Fig. 1

Transport in inhomogeneous spin chains. a An inhomogeneous quantum spin-1/2 chain composed of an XX and of an XXZ half is initialized in a pure state with energy or magnetization imbalance and subsequently evolved in time. The relaxation dynamics inside the light cone (thick black lines, velocities \({v}_{L,R}\)) witnesses the coexistence of two (intermediate) ballistic regions and of two slow relaxation regions. The slow dynamics initially takes place inside an internal light cone with velocities \({v}_{L,R}^{^{\prime} }\), while, at long times, the extension of these regions remains constant in time. b Space-time profile of the energy current for \(\Delta =\cos (\pi /4)\) — see Eq. (1). At long enough times, a decay of the current at the junction appears as a consequence of a thermalization process