The Microscopic Quantum Theory of Low Temperature Amorphous Solids

Abstract

The quantum excitations in glasses have long presented a set of puzzles for condensed matter physicists. A common view is that they are largely disordered analogs of elementary excitations in crystals, supplemented by two level systems which are chemically local entities coming from disorder. A radical revision of this picture argues that the excitations in low temperature glasses are deeply connected to the energy landscape of the glass when it vitrifies: the excitations are not low excited states built on a single ground state but locally defined resonances, high in the energy spectrum of a solid. According to a semiclassical analysis, the two level systems involve resonant collective tunneling motions of around two hundred molecular units which are relics of the mosaic of cooperative motions at the glass transition temperature Tg. The density of states of the TLS is determined by Tg and the mosaic's length scale, which is a weak function of the cooling rate. The universality of phonon scattering in insulating glasses is explained. The Boson Peak and the plateau in thermal conductivity, observed at higher temperatures, are also quantitatively understood within the picture as arising from the same cooperative motions, but now accompanied by thermal activation of the mosaic's vibrational modes. The dynamics of some of the local structural transitions have significant quantum corrections to the semiclassical picture. These corrections lead to a deviation of the heat capacity and conductivity from the standard tunneling model results and explain the anomalous time dependence of the heat capacity. Interaction between tunneling centers contributes to the large and negative value of the Grüneisen parameter often observed in glasses.

Shear thinning in deeply supercooled melts

“…The displacements at the boundary are smaller than in the domain bulk, and are approximately equal to (a/ξ)d L (23,25)…”

“…The gradient obviously does not exceed 1/a, whereas the domain surface area is ξ 2 , leading to the following approximate estimate of the surface integral: transitions to phonons being independent of ξ (23,25). This is expected because a single domain is the smallest relaxing unit in the liquid (essentially a two-state system) and its entropy production should depend explicitly only on the relaxation rate and the degree of deviation from equilibrium.…”

“…This framework has yielded predictions or quantitative explanations of the signature phenomena associated with the structural glass transition. These include the connection between the thermodynamic crisis and the diverging relaxation times (14,17,19), the length scale of the cooperative rearrangements (14), deviations from Stokes-Einstein hydrodynamics (21), aging (20), cross-over between activated and collisional transport (15,22), the cryogenic anomalies in glasses (23)(24)(25), and decoupling between momentum and charge transfer (16). Several other, distinct formalisms have yielded qualitatively similar conclusions on the liquid dynamics near the glass transition (26-32).…”

Why Phonon Scattering in Glasses is Universally Small at Low Temperatures

“…Yu and Leggett [7] (YL) made the first attempt to understand this coincidence. They assumed that phonon mediated interactions between TLS dominate the physics.…”

“…We propose a novel explanation based on three aspects implicit in the standard TLS model that were ignored in the original model [4,5] and were only partially considered subsequently. First, the coupling between phonons and TLS implies that the TLS can interact with each other [7]. Second, this coupling produces an exponential renormalization of the tunneling matrix element due to phonon overlap between the two wells (a kind of polaron effect) [13].…”