The "glass problem" is nontrivial in a unique sense: unlike many other problems in physics, there is no established theoretical framework in which to pose it cleanly. In daily life, amorphous solids and glasses are no less (and arguably more) prevalent than crystals. Thanks to the periodic locations of atoms in a crystal, quantum mechanical behavior becomes manifest on the macroscopic scale of the solid, as the discrete energy levels of electrons in single atoms reorganize into extended band structures. Understanding these electronic bands and band gaps paved the way for the invention of the transistor and the solid-state electronics revolution. While, at the microscopic level, the interactions between atoms in glass formers contain no quenched disorder and are identical to those in crystals, their spatial structure is aperiodic and generally far more complex. The absence of periodicity in supercooled liquids and glasses removes powerful simplifications. Glass formers develop rigidity and staggering dynamical slowing without symmetry breaking or a sharp thermodynamic transition. This leaves standard tools of equilibrium statistical mechanics and common simplifications with no obvious foothold. This singular character raises a natural question: how can slow, solid-like behavior emerge so universally? By returning to the basic roots of many-body physics, we explore whether some of its core principles can be extended to supercooled fluids. This approach leads to testable predictions, including a collapse of viscosity and dielectric response with the aid of a single, nearly constant, dimensionless parameter. This collapse is found to be satisfied across all experimentally measured glass former types over more than sixteen decades in relaxation time. Numerically, we also observe nontrivial deviations from conventional equilibrium dynamics when thermostats emulating the supercooling process are used. Time permitting, we will discuss how these considerations may be further extended and applied more broadly to suggest quantum mechanical “Planckian” bounds on viscosity and diffusion. These bounds appear to be nearly saturated in common systems such as water and aluminum.

Note: Part of this work was done with our dearly missed colleague, Professor Ken Kelton.

This lecture was made possible by the William C. Ferguson Fund.