The first part of this dissertation is concerned with statistical properties of complex quantum systems that depend on an external parameter. The framework of the Gaussian random-matrix process is introduced and used to demonstrate that all parametric correlation functions become universal under the level-diffusion scaling of the parameter. Several eigenfunction correlators are obtained in their universal forms, including the parametric correlator of conductance peaks in quantum dots in the Coulomb-blockade regime. A new scaling procedure is introduced using a scaling factor that can be extracted from the eigenfunctions. The second part of this dissertation deals with aspects of the nuclear many-body problem. An approximation scheme for finite Fermionic systems at non-zero temperature, the perturbed static-path approximation, is presented. This method goes beyond both the random-phase and static-path approximations by incorporating small time-dependent fluctuations at each static configuration. Accurate results are obtained for observable expectation values and low moments of the strength function. The rotating-frame approach to nuclear reactions is used to show that a general multi-channel scattering problem can be transformed, under certain conditions, into a problem of single-channel scattering in a fluctuating potential.
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