Some Generic Aspects of Bosonic Excitations in Disordered Systems

We consider noninteracting bosonic excitations in disordered systems, emphasizing generic features of quadratic Hamiltonians in the absence of Goldstone modes. We discuss relationships between such Hamiltonians and the symmetry classes established for fermionic systems. We examine the density $\rho (\omega )$ of excitation frequencies $\omega$, showing how the universal behavior $\rho (\omega )\sim {\omega }^4$ for small $\omega$ can be obtained both from general arguments and by detailed calculations for one-dimensional models.

Figure 1

The integrated density of stiffnesses, compared with the theoretically predicted powers, $\beta +1=5/2$ for $E\ll E_p$ and $\beta +1=1/2$ for $E\gg E_p$.