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2016

Disorder in the Sachdev-Yee-Kitaev Model

Liu, Yizhuang, Nowak, Maciej A., Zahed, Ismail

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We give qualitative arguments for the mesoscopic nature of the Sachdev-Yee-Kitaev (SYK) model in the holographic regime with $q^2/N\ll 1$ with $N$ Majorana particles coupled by antisymmetric and random interactions of range $q$.

Using a stochastic deformation of the SYK model, we show that its characteristic determinant obeys a viscid Burgers equation with a small spectral viscosity in the opposite regime with $q/N=1/2$, in leading order.
The stochastic evolution of the SYK model can be mapped onto that of random matrix theory, with universal Airy oscillations at the edges.
A spectral hydrodynamical estimate for the relaxation of the collective modes is made.

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