Abstract
At low temperatures the dynamical degrees of freedom in amorphous solids are tunnelling two-level systems (TLSs). Concentrating on these degrees of freedom, and taking into account disorder and TLS-TLS interactions, we obtain a "TLS-glass", described by the random field Ising model with random $1/r^3$ interactions. In this paper we perform a self consistent mean field calculation, previously used to study the electron-glass (EG) model [A.~Amir {\it et al.}, Phys. Rev. B {\bf 77}, 165207, (2008)]. Similar to the electron-glass, we find $\frac{1}{\lambda}$ distribution of relaxation rates $\lambda$, leading to logarithmic slow relaxation. However, with increased interactions the EG model shows slower dynamics whereas the TLS glass model shows faster dynamics. This suggests that given system specific properties, glass dynamics can be slowed down or sped up by the interactions.
Highlights
At low temperatures amorphous solids show anomalous behaviour with respect to their ordered counterparts
The standard tunnelling model (STM) states that at low temperatures the dominant dynamical degrees of freedom are two-level systems (TLSs), each TLS represents an atom or a group of atoms that occupy one of two localized configuration-states that result from an asymmetric double-well potential
We present the numerical solution of the self-consistent equations (Eq (3)), which gives the same logarithmic dependence, and in addition the behaviour for larger energy values far from the gap region
Summary
At low temperatures amorphous solids show anomalous behaviour with respect to their ordered counterparts. Superconducting quantum bits (qubits) have shown extreme sensitivity to even a single TLS10,11 This coupling of the qubit system to TLSs was used to investigate the caracharistics of individual TLSs9,12–14 and the nature of TLS-TLS interactions up to the accuracy of a single interacting pair[15]. The logarithm depends on interactions and disorder through the minimum cutoff rate, λmin Using this dependence we examine the qualitative affect of the interactions, disorder and systems size on the dynamics, and compare it with the EG model. The structure of the paper is as follows: In Sec. II we define the local-equilibrium state of the system, present the model in the mean-field approximation and obtain numerically the single particle density of states (DOS) which contains the dipole gap.
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