Reactive force on a moving vortex from the adiabatic spectral flow

Makhlin Yu.G., Misirpashaev T.Sh.

**We calculate the contribution to the parameter ***D' *of the reactive force acting on a moving vortex, which arises from the spectral flow of localized gapless fermions. Our consideration is valid in the regime *u>qt ***<^ 1 and also limited to the adiabatic case ***v^kjrr *<[ 1 since we use the stationary density matrix. We assume discrete equidistant fermion spectra and show that the answer is the same as that obtained by Volovik in the continuous limit, namely, *D*^{9} _{c} _{flow} -mfc^,/6ir^{2} per each anomalous branch. The result applies for the temperatures Τ < ç«. **A possible extension to the temperatures close to ***T*_{c} is suggested.