Anatomy of spin wave driven magnetic texture motion via magnonic torques

The interplay between spin wave and magnetic texture represents the information exchange between the fast and slow dynamical parts of magnetic systems. Here we formulate a set of magnonic torques acting on background magnetic texture, by extracting time-invariant information from the fast precessing spin waves. Under the frame of magnonic torques, we use theoretical formulations and micromagnetic simulations to investigate the spin wave driven domain wall motion in two typical symmetry-breaking situations: the rotational symmetry broken by the Dzyaloshinkii-Moriya interaction, and the translational symmetry broken by magnetic damping. The torque-based microscopic analyses provide compact yet quantitative tools to reinterpret the magnetic texture dynamics induced by spin wave, beyond the conventional framework of global momentum conservation.Comment: 12 pages, 4 figure

Karhunen-Lo\`eve expansion for a generalization of Wiener bridge

We derive a Karhunen-Lo\`eve expansion of the Gauss process $B_t - g(t)\int_0^1 g'(u)\,d B_u$, $t\in[0,1]$, where $(B_t)_{t\in[0,1]}$ is a standard Wiener process and $g:[0,1]\to R$ is a twice continuously differentiable function with $g(0) = 0$ and $\int_0^1 (g'(u))^2\,d u =1$. This process is an important limit process in the theory of goodness-of-fit tests. We formulate two special cases with the function $g(t)=\frac{\sqrt{2}}{\pi}\sin(\pi t)$, $t\in[0,1]$, and $g(t)=t$, $t\in[0,1]$, respectively. The latter one corresponds to the Wiener bridge over $[0,1]$ from $0$ to $0$.Comment: 25 pages, 1 figure. The appendix is extende