troducing a time-dependent Hamiltonian. In the linear response situation, all the sensitivity of the scattering matrix to the perturbations lies in its parametric derivatives. Considering an adiabatic pump, the modulation frequency ω is assumed to be extremely small relative to the interaction time of the system. The current and noise vary linearly with ω , which is within the theory of an adiabatic pump 3 and demonstrated in experiment $^{1}$. The first term in Eq. (7) reflects the strength of the energy flow while the second one describes the effect of correlations between (quasi)-particles. A convenient measure of the correlation is F = ℏ ω 4 e 2 S$_{αβ}$ H$_{α}$ , which is the ratio of the dimensionless strength of the shot noise S$_{αβ}$ and the heat flow. The pump current and the noise experience sinusoidal and cosinusoidal variations as functions of the phase difference Δ ϕ = ϕ$_{1}$ − ϕ$_{2}$ respectively, as is evident in Eqs. (5) and (7). The relative noise F does not vary with Δ ϕ . In a magnetic nanowire with double sharp magnetic DWs, quantum interference results in the formation of spin-split quasistationary states localized mainly between the domain walls $^{24}$. Consequently, the DWs conductance exhibits typical resonant tunneling behaviour. The width of the resonance peaks is related to τ , the lifetime of the quasistationary spin quantum well states. τ is determined by the spin-mixing due to the spin noncollinearity at the DWs and can be quantified by the spin-mixing parameter Δ ≡ 4 m Θ δ/ ℏ $^{2}$. Decreasing Δ, the lifetime of the localized spin quantum-well states increases and the conductance resonance peaks become correspondingly narrower. By oscillating the gate potential and the magnetic field strength out of phase at zero bias, a quantum pump is realized as the electronic system gains energy from the oscillating scatterer. Absorption of an energy quantum ℏ ω leads to creation of a nonequilibrium quasi-electron-hole pair. If they are scattered into different leads, their motion generates current. In the adiabatic quantum pump based on domain walls in a magnetic nanowire considered here, the two parameters are the Fermi energy and the magnetization strength, which excite the pump. The Fermi energy can be modulated by an ac gate voltage and the magnetization strength can be modulated by an ac magnetic field. Analogously to the adiabatic quantum electron pump theoretically proposed in Ref. 2 and experimentally realized in the quantum dot system $^{1}$, in our case the oscillating magnetization acts as an oscillating energy potential 8 III. NUMERICAL RESULTS AND INTERPRETATIONS