We determine the complete trans-series solution for the (non-relativistic) moments of the rapidity density in the Lieb-Liniger model. The trans-series is written explicitly in terms of a perturbative basis, which can be obtained from the already known perturbative expansion of the density by solving several ordinary differential equations. Unknown integration constants are fixed from Volin's method. We have checked that our solution satisfies the analytical consistency requirements including the newly derived resurgence relations and agrees with the high precision numerical solution. Our results also provides the full analytic trans-series for the capacitance of the coaxial circular plate capacitor.
A complete trans-series solution is given for the non-relativistic moments (conserved charges) of the rapidity density in the Lieb-Liniger model, expressed in a perturbative basis obtained by solving ODEs, with integration constants fixed via Volin's method, and verified against resurgence relations and high-precision numerics.
That the integration constants extracted via Volin's method, combined with ODE-derived perturbative basis functions, fully and uniquely determine all non-perturbative sectors — i.e., that no further hidden trans-series sectors exist beyond those captured. Without the full text, the completeness argument cannot be independently checked.
1/ The Lieb-Liniger model is a textbook 1D Bose gas with delta-function interaction. Its conserved charges (moments of the rapidity density) admit asymptotic expansions in coupling that don't converge — they need non-perturbative ("trans-series") corrections. 2/ The authors give the *complete* trans-series: a perturbative basis obtained by solving ODEs starting from the known perturbative density expansion, with integration constants fixed via Volin's method. They check resurgence relations and high-precision numerics. 3/ As a bonus, the same machinery yields the full analytic trans-series for the capacitance of a coaxial circular plate capacitor — a classical electrostatics problem mapped onto the same integral equation.
Scientists wrote down every tiny correction to a famous quantum gas problem, and accidentally solved a capacitor problem too.
Abstract-only review; cannot verify the ODE derivations, the resurgence relation checks, or the matching to numerics. The claim is plausible and continues a well-established line of work by these authors and others on Volin's method, resurgence in integrable models, and the Love equation / coaxial capacitor problem (which is known to share an integral kernel with Lieb-Liniger). The methodology described — perturbative basis from ODEs, integration constants from Volin, cross-checks via resurgence and numerics — is standard in this subfield. Without the full text I set confidence LOW and verdict UNVERDICTED on the technical content; the abstract itself contains no red flags. The "complete" qualifier is the load-bearing word and would need scrutiny in the body.