TLS Interaction in glasses - P

1975 Joffrin - Lovelut

.... we demonstrate the importance of the indirect interaction via the phonon field between pairs of defects in an amorphous material.

In fact, as we show below, the indirect interaction is easily represented by an exchange constant between pairs of spins; we shall first calculate the order of magnitude of this interaction.

In the appendix, we also make corrections to the many-body interaction of low-temperature amorphous solids derived by Joffrin and Levelut (1975 J. Physique 36 811). Zhou-Leggett 2016

1987 Spectral diffusion, phonon echoes, and saturation recovery in glasses at low temperatures J. L. Black and B.I. Halperin

Thus one of the key issues in the tunneling model is understanding the relationship between the strongly coupled excitations, which determine the ultrasonic properties, and the totality of excitations contributing to the specific heat

As is shown in Sec. II, the value of P is too small to be consistent with the specific-heat density of states $n_0$ which is observed '"" on a longtime scale (5 sec)

Having introduced anomalous levels to help explain specific-heat results, we will focus our attention on the standard levels throughout the remainder of this paper

1975 Efros-Shklovskii - Coulomb gap

1989 Interactions of two-level systems in glasses Kassner and Silbey

Using methods from polaron theory, we re-derive the elastic interaction between
two-level systems (TLS) in glasses in a non-perturbative manner. We then calculate the relaxation rate of the interacting dressed ns perturbatively

... the dynamics of TLS in glasses are still not well understood. At the very least, it has to be explained (i) why weak-coupling
theories have been so successful, (ii) which parameters must be changed in which direction in order to account for strong coupling, and (iii) why this is uncritical.
....erroneous or unrealistic assumptions in these theories must be found