Starts 5 Apr 2022 17:00

Ends 5 Apr 2022 18:00

Central European Time

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CMSP Seminar (Joint ICTP/SISSA Statistical Physics): A geometric conjecture about phase transitions

Starts 5 Apr 2022 17:00

Ends 5 Apr 2022 18:00

Central European Time

Virtual seminar

via Zoom

(UC Davis)

Abstract:

As phenomena that necessarily emerge from the collective behavior of interacting particles, phase transitions continue to be difficult to predict using statistical thermodynamics. A recent proposal called the topological hypothesis suggests that the existence of a phase transition could perhaps be inferred from changes to the topology of the accessible part of the configuration space. We instead suggest that such a topological change is often associated with a dramatic change in the configuration space geometry, and that the geometric change is the actual driver of the phase transition. More precisely, a geometric change that brings about a discontinuity in the mixing time required for an initial probability distribution on the configuration space to reach steady-state is conjectured to be related to the onset of a phase transition in the thermodynamic limit. This conjecture is tested by evaluating the diffusion diameter and epsilon-mixing time of the configuration spaces of hard disk and hard sphere systems of increasing size. Explicit geometries are constructed for the configuration spaces of these systems, and numerical evidence suggests that a discontinuity in the epsilon-mixing time coincides with the solid-fluid phase transition in the thermodynamic limit.