Statistical features of quantum evolution

摘要

It is shown that the integral of the uncertainty of energy with respect to time is independent of the particular Hamiltonian of the quantum system for an arbitrary pseudo-unitary (and hence PT-) quantum evolution. The result generalizes the time-energy uncertainty principle for pseudo-unitary quantum evolutions. Further, employing random matrix theory developed for pseudo-Hermitian systems, time correlation functions are studied in the framework of linear response theory. The results given here provide a quantum brachistochrone problem where the system will evolve in a thermodynamic environment with spectral complexity that can be modelled by random matrix theory.