Some generic aspects of bosonic excitations in disordered systems

TL;DR

This paper explores the universal behavior of bosonic excitations in disordered systems, revealing a common  frequency dependence and connecting quadratic Hamiltonians to fermionic symmetry classes.

Contribution

It demonstrates the universal  behavior of the density of states for bosonic excitations and relates these Hamiltonians to fermionic symmetry classifications.

Findings

Density of states  at low frequencies.

Universal behavior derived from general principles and 1D models.

Connection between bosonic Hamiltonians and fermionic symmetry classes.

Abstract

We consider non-interacting bosonic excitations in disordered systems, emphasising 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) ~ \omega^4 for small \omega can be obtained both from general arguments and by detailed calculations for one-dimensional models.