Time delay statistics for chaotic cavities with absorption

We present a semiclassical approach for time delay statistics in quantum chaotic systems, in the presence of absorption, for broken time-reversal symmetry. We derive three kinds of expressions for Schur-moments of the time delay operator: as a power series in inverse channel number, $1\mathrm{/}M$, whose coefficients are rational functions of absorption time, ${\tau }_a$; as a power series in ${\tau }_a$, tailored to strong absorption, whose coefficients are rational functions of $M$; as a power series in $1\mathrm{/}{\tau }_a$, tailored to weak absorption, whose coefficients are rational functions of $M$.