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arXiv · 1612.05233

Disorder in the Sachdev-Yee-Kitaev Model

Yizhuang Liu·Maciej A. Nowak·Ismail Zahed
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Abstract

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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Yizhuang Liu, Maciej A. Nowak, Ismail Zahed. 2016-12-15. Disorder in the Sachdev-Yee-Kitaev Model. https://doi.org/10.1016/j.physletb.2017.08.054

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