1210.1503 (K. Berkane et al.)

Gradient expansion of the Bloch propagator for position dependent
effective mass hamiltonians in dimensions d=1,2,3,4    [PDF]

K. Berkane, K. Bencheikh

We derive the gradient expansion for the diagonal elements of the Bloch propagator up to order $\hbar^2$. We consider hamiltonians with position dependent effective mass and slowly varying local potential in spatial dimensions d=1,2,3,4. In our approach, we use the semiclassical $\hbar$ expansion of the density matrix in [Phys. Rev. A72, 022508 (2005)] with the help of Laplace transform to derive such gradient expansion in the one-body potential and also in the effective mass distribution.

View original: http://arxiv.org/abs/1210.1503