We study Big-Bang or-Crunch cosmological singularities in 2-dimensional dilaton-gravity-scalar theories, in general obtained by dimensional reduction of higher dimensional theories. The dilaton potential encodes information about the asymptotic data defining the theories, and encompasses various families such as flat space, AdS, conformally AdS as arising from nonconformal branes, and more general nonrelativistic theories. We find a kind of universal near singularity behaviour independent of the dilaton potential, giving universal interrelations between the exponents defining the time behaviour near the cosmological singularity. More detailed analysis using a scaling ansatz enables finding various classes of cosmological backgrounds, recovering known examples such as the AdS Kasner singularity as well finding as new ones. We give some comments on the dual field theory from this point of view.

Abstract:We study the SYK model with complex fermions, in the presence of an all-toall q-body interaction, with a non-vanishing chemical potential. We find that, in the large q limit, this model can be solved exactly and the corresponding Lyapunov exponent can be obtained semi-analytically. The resulting Lyapunov exponent is a sensitive function of the chemical potential µ. Even when the coupling J, which corresponds to the disorder averaged values of the all to all fermion interaction, is large, values of µ which are exponentially small compared to J lead to suppression of the Lyapunov exponent.

We study non-equilibrium dynamics in SYK models using quantum quench. We consider models with two, four, and higher fermion interactions (q = 2, 4, and higher) and use two different types of quench protocol, which we call step and bump quenches. We analyse evolution of fermion two-point functions without long time averaging. We observe that in q = 2 theory the two-point functions do not thermalize. We find thermalization in q = 4 and higher theories without long time averaging. We also calculate two different exponents of which one is equal to the coupling and the other is proportional to the final temperature. This result is more robust than thermalization obtained from long time averaging as proposed by the eigenstate thermalization hypothesis(ETH). Thermalization achieved without long time averaging is more akin to mixing than ergodicity. arXiv:1811.06006v2 [hep-th]

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