Abstract:
In the frame of the random matrix theory, it was shown, that the relaxation of the projection of the initial plane wave with the wave vector $\mathbf{q}$ is described by the equation of motion with the memory function which corresponds to the complex dynamical Young modulus $E(\omega)$. In the harmonic scalar model of displacements with the absence of energy dissipation, the Ioffe–Regel crossover arises universally in amorphous systems with the dimension $d\ge3$. Vibrations above the Ioffe–Regel crossover are related to the diffusive nature and can be described by the diffusion equation with the damping $\Gamma(\mathbf{q})\propto q^2$.
Keywords:amorphous solids, diffusons, random matrices.
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