Quantum fluctuation-dissipation theorem: a time domain formulation

A time-domain formulation of the equilibrium quantum fluctuation-dissipation theorem (FDT) in the whole range of temperatures is presented. In the classical limit, the FDT establishes a proportionality relation between the dissipative part of the linear response function and the derivative of the corresponding equilibrium correlation function. At zero temperature, the FDT takes the form of Hilbert transform relations between the dissipative part of the response function and the corresponding symmetrized equilibrium correlation function, which allows to establish a connection with analytic signal theory. The time-domain formulation of the FDT is especially valuable when out-of-equilibrium dynamics is concerned, as it is for instance the case in the discussion of aging phenomena.