The Principle of G-Equivariant Universality
When
Speaker
Abstract
The statistical physics governing phase-ordering dynamics following a symmetry breaking first-order phase transition is an area of active research. The Coarsening/Ageing of the ensemble of phase domains, wherein irreversible annihilation or joining of domains yields a growing characteristic domain length, is a omniprescent feature whose universal characteristics one would wish to understand. Driven kinetic Ising models and growing nano-faceted crystals are theoretically important examples of such Coarsening (Ageing) Dynamical Systems (CDS), since they additionally break thermodynamic fluctuation-dissipation relations.
Power-laws for the growth in time of the characteristic size of domains (e.g., lengths) of CDS, and a concomitant {\em scale-invariance} of the associated length distributions,
has so frequently been empirically observed that their presence has acquired the status of a principle; the so-called Dynamic-Scaling Hypothesis.
But the dynamical symmetries of a given CDS- its Coarsening Group $G$ - may include more than the global spatio-temporal scalings underlying the {\em Dynamic Scaling Hypothesis}.
In this talk, I will present a recently developed theoretical framework (Ref.[1]) that shows how the symmetry group G of a Coarsening (ageing) Dynamical System (CDS) necessarily yields G-equivariance (covariance) of the CDS's universal statistical observables. We exhibit this theory for a variety of model systems, of both thermodynamic and driven type, with symmetries that may also be {\em emergent} (Ref. [2,3]) and/or {\em hidden}. We will close with a remarkable theoretical coarsening law that combines Lorentzian and Parabolic symmetries. References:
[1] Lorentzian symmetry predicts universality beyond scaling laws,
SJ Watson, EPL 118 (5), 56001, (Aug.2, 2017) (Editor's Choice)
( http://iopscience.iop.org/article/10.1209/0295-5075/118/56001/meta )
[2] Emergent parabolic scaling of nano-faceting crystal growth,
Stephen J. Watson, Proc. R. Soc. A 471: 20140560 (2015)
( http://rspa.royalsocietypublishing.org/content/471/2174/20140560 )
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[3]
Scaling Theory and Morphometrics for a Coarsening Multiscale Surface, via a Principle of Maximal Dissipation,
Stephen J. Watson and Scott A. Norris, Phys. Rev. Lett. 96, 176103 (2006)
( http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.96.176103 )
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