Markov Approximation

The Markov Approximation assumes that the Correlation time is very short, namely ${\int }_0^t\mathrm{Tr}[V(t)V(\tau ){\rho }_B]d\tau ={\int }_0^t\mathrm{Tr}[V(t-\tau )V(0){\rho }_B]d\tau \approx {\int }_0^{\infty }\mathrm{Tr}[V(t-\tau )V(0){\rho }_B]d\tau$, where

• $\mathrm{Tr}[\cdot ]$ is the Trace
• $V$ is the … Help me ❓

The above results in the 2-time correlation function having most of it’s weight when the time is approximately equal to the Correlation time, i.e. $t\approx \tau$.