Abstract
We give qualitative arguments in support of the mesoscopic nature of the Sachdev–Ye–Kitaev (SYK) model in the regime with q2/N≪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 regime with q/N=1/2. In particular, the stochastic evolution of the SYK model can be mapped exactly onto that of random matrix theory, with universal Airy oscillations at the edges.
Highlights
The understanding of how entropy is produced and developed in heavy-ion collisions at ultra-relativistic energies is the subject of intensive interest at collider energies [1]
The purpose of this paper is two-fold: 1/ to suggest qualitatively that the numerical results for the spectral form factor for the SYK model recently reported in [14] for q2/N 1, reflect on a hierarchy of mesoscopic scales much like those encountered in disordered metals; 2/ to show rigorously using spectral determinants that for q2/N 1 a viscid fluid description emerges with a small spectral viscosity that maps exactly on random matrix theory
The main and quantitative new results of the paper will be presented in section 4, where we show how to map the SYK model on random matrix theory for the special case of q/N = 1/2, and note that the microscopic accumulation of the states at the edge of the spectrum follows from Airy universality
Summary
The understanding of how entropy is produced and developed in heavy-ion collisions at ultra-relativistic energies is the subject of intensive interest at collider energies [1]. The purpose of this paper is two-fold: 1/ to suggest qualitatively that the numerical results for the spectral form factor for the SYK model recently reported in [14] for q2/N 1, reflect on a hierarchy of mesoscopic scales much like those encountered in disordered metals; 2/ to show rigorously using spectral determinants that for q2/N 1 a viscid fluid description emerges with a small spectral viscosity that maps exactly on random matrix theory Our interest in both regimes stems from their relation to random matrix theory for large times in general, with in particular a fermionic ground state that is dual to a black hole in both cases, and very likely for all permissible q/N ≤ 1/2.
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