Abstract:
In this work we explore the thermalization of two point functions of free scalars in $d+1$ dimensions after a quantum quench. The mass is time dependent and is taken to zero. A detailed analysis of this problem has been done in 1+1 dimensions, in \cite{Mandal:2015kxi}. My goal here is to extend this understanding to higher dimensions. In previous works,\cite{Mandal:2015jla}\cite{Mandal:2015kxi}, we have seen that the post quench system equilibriates to a generalised Gibb's Ensemble. The post-quench observables retain a memory of the quench by having signatures set by the scale of the pre-quench state. We restrict our calculations to two kinds of pre-quench states: the ground state of the pre-quench Hamiltonian, and specific excited states called the squeezed states (CC and GCC).
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All observables seem to reach an equilibrium. The correlation functions in the CC approach a thermal ensemble and those in the GCC approach a GGE, at late times, and are related by, $\beta=4\kappa_2$ and $\mu=4\kappa_4$. We observe a distinction between odd and even dimensions. The approach to equilibrium is exponentially decaying in time for odd $d$ and fall off as a power law for even $d$. We also calculate the time dependent thermal correlator and observe a similar difference in odd and even dimensions.
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In the second last section, we discuss the possibility of UV-IR mixing in the GCC and GGE. The post-quench state is characterized by infinite number of conserved charges which may correspond to irrelevant operators in the theory. Observables seem to be affected by all such operators even at low energies, which is interesting given our intuitions set by Wilsonian renormalization.
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Finally, we wish to understand the implications of this result in the context of holography, with the knowledge that thermalization in the gauge theory corresponds to a quasi-normal decay to a black-hole. A quench itself can correspond to an excitation in the bulk.
