We investigate the short-distance statistics of the local density of states <InlineEquation ID="Equ1"> <EquationSource Format="TEX">$\nu$</EquationSource> </InlineEquation> in long one-dimensional disordered systems, which display Anderson localization. It is shown that the probability distribution function <InlineEquation ID="Equ2"> <EquationSource Format="TEX">$P(\nu)$</EquationSource> </InlineEquation> can be recovered from the long-distance wavefunction statistics,...</equationsource></inlineequation></equationsource></inlineequation>

The quantum-limited line width of a laser cavity is enhanced above the Schawlow–Townes value by the Petermann factor K, due to the non-orthogonality of the cavity modes. We derive the relation between the Petermann factor and the residues of poles of the scattering matrix and investigate the...