Some generic aspects of bosonic excitations in disordered systems
V. Gurarie, J. T. Chalker
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 ρ(ω) of excitation frequencies ω, showing how the universal behavior ρ(ω) ~ ω4 for small ωcan be obtained both from general arguments and by detailed calculations for one-dimensional models.
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