Cohomology in algebra, geometry, physicsand statistics

Lorentzian Symmetry Predicts Universality Beyond Power Laws

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 magical theoretical coarsening law which reflects Lorentzian and parabolic symmetries!

 

 

 [1]  http://iopscience.iop.org/article/10.1209/0295-5075/118/56001/meta

Lorentzian symmetry predicts universality beyond scaling laws,

SJ Watson, EPL 118 (5), 56001, (Aug.2, 2017), Editor's Choice

 Emergent parabolic scaling of nano-faceting crystal growth,

Stephen J. Watson,  Proc. R. Soc. A 471: 20140560 (2015)
[3]  http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.96.176103

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)

----------------------------------------------------------------------------------------------------------------------------------------------------------
Zoom Meeting is open at 11.15 AM

 https://cesnet.zoom.us/j/99598413922?pwd=Ym4velNHckh2TlNxK2R2SzRpVXRhdz09

 Meeting ID: 995 9841 3922
Password: 097923