Speaker
Description
Schroedinger-like equations (Sle) in one dimension have been playing a mayor rôle in modern theoretical physics. In fact, they enter many concrete and even experimental problems in higher dimensions, usually as a reduction, and are suitable for powerful semi-classical analysis since the very beginning of Quantum Mechanics when this method has started shading light on the deep meaning of quantisation. In this respect, one of the most important appearance of Sle equations (of Heun-type, with regular and irregular singularities) occurs, in recent times, in the theory of General Relativity (GR) perturbation by scalars or tensor excitations: with particular relevance for Black Holes (BHs) and their scattering, as they produce ultimately Gravitational Waves. In specific, what matters for theoretical understanding and experimental data is the spectrum of the so-called Quasi Normal Modes (QNMs), the characteristic frequencies of a gravitational object, like a BH. Actually, important is also the computation of the associated wave-functions and Floquet functions, being the latter associated to the Love numbers. A very new method for this investigation has become, more and more, the use of the Nekrasov-Shatashvily partition functions of susy gauge theories. Moreover, it has been shown to be captured by a deep integrability structure encompassing the (direct and inverse) monodromy problem of the Sle. The originality and efficiency of these new powerful idea and method will be described in computing exactly QNMs — via new thermodynamic Bethe Ansatz equations —, the related eigen-functions and the Floquet perturbations. As a byproduct these Sle are produced as limit of the isospectral Painlevé flow to the pole.
