A one parameter fit for glassy dynamics as a quantum corollary of the liquid to solid transition

Abstract

We apply microcanonical ensemble considerations to suggest that, whenever it may thermalize, a general disorder-free many-body Hamiltonian of a typical atomic system has solid-like eigenstates at low energies and fluid-type (and gaseous, plasma) eigenstates associated with energy densities exceeding those present in the melting (and, respectively, higher energy) transition(s). In particular, the lowest energy density at which the eigenstates of such a clean many body atomic system undergo a non-analytic change is that of the melting (or freezing) transition. We invoke this observation to analyze the evolution of a liquid upon supercooling (i.e., cooling rapidly enough to avoid solidification below the freezing temperature). Expanding the wavefunction of a supercooled liquid in the complete eigenbasis of the many-body Hamiltonian, only the higher energy liquid-type eigenstates contribute significantly to measurable hydrodynamic relaxations (e.g., those probed by viscosity) while static thermodynamic observables become weighted averages over both solid-and liquid-type eigenstates. Consequently, when extrapolated to low temperatures, hydrodynamic relaxation times of deeply supercooled liquids (i.e., glasses) may seem to diverge at nearly the same temperature at which the extrapolated entropy of the supercooled liquid becomes that of the solid. In this formal quantum framework, the increasingly sluggish (and spatially heterogeneous) dynamics in supercooled liquids as their temperature is lowered stems from the existence of the single non-analytic change of the eigenstates of the clean many-body Hamiltonian at the equilibrium melting transition present in low energy solid-type eigenstates. We derive a single (possibly computable) dimensionless parameter fit to the viscosity and suggest other testable predictions of our approach.

Macroscopic length correlations in non-equilibrium systems and their possible realizations

“…As we highlighted above, the chief goal of the current article is to demonstrate that when a system that was initially in equilibrium is driven at intermediate times (by, e.g., rapid cooling) such that its energy density varies at a finite rate as a function of time, the distribution P ( ) will need not remain a delta-function. A caricature of this feature is provided in the central panel of Figure 1 [21]. Because the final state displays a broad distribution of energy densities, our result implies that the "work" per site, in the context of its quantum mechanical definitions as energy differences between final and initial states [13][14][15][16]22] is not necessarily sharp (even in the N → ∞ limit).…”

“…A simple calculation (along the lines of that performed in Ref. [21] for the long time average of general observables) then yields…”

Nonequilibrium structural phase transitions of the vortex lattice in MgB2

“…Similarities between the metastable VL states and supercooled liquids and other structural glasses includes an activated transitions between states resulting from a complicated energy landscape, and a behavior that is governed by domains and domain walls. 9,41,42 Further support for this analogy comes from the slowing kinetics (aging) in Fig. 8(b).…”

A Phase Space Approach to Supercooled Liquids and a Universal Collapse of Their Viscosity

“…Similar to Eq. (7), the long time average of O for a general distribution ρ including that associated with the supercooled liquid (sc) reads [36] O ∞,sc = dT ρ(T )Õ can (T ).…”