Correlation functions and correlation widths in Quantum-Chaotic Scattering for mesoscopic systems and nuclei

We derive analytical expressions for the correlation functions of the electronic conductance fluctuations of an open quantum dot under several conditions. Both the variation of energy and that of an external parameter such as an applied perpendicular or parallel magnetic fields are considered in the general case of partial openness.. These expressions are then used to obtain the ensemble averaged density of maxima, a measure recently suggested to contain invaluable information concerning the chaoticity of the system. The correlation width is then calculated for the case of energy variation and a significant deviation from the Weisskopf estimate is found in the case of two terminals. The results are extended to more than two terminals. All our results are analytical.The use of these results in other fields, such as nuclei, where the system can only be studied through a variation of the energy, is then discussed.