A far-wing line shape theory which satisfies the detailed balance principle

Abstract

A far-wing line shape theory in which the validity of the detailed balance principle is maintained in each step of the derivation is presented. The role of the total density matrix including the initial correlations is analyzed rigorously. By factoring out the rapidly varying terms in the complex-time development operator in the interaction representation, better approximate expressions can be obtained. As a result, the spectral density, the Fourier transform of the dipole correlation function, can be expressed in terms of line-coupling functions in which two coupled lines are arranged symmetrically and whose frequency detunings are ω − 1 2 (ω ji + ω j′i′ ) . Using the approximate detunings ω — ω ji results in expressions that do not satisfy the detailed balance principle. However, this principle remains satisfied for the symmetrized spectral density in which not only the coupled lines are arranged symmetrically, but also the initial and final states belonging to the same lines are arranged symmetrically as well.