Damping-like effects in Heisenberg spin chain caused by the site-dependent bilinear interaction

Yu-Juan Zhang,Dun Zhao,Zai-Dong Li

Figure 2. Damping-like effects and oscillation of the spin components caused by β(t). In (a)–(c), β(t) = t, it is shown that with the time increasing, S1 → 1 and S2 → 0, S3 → 0 (the case of β(t) = 1 is similar), here β(t) gives rise to a damping-like effect. In (d)–(f), $\beta (t)=2\sin (t)$, it is clear that the spin components oscillate with β(t). The other parameters used are ω1 = 1, ω2 = 0, α(t) = 1, γ(t) = 0.