We develop a perturbative method of computing spectral singularities of a Schrödinger operator defined by a general complex potential that vanishes outside a closed interval. These can be realized as zero-width resonances in optical gain media and correspond to a lasing effect that occurs at the threshold gain. Their time-reversed copies yield coherent perfect absorption of light that is also known as antilasering. We use our general results to establish the exactness of the n-th order perturbation theory for an arbitrary complex potential consisting of n delta-functions, obtain an exact expression for the transfer matrix of these potentials, and examine spectral singularities of complex barrier potentials of arbitrary shape. In the context of optical spectral singularities, these correspond to inhomogeneous gain media.

We study the conductivity of two-dimensional graphene-type materials with tilted cones as well as their three-dimensional Weyl counterparts and show that a covariant quantum Boltzmann equation is capable of providing an accurate description of these materials' transport properties. The validity of the covariant Boltzmann approach is corroborated by calculations within the Kubo formula. We find a strong anisotropy in the conductivities parallel and perpendicular to the tilt direction upon an increase of the tilt parameter η, which can be interpreted as the boost parameter of a Lorentz transformation. While the ratio between the two conductivities is 1 − η 2 in the twodimensional case where only the conductivity perpendicular to the tilt direction diverges for η → 1, both conductivities diverge in three-dimensional Weyl semimetals, where η = 1 separates a type-I (for η < 1) from a type-II Weyl semimetal (for η > 1).