VIRTUAL SEMINAR SERIES -- INTEGRABLE SYSTEMS: Integrability and complexity in statistical mechanics: thermodynamic limit vs viscous/dispersive regularisation

Antonio Moro (Northumbria University)

Wednesday 20th May, 2020 14:00-15:00 Zoom seminar


The theory of integrable nonlinear conservation laws arises as a universal paradigm for the description and classification of phase transitions, cooperative and catastrophic behaviours in many body systems at the crossroad of integrable systems, statistical mechanics and random matrix theory.

A key element of this paradigm is the construction of suitable differential identities for partition functions from which one can deduce nonlinear partial differential equations - typically a hierarchy of hydrodynamic conservation laws -  for the order parameters of the theory. Critical phenomena and phase transitions are therefore understood in terms of asymptotic properties of solutions to this equations in the low viscosity/weak dispersion regime.

We illustrate, via specific examples, how viscosity underpins the occurrence of phase transitions in simple systems while dispersion arises as a possible mechanism for the description of emergent complex behaviours and out of equilibrium thermodynamics.


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