Figure 1

Dynamics of two-time correlation functions in the short-time limit for (a) \(\langle \sigma _x(t)\sigma _y(0)\rangle\) and (c) \(\langle \sigma _+(t)\sigma _-(0)\rangle\), in the Markov limit (green dotted line, \(\gamma =10\)), and the non-Markovian regime (\(\gamma =0.5\) red solid line, and \(\gamma =2\) blue dashed line). The Fourier spectral functions, \(\mathrm {S}(\omega )\), of \(\langle \sigma _x(t)\sigma _y(0)\rangle\) and \(\langle \sigma _+(t)\sigma _-(0)\rangle\) are shown in (b,d) respectively. Other parameters are chosen as \(\omega =1\), \(\Gamma =1\).