In the parabolic case the energy is
In this special case we can choose the observables to be polynomials in .
The moments derived from these observables are denoted by . This set of moments naturally corresponds to the use of a ``shifted'' distribution function (diffusion approximation) as defined in Equation 2.17.
For the non-parabolic case the following set of observables is more appropriate and is used in [GJK+04]:
In the parabolic band case the energy and the velocity set of moments are equivalent descriptions. In this case the quotient between the velocity moments and the energy moments depends on . We have
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