Linear response theory: from black holes to Weyl systems and back

Abstract: Linear response theory is a powerful calculation tool in quantum field theory. We apply this framework to a variety of models originating from distinct areas in theoretical physics and for different reasons. In the context of black hole holography, we consider a quench model where we investigate effective thermalization, as well as the boundary signal of so-called evanescent modes which indicate the presence of a black hole-like object in the bulk. The problem of quantum thermalization plays a central role within the holographic duality between thermal states in the boundary field theory and black hole-like objects in the bulk. However, quantum thermalization is also an interesting question in itself from a fundamental point of view. Inspired by recent progress in understanding how operators in quantum field theories thermalize, which occurs even when considering integrable models, we investigate the so-called operator thermalization hypothesis. We focus on gauge theories at finite temperature with a large number of fields which present a phase transition between the low-temperature and high-temperature regimes. In a separate application of linear response theory, we investigate transport properties in a family of Weyl semimetal systems. Concretely, we develop a general analytic method to compute the magneto-optical conductivity of these systems in the presence of an external magnetic field aligned with the tilt of the spectrum. Last, we examine non-Hermitian Weyl-like systems as potential analogue black hole models and suggest a specific parity-time-symmetric dissipative Hamiltonian displaying analogue Hawking radiation.