Abstract
Abstract In this paper we study the thermalization of a spatially homogeneous system in a strongly coupled CFT. The non-equilibrium initial state is created by switching on a relevant perturbation in the CFT vacuum during Δt ≳ t ≳ − Δt. Via AdS/CFT, the thermalization process corresponds to the gravitational collapse of a tachyonic scalar field (m 2 = −3) in the Poincare patch of AdS 5. In the limit $ \varDelta t<\frac{0.02 }{T} $ , the thermalization time t T is found to be quantitatively the same as that of a non-equilibrium state created by a marginal perturbation discussed in ref. [5]. In the case $ \varDelta t\gtrsim \frac{1}{T} $ we also obtain double- collapse solutions but with a non-equilibrium intermediate state at t = 0. In all the cases our results show that the system thermalizes in a typical time $ {t_T}\simeq \frac{O(1) }{T} $ . Besides, a conserved energy-moment current in the bulk is found, which helps understand the qualitative difference of the collapse process in the Poincare patch from that in global AdS [10, 11].
Highlights
The thermalization time tT is found to be quantitatively the same as that of a non-equilibrium state created by a marginal perturbation discussed in ref. [5]
Via AdS/CFT, the thermalization process corresponds to the gravitational collapse of a tachyonic scalar field
On the gravity side the thermalization processes in these two cases respectively correspond to the gravitational collapse of massless or tachyonic scalar fields
Summary
Tab = 2∂aφ∂bφ − gab (∂φ)2 + m2φ2. For the spatially homogeneous system on the boundary M 4, we use the Schwarzschild coordinates of the form ds. Where f and δ are functions of t and u only. In this coordinate system, one obtains from eqs. (2.1) and (2.2) the following equations of motion. + 4 (f − 1) , u (2.5a) (2.5b) (2.5c) (2.5d) (2.5e) where the derivatives with respect to t and u are denoted respectively by overdots and primes, P ≡ φ′ and V ≡ f −1eδφ
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