Why Use Homogeneous Dispersion for Group Velocity in Inhomogeneous Lattice?

[Niles]

Hi

The group velocity of an electron wavepacket in a homogeneous lattice is

v_group(k) = ∇_kE_k,

where E_k is the dispersion. I have just read an article, where they use this to find the group velocity of a wavepacket in an inhomogeneous lattice, but they use the homogeneous dispersion. I don't quite understand why this is allowed. Can you clarify this?


Niles.

 

[stephenhky]

would u clarify what you mean by homogeneous dispersion? what is an inhomogeneous lattice?

 

[Niles]

I mean homogeneous when there is no impurity. Likewise I mean inhomogeneous when there is an impurity.

 

[stephenhky]

icic... I am not sure if I understand your question. But your given formula is actually the definition of the group velocity, and it applies to any dispersion relation. This group velocity means the velocity of the overall shape of the wave and it doesn't matter what your system is.

I guess what matters, probably in your problem, is how different it would be when you calculate it in homogeneous and inhomogeneous system.