Vortex transport and screening in a closed two-dimensional Bose field: friction, transverse force and diffusion of quantized vortices, and the polarisability of the thermal vortex-pair gas, measured in an energy-conserving classical field with no reservoir and no fit parameter (version 2, revised after peer review)

Abstract

A quantized vortex in a thermal two-dimensional Bose gas is dragged by the normal fluid (friction α), pushed sideways by it (transverse coefficient α′) and kicked by it (diffusion η). We measure the three coefficients in the projected Gross-Pitaevskii equation — microcanonical, no damping term, no noise put in by hand — with sub-grid vortex tracking and estimators that are identities of the dissipative point-vortex model, machine-checked in Lean 4. Every hypothesis, gate and decision rule was committed before the corresponding run; the instrument failed its T = 0 control twice before it passed, an earlier gate verdict built on the flawed instrument is withdrawn, and both are reported. Results. At T/TBKT = 0.14, 0.27, 0.43: α = 0.0062(4), 0.014(2), 0.02(1), size- and estimator-independent, α ≈ 0.24 ρn/ρ. α′ is zero within 1% once the T = 0 compressible pair speed is subtracted; the Iordanskii value ρn/ρ is excluded at 18σ and the registered Iordanskii-like prediction is refuted. The Einstein relation is inconclusive by the registered rule (one admitted temperature at ηK/α = 2.1 ± 0.7; informally 1.4-3x, not 100x). Single pairs stop shrinking while the phonon band takes the impulse they shed (a self-generated counterflow with a published precedent in the truncated GPE); the decisive box-size control is not run. The single non-equilibrium pair that corrupts the superfluid-stiffness estimator in finite boxes decays by 4-27x given Lz-scaled time (six of six L = 192 trajectories admitted, one unfinished at t = 14 500). The pre-registered mode-by-mode dielectric relation fails in the thermal pair gas (coherence 0.06-0.28), while the vortex-charge structure factor equals the Kosterlitz-Thouless polarisability Σd2 from the measured pair sizes to 5-21%. The Josephson offset ηK − 1 = +0.3 survives at L = 192 in equilibrium, independent of fit window and torus geometry. Formal companions (Lean 4 / Mathlib, standard axioms): energy dissipation of any skew-plus-gradient vortex flow, the d2 law and lifetime bound, the centre-velocity identity, the wind stall, the zero-flux/Einstein equivalence, the pair-polarisation form and response ceiling, the charge-density/matching bound, the Kosterlitz-flow invariant, the bounded increments of quasi-periodic signals. Pre-registrations, amendments, gate records, data and code are in the software repository (concept DOI 10.5281/zenodo.22855581). No physics is claimed as new; the numbers, the refutations and the method are.