Energy flow in quantum critical systems far from equilibrium

Time evolution of entanglement for holographic steady state formation

“…The holographic dual of the initial state with the temperature profile (1.1) is thus given by a geometry consisting of two AdS black holes at two different temperatures both cut at x = 0, and a half of each glued together at t = 0. For this particular scenario, the asymptotic late-time geometry is known and the steady-state region was shown to be equivalent to a boosted AdS Schwarzschild black hole at temperature √ T L T R [41]. This result is in agreement with the earlier CFT result.…”

“…Studying the hydrodynamic expansion to first order, the authors of [37] conjectured the universality of the steady state regime in a sense that its emergence at late times is universal and irrespective of the dynamical details of the system or details of the initial state configuration and that the heat current can be described with a universal formula. The assumptions on which the conjecture is based are similar to the ones in [41] namely that at late times the system can be described by three regions, the two heat reservoirs and a steady state regime growing in time as two shockwaves move towards spatial infinity.…”

“…A numerical analysis of the 2+1 dimensional boundary CFT [45] shows very good agreement with the conjecture. However, while in [41] the two wavefronts in the higher-dimensional case are both shockwaves, it was later shown in [46] and [47] that the solution with one shockwave and one rarefaction wave is preferred.…”

“…Such a local quench-like system can be modeled for example as in [25,40], where two independently thermalised BCFTs are joined at t = 0. In this work, in contrast, we will follow [41] and utilise a different setup where equation (1.1) holds at t = 0, and a steady state forms when evolving the state both forwards and backwards in time. However, we will only consider the regime t ≥ 0 as physically interesting.…”

“…Taking the holographic approach, according to [41], the steady-state region in the late-time limit can be described by a boosted thermal state in the higher-dimensional case as well if the system shows time-independent asymptotic behaviour. The corresponding argument is based on black hole uniqueness theorems.…”