Quantum curl forces

Abstract Classical nonhamiltonian dynamics, driven by external ‘curl forces’ (which are not the gradient of a potential) is extended to the quantum domain. This is a generalisation of the two-stage Madelung procedure for the quantum Hamiltonian case: (i) considering not individual trajectories but families of them, characterised by their velocity and density fields (both functions of position and in general time); and (ii) adding the gradient of the quantum potential to the external curl force. Curl forces require the velocity field to have nonzero vorticity, so there is no underlying singlevalued wavefunction. Two explicit examples are presented. A possible experiment would be the motion of small particles with complex polarisability, influenced by forces from optical fields.