Non-Hamiltonian Dynamics of Quantized Vortices

The dynamics of quantized vortices in Bose-Einstein condensates are often modeled by a nonlinear Schr\"odinger equation. In contrast, we show that quantized vortices in fact obey a non-Hamiltonian evolution equation, which enhances dispersion and introduces a gain mechanism. These modifications allow the vortex medium to support helical excitations propagating ahead of a dissipative soliton capable of relaxing localized curvature events into packets of Kelvin waves. Such excitations, absent from previous local induction models, provide a pathway for decay in low-temperature quantum turbulence.