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We apply microcanonical ensemble considerations to suggest that, whenever itmay thermalize, a general disorder-free many-body Hamiltonian of a typicalatomic system has solid-like eigenstates at low energies and fluid-type (andgaseous, plasma) eigenstates associated with energy densities exceeding thosepresent in the melting (and, respectively, higher energy) transition(s). Inparticular, the lowest energy density at which the eigenstates of such a cleanmany body atomic system undergo a non-analytic change is that of the melting(or freezing) transition. We invoke this observation to analyze the evolutionof a liquid upon supercooling (i.e., cooling rapidly enough to avoidsolidification below the freezing temperature). Expanding the wavefunction of asupercooled liquid in the complete eigenbasis of the many-body Hamiltonian,only the higher energy liquid-type eigenstates contribute significantly tomeasurable hydrodynamic relaxations (e.g., those probed by viscosity) whilestatic thermodynamic observables become weighted averages over both solid- andliquid-type eigenstates. Consequently, when extrapolated to low temperatures,hydrodynamic relaxation times of deeply supercooled liquids (i.e., glasses) mayseem to diverge at nearly the same temperature at which the extrapolatedentropy of the supercooled liquid becomes that of the solid. In this formalquantum framework, the increasingly sluggish (and spatially heterogeneous)dynamics in supercooled liquids as their temperature is lowered stems from theexistence of the single non-analytic change of the eigenstates of the cleanmany-body Hamiltonian at the equilibrium melting transition present in lowenergy solid-type eigenstates. We derive a single (possibly computable)dimensionless parameter fit to the viscosity and suggest other testablepredictions of our approach.

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