Ph.D HBNI 2023

The existence of hydrodynamic attractors in various microscopic theories and phenomenological models has paved the way for understanding hydrodynamization in out-of-equilibrium systems. The thesis studies a far-away-from equilibrium system undergoing Bjorken flow, a boost-invariant expansion in the longitudinal direction. It explores the effect of continuous symmetry breaking and the corresponding phase transition on hydrodynamization in the Bjorken expanding system. Followed by this, it computes the real-time hydrodynamic correlation functions of the expanding system using the holographic method. In addition, the thesis also investigates the thermalisation of a hybrid system coupled in a semi-holographic framework. <br><br> We begin with a review of the necessary theoretical background required to follow the work included in the thesis. Then we discuss the construction of an effective description of a dissipative superfluid by extending the quantum effective approach of Son and Nicolis and incorporating dissipation in Müller-Isreal-Stewart (MIS) formalism. We include the Goldstone boson and the condensate together with the hydrodynamic modes as the effective degrees of freedom. We show that the evolution of the superfluid undergoing boost invariant expansion is governed by the conventional hydrodynamic attractor with unbroken U(1) symmetry and an even number of novel non-dissipative fixed points with broken symmetry. If the initial temperature is super-critical, then the condensate becomes exponentially small very rapidly and the system is trapped by the hydrodynamic attractor for a long intermediate time before it reheats rapidly and switches to one of the symmetry-breaking fixed points eventually. Finally, we show that the fixed points are unstable against inhomogeneous perturbations that should lead to spinodal decomposition. We conclude that these features should be generic beyond the MIS formalism. <br><br> Next, we develop a method to compute the Schwinger-Keldysh correlation functions of an expanding system in a holographic approach in the limit in which the state hydrodynamizes. <br><br> We implement the horizon cap prescription of Crossley-Glorioso-Liu to an asymptotically dynamical AdS d+1 geometry which is dual to Bjorken flow in the boundary. We provide a new and elegant proof of consistency of the horizon cap prescription with the KMS (Kubo-Martin-Schwinger) periodicity and the ingoing boundary condition for the retarded propagator at any arbitrary frequency and momentum. The trick of Weyl rescaling the Bjorken flow at the boundary lifts to appropriate bulk di↵eomorphism, which implies that the dual black hole’s event horizon attains constant surface gravity and area at a late time. Subsequently, at late time the temperature and entropy density for the dual state maps to a constant which otherwise has a perfect fluid-like expansion. One of our key results is that in the limit of perfect fluid expansion, the Schwinger-Keldysh correlation functions are simply thermal at an appropriate temperature when expressed in terms of reparametrized spacetime arguments. A generalized bi-local thermal structure holds to all orders. We also argue a transseries form of the hydrodynamic correlation functions that can decode the details of the initial state. <br><br> Finally, we investigate the thermalization of a hybrid system involving a weakly self interacting perturbative and a strongly self-interacting non-perturbative (holographic) sector, democratically coupled in semi-holographic framework. We first provide a generic proof of thermalisation, in which the entropy of the full system is maximised only when the physical temperatures of the respective sectors coincide at any fixed total energy. We show that if we consider a generic state in which observable like the full energy-momentum tensor is like in a pseudo-equilibrium state, the total entropy of this non-equilibrium state is that of global equilibrium. Then we study dynamical situations such as an e↵ective two-fluid model described by BRSSS formalism. We show that there exist macroscopic fluctuations about any pseudo- equilibrium state which keep the total energy fixed and take the system to a non-equilibrium state whose total entropy is close to that of global equilibrium entropy up to a good degree of precision. Based on these results we formulate how to study the thermalization of the full isolated hybrid system in the full quantum theory in the large N limit.