Anomalous scattering of low-lying excitations in a spin-1 Bose-Einstein condensate

We study the scattering of the transverse spin wave by an impurity potential in the ferromagnetic spin-1 Bose-Einstein condensate (BEC) by using the mean-field theory. We present a simpler framework of anomalous tunneling effect, the perfect transmission in the low-energy limit through an external potential barrier. The transverse spin wave obeys a Schrödinger-type equation; yet, the effects of the potential barrier on its transmission coefficient and on its scattering cross-section vanish in the low-energy limit. The modulus of the order parameter alone determines its transmission coefficient. The momentum p-dependence of the scattering cross-section σ exhibits a Rayleigh scattering type (σ ∝ p⁴). These properties are common to the transverse spin wave and the Bogoliubov mode, which belong to different types of Nambu-Goldstone modes.