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

TL;DR

This paper proposes a quantum framework linking the glass transition to the equilibrium melting transition, explaining supercooled liquid dynamics through eigenstate analysis and deriving a universal parameter fit for viscosity.

Contribution

It introduces a novel quantum perspective on glassy dynamics, connecting eigenstate properties to supercooled liquids and providing a single-parameter fit for viscosity.

Findings

Eigenstates of many-body Hamiltonians exhibit a non-analytic change at melting.

Supercooled liquids' relaxation times diverge near the extrapolated entropy crossing.

A universal dimensionless parameter can fit viscosity data across different systems.

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.