Quenched coupling and thermal behavior in the O(N) vector model

Abstract: Thermalization is an elusive phenomenon in quantum mechanics. Since according to the AdS/CFT correspondence, a thermal state in the boundary CFT is dual to a black hole in the bulk spacetime, thermalization in the CFT is dual to black hole formation in AdS. Thus, understanding quantum thermalization is likely a key component in understanding the information paradox---the contradiction between QFT and general relativity occurring when a black hole seemingly erases the information of whatever went into creating it.(Apparent) thermalization in QFT can be investigated by imposing a quench, i.e., a sudden change of some parameter of the theory, and subsequently studying the equilibration process. In this thesis we aim to gain understanding of quantum thermalization by investigating the late-time quench dynamics of a simple free field theory, namely the $O(N)$ vector model. Since the theory is integrable, ``true'' thermalization will not occur but an approximate thermalization. We use different probes such as the effective density matrix and the spectral density function to investigate the extent to which the (pure) state ``looks'' thermal and how this deviates from conventional thermality.