Convergence of hydrodynamic modes: insights from kinetic theory and holography
Heller, M., Serantes, A., Spaliński, M., Svensson, V., Withers, B.
Abstract
We study the mechanisms setting the radius of convergence of hydrodynamic<br>dispersion relations in kinetic theory in the relaxation time approximation.<br>This introduces a qualitatively new feature with respect to holography: a<br>nonhydrodynamic sector represented by a branch cut in the retarded Green's<br>function. In contrast with existing holographic examples, we find that the<br>radius of convergence in the shear channel is set by a collision of the<br>hydrodynamic pole with a branch point. In the sound channel it is set by a<br>pole-pole collision on a non-principal sheet of the Green's function. More<br>generally, we examine the consequences of the implicit function theorem in<br>hydrodynamics and give a prescription to determine a set of points that<br>necessarily includes all complex singularities of the dispersion relation. This<br>may be used as a practical tool to assist in determining the radius of<br>convergence of hydrodynamic dispersion relations.<br>