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.
For more information see the webpage of the events here.