The Role of Boltzmann Factors in Line Shape

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Abstract
A study is made of the effect of temperature and environment on the absorption spectra of simple systems. In part I the longitudinal and transverse susceptibilities of a two-level system are analyzed in terms of simple stochastic models. Particular attention is paid to the different roles played by the phase-interruption and frequency-modulation mechanisms. A calculation is given of the susceptibility of a harmonic oscillator perturbed by interaction with other oscillators. In part II the same systems are studied using Green's function methods. It is assumed that the two-level system is coupled to a crystal lattice by an isotropic interaction that is linear in the lattice displacement. Expressions are obtained for the longitudinal and transverse susceptibilities and comparison is made with the results of part I. The susceptibility of the harmonic oscillator is calculated and found to be identical to the susceptibility obtained by more elementary methods.