Lorentzian symmetry predicts universality beyond scaling laws

Who: Stephen J. Watson, University of Glasgow
When: 
Wednesday, August 15, 2018 - 11:00am to 12:00pm
Where: 
Thackeray Hall, room 427

We present a covariant theory for the ageing characteristics of phase-ordering systems that possess dynamical symmetries beyond mere scalings. A chiral spin dynamics which conserves the spin-up (+) and spin-down (−) fractions, $\mu_+$  and $\mu_-$ , serves as the emblematic paradigm of our theory. Beyond a parabolic spatio-temporal scaling, we discover a hidden Lorentzian dynamical symmetry therein, and thereby prove that the characteristic length L of spin domainsgrows in time t according to $L = \frac{\beta}{\sqrt{1 - \sigma^2}}t^{\frac{1}{2}}$ , where $\sigma:= \mu_+ - \mu_-$  (the invariant spin-excess) and βis a universal constant. Furthermore, the normalised length distributions of the spin-up and the spin-down domains each provably adopt a coincident universal (σ-independent) time-invariant form, and this supra-universal probability distribution is empirically verified to assume a form reminiscent of the Wigner surmise.

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