Statistics of resonance width shifts as a signature of eigenfunction   non-orthogonality
  We consider an open (scattering) quantum system under the action of a perturbation of its closed counterpart. It is demonstrated that the resulting shift of resonance widths is a sensitive indicator of the non-orthogonality of resonance wavefunctions, being zero only if those were orthogonal. Focusing further on chaotic systems, we employ random matrix theory to introduce a new type of parametric statistics in open systems, and derive the distribution of the resonance width shifts in the regime of weak coupling to the continuum. 
Y. V. Fyodorov and D. V. Savin
cond-mat.mes-hall math-ph math.MP nlin.CD nucl-th