Tunneling and interaction effects in two-level systems in glasses studied by atomistic simulations

We use molecular dynamics simulations to characterize low-energy two-level systems (TLS) in glasses. We estimate that in silica glass, TLS parameters are broadly distributed in such a way that the tunnel splitting is in the $0.01–1\mathrm{K}$ range. We also observe simultaneous atomic jumps in different TLS below $30\mathrm{K}$ and suggest that this is evidence of strong interaction between TLS below this temperature scale.

Figure 1

(Color online) An example of two-level systems in the MD simulation (a), and jump motion in a single TLS (b). Initial and final configurations are superimposed in (b) to highlight the amplitude of atomic jumps.

Figure 2

Typical trajectories of central atoms in different TLS, showing larger $\sim 0.6–0.8\mathrm{\AA }$ (a) and (b) and smaller $\sim 0.3–0.4\mathrm{\AA }$ (c) jumps. For convenience in comparison, the coordinates of atoms are shifted by constant values. The simulation temperature is $50\mathrm{K}$.

Figure 3

Atomic coordinates of central atoms from three different TLS. For convinience in comparison, the coordinates of atoms are shifted by constant values. The simulation temperature is $30\mathrm{K}$.