Decoherence Time

$\tau :=\frac{2}{(e_i-e_j{)}^2}$ is known as the decoherence time. This term shows up during the evolution of a Reduced system, where the entry ${\rho }_{ij}$ of the Density Operator is given by ${\rho }_{ij}(t)={\rho }_{ij}(0)e^{-\frac{1}{2}(e_i-e_j{)}^{2}t}={\rho }_{ij}(0)e^{t{\tau }_{ij}^{-1}}$.

The shorter the decoherence time, the faster our system’s Density Matrix moves towards the diagonal.