Reply to Comment on: ``Rashba precession in quantum wire with interaction''

Recently a Comment appeared on the ArXiv preprint server [1] on my article ‘Rashba precession in quantum wires with interaction’ [2]. Its main statement is to question the dependence of the Rashba spin-orbit generated persistent spin current on the interaction. I demonstrate now that Comment [1] contains numerous faults, one of which leading to the above (mis)conclusion. The Author begins by stating that non-integer valued Jν would contradict to the seminal work by Haldane [3]. In this regard [2] carefully distinguishes between eigenvalues and expectation values at non-zero α and it are the latter for which Eq. (2) of [1] is correct (as clearly stated before Eq. (7) in [2]). It should be pointed out that the expression J̃σ found after Eq. (9) in [1] is noninteger either (qR = mα is tuned externally), contrary to what is stated one sentence later. Secondly, the Fermi velocities vFa in [1] are taken as spin dependent which in the effective mass description is erroneous at given Fermi energy. The effective mass description holds up to the perturbative order O(α), as is carefully derived in [2], cf. also [4]. The vFa in [1] describe a non-equilibrium situation. The main error, however, occurs in Eq. (10) of [1] where the shifted current J̃σ is inserted into the interaction, instead of the current Jσ. For not explicitly spin dependent interactions the Jσ = 0 state is of course the state of lowest interaction energy and not the state J̃σ = 0. Correct insertion would immediately lead to the (correct) result, Eq. (2) of [1]. In Eq. (10) of [1] the interaction depends on the Rashba coupling qR while the Rashba spin-orbit term depends explicitly on the interaction strength. Both is clearly not representing the model under consideration, the Rashba spin-orbit coupling being a single particle operator, cf. Eq. (1) of [2].