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Amorphous solids, and many disordered lattices, exhibit a remarkablequalitative and quantitative universality in their acoustic properties attemperature $\lesssim 3$K. This phenomenon is attributed to the existence oftunneling two level systems (TTLSs), characterized by a homogenous density ofstates (DOS) at energies much lower than the disorder energy ($\approx 0.1$eV).Here we calculate numerically, from first principles, the DOS of KBr:CN glass,the archetypal disordered lattice showing universality. In contrast to thestandard tunneling model, we find that the DOS diminishes abruptly at $\approx3$ K, and that tunneling states differ essentially by their symmetry underinversion. This structure of the TTLSs dictates the low temperature below whichuniversality is observed, and the quantitative universality of the acousticproperties in glasses. Consequences to the properties of glasses atintermediate temperatures, as well as to the microscopic structure of amorphoussolids, are discussed.

Non-homogeneity of the density of states of tunneling two-level systems at low energies