Fig. 3
From: Ballistic transport and boundary resistances in inhomogeneous quantum spin chains
Profiles of the energy and magnetization currents during the relaxation process. Energy-transport scenario: a energy current profile for \(\gamma =\pi /4\) and several values of time. Spin-transport scenario: b spin current profile for \(\gamma =\pi /4\) and several value of time. In both (a) and (b), the dashed lines for negative/positive values of \(n/t\) are the results of the simulation of an homogeneous systems with the parameters of the left/right halves for \(t=40\), respectively. Internal light cone: c space-time plot of the left/right maxima \({n}_{L/R}^{^{\prime} }\) of the energy current profile for several values of \(\gamma\) (when only one maximum is detected we set \({n}_{L}^{^{\prime} }={n}_{R}^{^{\prime} }=0\)); d extrapolated velocity \({v}_{R}^{^{\prime} }\) of the internal light cone computed by fitting the data of (c) for \(30\le t\le 40\). The red line is obtained by fitting the data with \({v}_{R}^{^{\prime} }={\mathcal{A}}\,\Delta +{\mathcal{B}}\) which gives \({\mathcal{A}}=1.33\pm 0.06\) and \({\mathcal{B}}=-0.03\pm 0.03\). Error bars represent the standard deviation of the fitting parameters
