Stability Estimate in Scattering Theory and Its Application to Mesoscopic Systems and Quantum Chaos

We consider scattering of a free quantum particle on a singular potential with rather arbitrary shape of the support of the potential. In the classical limit $\mathrm{\hslash }=0$ this problem reduces to the well known problem of chaotic scattering. The universal estimates for the stability of the scattering amplitudes are derived. The application of the obtained results to the mesoscopic systems and quantum chaos are discussed. We also discuss a possibility of experimental verification of the obtained results.