We study the long time behaviour of local observables following a quantum quench in 1+1 dimensional conformal field theories possessing additional conserved charges besides the energy. We show that the expectation value of an arbitrary string of local observables supported on a finite interval exponentially approaches an equilibrium value. The equilibrium is characterized by a temperature and chemical potentials defined in terms of the quenched state. For an infinite number of commuting conserved charges, the equilibrium ensemble is a generalized Gibbs ensemble (GGE). We compute the thermalization rate in a systematic perturbation in the chemical potentials, using a new technique to sum over an infinite number of Feynman diagrams. The above technique also allows us to compute relaxation times for thermal Green's functions in the presence of an arbitrary number of chemical potentials. In the context of a higher spin (hs[λ]) holography, the partition function of the final equilibrium GGE is known to agree with that of a higher spin black hole. The thermalization rate from the CFT computed in our paper agrees with the quasinormal frequency of a scalar field in this black hole.
We consider quantum quenches in models of free scalars and fermions with a generic time-dependent mass m(t) that goes from m 0 to zero. We prove that, as anticipated in MSS [1], the post-quench dynamics can be described in terms of a state of the generalized Calabrese-Cardy form |ψ = exp[−κ 2 H − ∞ n>2 κ n W n ]|Bd . The W n (n = 2, 3, . . ., W 2 = H) here represent the conserved W ∞ charges and |Bd represents a conformal boundary state. Our result holds irrespective of whether the pre-quench state is a ground state or a squeezed state, and is proved without recourse to perturbation expansion in the κ n 's as in MSS. We compute exact time-dependent correlators for some specific quench protocols m(t). The correlators explicitly show thermalization to a generalized Gibbs ensemble (GGE), with inverse temperature β = 4κ 2 , and chemical potentials µ n = 4κ n . In case the prequench state is a ground state, it is possible to retrieve the exact quench protocol m(t) from the final GGE, by an application of inverse scattering techniques. Another notable result, which we interpret as a UV/IR mixing, is that the long distance and long time (IR) behaviour of some correlators depends crucially on all κ n 's, although they are highly irrelevant couplings in the usual RG parlance. This indicates subtleties in RG arguments when applied to non-equilibrium dynamics.
We present the complete family of solutions of 3D gravity (Λ < 0) with two asymptotically AdS exterior regions. The solutions are constructed from data at the two boundaries, which correspond to two independent and arbitrary stress tensors T R ,T R , and T L ,T L . The two exteriors are smoothly joined on to an interior region through a regular horizon. We find CFT duals of these geometries which are entangled states of two CFT's. We compute correlators between general operators at the two boundaries and find perfect agreement between CFT and bulk calculations. We calculate and match the CFT entanglement entropy (EE) with the holographic EE which involves geodesics passing through the wormhole. We also compute a holographic, non-equilibrium entropy for the CFT using properties of the regular horizon. The construction of the bulk solutions here uses an exact version of Brown-Henneaux type diffeomorphisms which are asymptotically nontrivial and transform the CFT states by two independent unitary operators on the two sides. Our solutions provide an infinite family of explicit examples of the ER=EPR relation of Maldacena and Susskind [1].
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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