We calculate the effect of a heat current on transporting $^3$He dissolved in superfluid $^4$He at ultralow concentration, as will be utilized in a proposed experimental search for the electric dipole moment of the neutron (nEDM). In this experiment, a phonon wind will generated to drive (partly depolarized) $^3$He down a long pipe. In the regime of $^3$He concentrations $\tilde < 10^{-9}$ and temperatures $\sim 0.5$ K, the phonons comprising the heat current are kept in a flowing local equilibrium by small angle phonon-phonon scattering, while they transfer momentum to the walls via the $^4$He first viscosity. On the other hand, the phonon wind drives the $^3$He out of local equilibrium via phonon-$^3$He scattering. For temperatures below $0.5$ K, both the phonon and $^3$He mean free paths can reach the centimeter scale, and we calculate the effects on the transport coefficients. We derive the relevant transport coefficients, the phonon thermal conductivity and the $^3$He diffusion constants from the Boltzmann equation. We calculate the effect of scattering from the walls of the pipe and show that it may be characterized by the average distance from points inside the pipe to the walls. The temporal evolution of the spatial distribution of the $^3$He atoms is determined by the time dependent $^3$He diffusion equation, which describes the competition between advection by the phonon wind and $^3$He diffusion. As a consequence of the thermal diffusivity being small compared with the $^3$He diffusivity, the scale height of the final $^3$He distribution is much smaller than that of the temperature gradient. We present exact solutions of the time dependent temperature and $^3$He distributions in terms of a complete set of normal modes.
Superfluid spin transport in ferro- and antiferromagnets
本文着重于自旋超流输运，最近在反铁磁体Cr $_2$ O $_3$中报道了对自旋超流输运的观察[Yuan et al.，Sci. Adv. 4，eaat1098（2018）]。本文分析了耗散在非相干磁振子注入自旋流到注入自旋界面附近的超流自旋流转变中的作用。Landau-Lifshitz-Gilbert理论中的Gilbert阻尼参数没有正确描述耗散，耗散参数是从缺陷散射的磁振子的Boltzmann方程计算的。双流体理论的发展类似于超流体的双流体理论。这一理论表明，在低温下，体温度变化对超流自旋输运（体塞贝克效应）的影响很弱。本文还讨论了Yuan等人的结果与自旋探测器与样品界面处的Seebeck效应有关的情况。由集体自旋模谱导出了反铁磁体在磁场中的朗道判据。朗道不稳定性开始在gapped模式早于在戈德斯通gapless模式，在易平面铁磁体的戈德斯通模式变得不稳定。确定了实验中磁涡旋的几何结构。涡核具有垂直于磁场的有限磁化分量的skyrmion结构。这种磁化在涡旋线从样品的出口点周围产生杂散磁场，其可用于涡旋的实验检测。
