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INTRODUCTION (I'm good at those...)

Studying transport phenomena in solid state physics is a relevant matter which is to be found in most solid-state physics books.Back home,in my third year,i have been taught this chapter by a teacher which followed closely the approach by Kireev in his extraordinary book "Semiconductor's Physics".In that book this simple chapter streches over more than 200 pages,so you can call it a thorough approach.

In the course on "Nonequilibrium Processes" i've been taught that,even until today,a general solution of the Boltzmann equation has not been given.Probably knowing that,Kireev tries to solve this equation perturbatively in a crystal in which is virtually irrelevant who carries energy and electric charge.He searches the sollution in the so-called "relexation time" approximation.He assumes the usual form for the interraction term (that delicious integral with transition amplitudes (the one who probably makes the virtually classical BE semi-classical,meaning it envolves quantum objects,like amplitudes of transition probability...)) and says that the zero-th approximation for the distribution function that he searches is Fermi-Dirac law for fermions (hence holes are to be looked upon as fermions)(sic),and then carries on to find the linear approximation for the distribution function for the free particles in crystal in both electric and magnetic fields acting symultaneously.

POSSIBLY THE QUESTION

This is definitely weird...I mean,the notion of zero-th approximation to an integral/integro-differential equation implies that it satisfies/it's a solution of the damn equation,but with certain restrictions.For exemple,the Maxwell-Boltzmann distribution law is a solution of the Boltzmann integro-differential equation but for time independent virtual statistical ensembles,and in the ugly interraction integral u make the Boltzmann symplifying assumption (that actually closes the equation itself)-the so called "molecular chaos ipothesis".

To resume,in my mind,for everything not to stink,there is only one question(this is the question ):

Is the Fermi-Dirac distribution function a solution of the BE on some (unknown to me) assumptions????

My answer is "no".Then if isn't,it should not be stated as the zero-th approximation of an equation who basically has little to do (or probably nothing) with it.

On the other hand,i'm well aware of the 1926 Sommerfeld model of free electron gas which states that free electrons in a solid obbey FD statistics.So it should be normal that in the absence of any exterior fields the distribution function be the one of FD.But what about (semiclassical) Boltzmann equation and it's devious coonection with FD statistics??

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# Cofused and dizzy

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