Matrix Fluctuation−Dissipation Theorem: Application to Quantum Relaxation Phenomena

We recently derived a matrix fluctuation−dissipation (MFD) theorem, which directly relates the spectral intensities to the eigenvalue fluctuations of a quantum system. Here additional properties of the MFD theorem are presented. MFD is a microcanonical version of the fluctuation−dissipation theorem for a single high-energy state embedded in a dissipative quantum-mechanical bath. This is useful in applications to vibrational relaxation, which can be exactly described by the MFD formula if a single initial state carries all the oscillator strength. MFD versions of formulas for the dilution factor (σ) and fraction of occupied phase space ( F ) are derived, which can be used to compute these quantities exactly without knowledge of the eigenfunctions. Computational applications are given in a companion paper.