.The lattice unit cell is a square with a small side.When electrons hit a cell side, they are reflected with a probability R and transmitted with probability T .A diffusion approximation of the model is performed and leads to a diffusion equation in position-energy variables ( SHE model).The diffusion constant can be expressed explicitly in terms of reflection-transmission coefficients.The mathematical problem is a two dimensional version of a previous work in the one dimensional case [ N.