Derivation of the density of states and distribution functions for two-level systems in glasses

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A formalism for calculating the density of states (DOS) function for tunneling systems in amorphous materials is described. Gaussian distribution functions for the asymmetry (..delta..) and the tunneling parameter (lambda) are employed. It is shown that over a broad energy range (E << planck's constant omega/sub 0/) the DOS function is an increasing function of energy proportional to E/sup ..mu../sub eff// with 0.3 less than or equal to ..mu../sub eff/ less than or equal to 0.5.