X iv : 0 90 3 . 53 76 v 1 [ m at h - ph ] 3 1 M ar 2 00 9 Lifshitz tails for the Interband Light Absorption Coefficient W Kirsch

Lifshitz tails for the Interband Light Absorption Coefficient

In this paper we consider the Interband Light Absorption Coefficient for various models. We show that at the lower and upper edges of the spectrum the Lifshitz tails behaviour of the density of states implies similar behaviour for the ILAC at appropriate energies. The Lifshitz tails property is also exhibited at some points corresponding to the internal band edges of the density of states.

ar X iv : 0 90 3 . 23 83 v 1 [ m at h . N T ] 1 3 M ar 2 00 9 WITTEN MULTIPLE ZETA VALUES ATTACHED TO sl ( 4 )

In this paper we shall prove that every Witten multiple zeta value of weight w > 3 attached to sl(4) at nonnegative integer arguments is a finite Q-linear combination of MZVs of weight w and depth three or less, except for the nine irregular cases where the Riemann zeta value ζ(w − 2) and the double zeta values of weight w − 1 and depth < 3 are also needed.

ar X iv : 0 90 3 . 23 83 v 2 [ m at h . N T ] 1 3 M ar 2 00 9 WITTEN MULTIPLE ZETA VALUES ATTACHED TO sl ( 4 )

In this paper we shall prove that every Witten multiple zeta value of weight w > 3 attached to sl(4) at nonnegative integer arguments is a finite Q-linear combination of MZVs of weight w and depth three or less, except for the nine irregular cases where the Riemann zeta value ζ(w − 2) and the double zeta values of weight w − 1 and depth < 3 are also needed.

ar X iv : 0 90 3 . 05 40 v 1 [ he p - ph ] 3 M ar 2 00 9 Methods for the Reduction of Three - Loop QCD Form Factors

Dissertation zur Erlangung der naturwissenschaftlichen Doktorwürde

ar X iv : 0 90 3 . 05 62 v 1 [ as tr o - ph . G A ] 3 M ar 2 00 9 Introduction to Millimeter / Sub - Millimeter