Yu. Makhlin and T. Misirpashaev
Landau Institute for Theoretical Physics, Kosygin St. 2, 117334 Moscow, Russia

Reactive force on a moving vortex from the adiabatic spectral flow

JETP Lett. 62, 83 (1995) [Pisma v ZhETF 62, 74 (1995)]

We calculate the contribution to the parameter D' from the reactive force acting on a moving vortex as a result of the spectral flow of localized gapless fermions. Our treatment is valid in the regime omega₀ tau<<1 and is restricted to the adiabatic case v_L k_F tau<<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'_spec.flow=mk³_F/6 pi² per anomalous branch. The result applies at temperatures T << T_c. A possible extension to temperatures close to T_c is suggested.