A macroscopic version of Einstein-Podolsky-Rosen entanglement is obtained by quenching a quadratic coupling between two O(N ) vector models. A quench of the mixed vacuum produces an excited entangled state, reminiscent of purified thermal equilibrium, whose properties can be studied analytically in the free limit of the individual field theories.The decoupling of different wavelength modes in free field theory prevents true thermalisation but a more subtle difference is that the density operator obtained by a partial trace does not commute with the post-quench Hamiltonian. Generalized thermal behaviour is obtained at late times, in the limit of weak initial mixing or a smooth but rapid quench. More surprisingly, late-time correlation functions of composite operators in the post-quench free field theory share interesting properties with correlators in strongly coupled systems. We propose a holographic interpretation of our result.

Weyl semimetals are predicted to host signature magneto-optical properties sourced by their peculiar Landau level structure, including the chiral level. Analytical studies are often leaving out the Hall component of the conductivity due to its complicated nature, and even though the chiral anomaly requires Weyl nodes to come in charge-conjugate pairs, toy-models hosting only one node are considered almost exclusively; numerical studies including several Weyl nodes are on the other hand often limited to high-field quantum limits or DC studies.Here, I present a twofold purpose study, where I a) analytically derive a closed-form expression also for the Hall conductivity of a generic Weyl semimetal using linear response theory, and b) apply this general framework to evaluate the transverse conductivity components for Weyl systems with two nodes. I study how various model parameters, including the tilt, momentum separation, and energy location of the nodes, as well as the chemical potential affect the magneto-optical conductivity, and complement these studies with deriving an analytical expression for the DC Hall conductivity, which is also evaluated in various systems. Including a chiral pair of nodes result two important differences compared to earlier studies; the contribution from the chiral level is equal in size but opposite at the two nodes, making the net contribution to disappear; the energy scales at which intraband transitions occur is smeared out and approaches that of interband transitions, strengthening the hypothesis that intraband transitions mask signature optical features in materials. This general formalism can be applied for a large family of generic Weyl semimetals, and comprise an important piece towards unravelling the source of the mismatch between theoretical predictions and experimental observations in candidate materials.

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Correlation functions of most composite operators decay exponentially with time at non-zero temperature, even in free field theories. This insight was recently codified in an OTH (operator thermalisation hypothesis). We reconsider an early example, with large N free fields subjected to a singlet constraint. This study in dimensions d > 2 motivates technical modifications of the original OTH to allow for generalised free fields. Furthermore, Huygens’ principle, valid for wave equations only in even dimensions, leads to differences in thermalisation. It works straightforwardly when Huygens’ principle applies, but thermalisation is more elusive if it does not apply. Instead, in odd dimensions we find a link to resurgence theory by noting that exponential relaxation is analogous to non- perturbative corrections to an asymptotic perturbation expansion. Without applying the power of resurgence technology we still find support for thermalisation in odd dimensions, although these arguments are incomplete.