Monday, 14 April, 2025, 16:45 h, HIT H 42
Apéro after the colloquium   

Zoltan Banjok
Wigner Research Centre for Physics, Budapest, Hungary

Resurgence in the Disk Capacitor, the Lieb-Liniger, and O(3) Sigma Models

Abstract:

The calculation of the capacitance of the Maxwell-Kirchhoff disk capacitor is a notoriously challenging problem that has captivated physicists for over a century. The renowned Love equation, which expresses the solution in terms of a linear integral equation, remarkably coincides with the Lieb equation describing the ground-state energy of the Lieb-Liniger model. The same equation also governs the free energy of the O(3) non-linear sigma model.

Although this integral equation lacks an exact analytical solution, Volin’s ingenious method of matching asymptotics can be used to provide a perturbative expansion. The resulting series is not convergent but only asymptotic, necessitating Borel resummation. The ambiguities that arise in this process signal the presence of non-perturbative corrections, requiring a double-series expansion that progresses in both perturbative and non-perturbative parameters. We fully determine this so-called trans-series, incorporating all non-perturbative corrections, and unveil its intrinsic resurgence structure.

Hosts: Niklas Beisert and Sybille Driezen