Further info
Analytic structure and the limits of hydrodynamics
A curated set of accessible background pages, reviews and lecture notes related to this research programme.
Wikipedia primers
Accessible introductions to the mathematical and physical structures that control the edge of hydrodynamic validity.
Quasinormal modeDamped normal modes with complex frequencies; in holography these organise the non-hydrodynamic excitation spectrum.Green's functionThe response functions whose poles, zeros and branch cuts encode the spectrum and analytic structure of the theory.Analytic continuationThe mathematical continuation of response functions and dispersion relations away from real frequency and momentum.Branch pointA basic introduction to multi-valued analytic functions and the branch points that terminate or connect spectral sheets.Sturm-Liouville theoryThe eigenvalue framework relevant to static screening problems and variational control of spatial spectra.
Reviews and research background
Papers that motivate the study of complex momentum, convergence radii, spectral sheets and the non-hydrodynamic sector.
Short-lived modes from hydrodynamic dispersion relationsShows how analytic continuation of a hydrodynamic series through complex-momentum branch cuts reveals non-hydrodynamic modes.On the convergence of the gradient expansion in hydrodynamicsStudies finite radii of convergence and level crossings of holographic quasinormal modes at complex momentum.Hydrodynamic Gradient Expansion in Gauge Theory PlasmasA foundational study of the high-order hydrodynamic gradient expansion in holographic plasma.Minkowski-space correlators in AdS/CFT correspondenceThe standard real-time holographic prescription linking bulk boundary conditions to retarded field-theory correlators.Quasinormal modes of black holes: from astrophysics to string theoryA broad review of quasinormal modes, including their role in black-hole physics and gauge-gravity duality.