I was interested in the spectral theory of non-Hermitian systems for two reasons: 1) analytical results on the spectral property of non-Hermitian systems were unknown and new techniques appear to be required, and 2) from the spectral property we can obtain time-dependent physically measurable quantities. For example, in the case of the Fokker-Planck operator, which describes the classic advection-diffusion problems, one can obtain from the spectra the time dependent diffusivity. John Chalker and I developed a general analytical technique using diagrammatic expansion to calculate the spectral properties of random non-Hermitian systems. By applying our technique to the diffusion-advection system, we discovered a novel scaling in effective diffusion at short times. The method also has broad applications to general non-Hermitian systems, such as the recently much discussed models of flux lines in superconductors.