Dynamics of Disordered Solids, Two-Level Systems

Since barrier parameters in a disordered system are broadly distributed, tvmneling rates are spread over many orders of magnitude, from picoseconds to hours or longer. 

In order to model glass properties and to discuss experimental observations, we need a model of tunneling systems. A schema of a TLS, and its potential along the generalized coordinate is presented in Fig. 1. Independently of the nature of this coordinate, which determines the mass m of the tuimeling particle, the TLS is characterized by the barrier width d (taken as the distance between minima in each well), the barrier height V, and the asymmetry A or energy difference between the wells. 

In the following, we restrict our discussion of single molecule spectra to the lowest temperatures, say below 5K. Therefore, the influence of matrix dynamics on the 

In a real disordered matrix, there usually are several TLS s able to interact with a single molecule, as schematically shown in Fig. 1. The first case is that of defects in crystals, where a non-random distribution of flipping TLS s in space interacts with the probe. Dislocations or grain boundaries can give rise to such one- or two-dimensional distributions of TLS s (see Section 1.4.2). Because of the translational symmetry of crystals, we may assume in this case that all TLS s have the same 

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