Time-dependent optical linewidth in fluctuating environments: Stochastic models

Time-resolved optical lineshapes are calculated using a second-order inhomogeneous cumulant expansion. The calculation shows that in the inhomogeneous limit the optical spectra are determined solely by two-time correlation functions. Therefore, measurements of the Stokes-shift correlation function and the inhomogeneous linewidth cannot provide information about the heterogeneity lifetime for systems exhibiting dynamic heterogeneities. The theoretical results are illustrated using a stochastic model for the optical transition frequencies. The model rests on the assumption that the transition frequencies are coupled to the environmental relaxation of the system. The latter is chosen according to a free-energy landscape model for dynamically heterogeneous dynamics. The model calculations show that the available experimental data are fully compatible with a heterogeneity lifetime on the order of the primary relaxation time.Comment: 19 pages, 4 figure

Nonresonant holeburning in the Terahertz range: Brownian oscillator model

The response to the field sequence of nonresonant hole burning, a pump-wait-probe experiment originally designed to investigate slow relaxation in complex systems, is calculated for a model of Brownian oscillators, thus including inertial effects. In the overdamped regime the model predictions are very similar to those of the purely dissipative stochastic models investigated earlier, including the possibility to discriminate between dynamic homogeneous and heterogeneous relaxation. The case of underdamped oscillations is of particular interest when low-frequency excitations in glassy systems are considered. We show that also in this situation a frequency selective modification of the response should be feasable. This means that it is possible to specifically address various parts of the spectrum. An experimental realization of nonresonant holeburning in the Terahertz regime therefore is expected to shed further light on the nature of the vibrations around the so-called boson peak.Comment: 23 pages, 6 figure

Nonlinear response theory for Markov processes IV: The asymmetric double well potential model revisited

The dielectric response of non-interacting dipoles is discussed in the framework of the classical model of stochastic reorientations in an asymmetric double well potential (ADWP). In the nonlinear regime, this model exhibits some pecularities in the static response. We find that the saturation behavior of the symmetric double well potential model does not follow the Langevin function and only in the linear regime the standard results are recovered. If a finite asymmetry is assumed, the nonlinear susceptibilities are found to change the sign at a number of characteristic temperatures that depend on the magnitude of the asymmetry, as has been observed earlier for the third-order and the fifth-order response. If the kinetics of the barrier crossing in the ADWP model is described as a two-state model, we can give analytical expressions for the values of the characteristic temperatures. The results for the response obtained from a (numerical) solution of the Fokker-Planck equation for the Brownian motion in a model ADWP behaves very similar to the two-state model for high barriers. For small barriers no clearcut time scale separation between the barrier crossing process and the intra-well relaxation exists and the model exhibits a number of time scales. In this case, the frequency-dependent linear susceptibility at low temperatures is dominated by the fast intra-well transitions and at higher temperatures by the barrier crossing kinetics. We find that for nonlinear susceptibilities the latter process appears to be more important and the intra-well transitions play only role at the lowest temperatures.Comment: 22 pages, 8 figures, revised version, accepted for publication in Phys. Rev.