Band Theory & Holes: Solving Electrical Conductivity Problem

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armandowww
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Can anybody solve me a problem about electrical conductivity in solid state? I think answer should be quite general: how do holes move within a certain band if they experience an external uniform electical field? I found some trouble when I think about current density, group velocity, crystal momentum...
I give you my thanks also if you just help me with any definitions. These ones will work... I hope.
 
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Ops... I must add... Above all, how can I think about a uniform field (in real space), and use dispersion relation on which that field acts in one dimension for example leftward... in k-space!
 
Holes in the valence band behave like electrons in the conduction band but differ by their effective mass tensor and charge. So if you know electron transport you know hole transport.
 
...and the field? It is uniform in real space... how could it be uniform (and have a verse) in k-space? Using a trick like Fourier transorm seems useless!