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Gregor Diezemann

Publications and source records attributed to Gregor Diezemann.

27 records · Page 2Linked to original sources
arXiv2005

Kerr effect as a tool for the investigation of dynamic heterogeneities

We propose a dynamic Kerr effect experiment for the distinction between dynamic heterogeneous and homogeneous relaxation in glassy systems. The possibility of this distinction is due to the inherent nonlinearity of the Kerr effect signal. We model the slow reorientational molecular motion in supercooled liquids in terms of non-inertial rotational diffusion. The Kerr effect response, consisting of two terms, is calculated for heterogeneous and for homogeneous variants of the stochastic model. It turns out that the experiment is able to distinguish between the two scenarios. We furthermore show that exchange between relatively 'slow' and 'fast' environments does not affect the possibility of frequency-selective modifications. It is demonstrated how information about changes in the width of the relaxation time distribution can be obtained from experimental results.

cond-mat.soft↗
arXiv2005

Aging in a free-energy landscape model for glassy relaxation

The aging properties of a simple free-energy landscape model for the primary relaxation in supercooled liquids are investigated. The intermediate scattering function and the rotational correlation functions are calculated for the generic situation of a quench from a high temperature to below the glass transition temperature. It is found that the re-equilibration of molecular orientations takes longer than for translational degrees of freedom. The time scale for re-equilibration is determined by that of the primary relaxation as an intrinsic property of the model.

cond-mat.soft↗
arXiv2003

Fluctuation-dissipation relations for a general class of master equations

The fluctuation-dissipation relation is calculated for a class of stochastic models obeying a master equation. The transition rates are assumed to obey detailed balance also in the presence of a field. It is shown that in general the linear response cannot be expressed via time-derivatives of the correlation function alone, but an additional function $ξ(t,t_w)$, which has been rarely discussed before is required. This function depends on the two times also relevant for the response and the correlation and vanishes under equilibrium conditions. It can be expressed in terms of the propagators and the transition rates of the master equation but it is not related to any physical observable in an obvious way. Instead, it is determined by inhomogeneities in the temporal evolution of the distribution function of the stochastic variable under consideration. $ξ(t,t_w)$ is considered for some examples of stochastic models, some of which exhibit true non-equilibrium dynamics and others approach equilibrium in the long term. In particular, models in which a relevant variable, e.g. a magnetization, is related in a prescribed way to the states of the system are considered as projections from a composite Markov process. From these model calculations, it is conjectured that $ξ(t,t_w)$ vanishes when one is concerned with measurements of the analogue of a structure factor for large wave-vectors or if every transition among the states randomizes the value of the stochastic variable considered.

cond-mat.stat-mech↗
arXiv2003

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.

cond-mat↗
arXiv2003

Dynamic heterogeneities in the out-of-equilibrium dynamics of simple spherical spin models

The response of spherical two-spin interaction models, the spherical ferromagnet (s-FM) and the spherical Sherrington-Kirkpatrick (s-SK) model, is calculated for the protocol of the so-called nonresonant hole burning experiment (NHB) for temperatures below the respective critical temperatures. It is shown that it is possible to select dynamic features in the out-of-equilibrium dynamics of both models, one of the hallmarks of dynamic heterogeneities. The behavior of the s-SK model and the s-FM in three dimensions is very similar, showing dynamic heterogeneities in the long time behavior, i.e. in the aging regime. The appearence of dynamic heterogeneities in the s-SK model explicitly demonstrates that these are not necessarily related to {\it spatial} heterogeneities. For the s-FM it is shown that the nature of the dynamic heterogeneities changes as a function of dimensionality. With incresing dimension the frequency selectivity of the NHB diminishes and the dynamics in the mean-field limit of the s-FM model becomes homogeneous.

cond-mat↗
arXiv2001

Stochastic models for heterogeneous relaxation: Application to inhomogeneous optical lineshapes

Dynamic heterogeneity has often been modeled by assuming that a single-particle observable, fluctuating at a molecular scale, is influenced by its coupling to environmental variables fluctuating on a second, perhaps slower, time scale. Starting from the most simple Gaussian Markov process we model the exchange between 'slow' and 'fast' environments by treating the fluctuating single-particle variable as a projection from a higher-dimensional Markov process. The moments of the resulting stochastic process are calculated from the corresponding Master equations or Langevin equations, depending on the model. The calculations show the importance of the way to treat exchange processes. The resulting stochastic process is non-Markovian for all models. However, the deviations from a Gaussian behavior depend on the details of the models. A comparison of our results with other model treatments and experiments should provide further insight into the concept of dynamic heterogeneity.

cond-mat↗
arXiv2001

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.

cond-mat↗
arXiv2000

Response-theory for nonresonant hole burning: Stochastic dynamics

Using non-linear response theory the time signals relevant for nonresonant spectral hole burning are calculated. The step-reponse function following the application of a high amplitude ac field (pump) and an intermediate waiting period is shown to be the sum of the equilibrium integrated response and a modification due to the preparation via ac irradiation. Both components are calculated for a class of stochastic dipole reorientation models. The results indicate that the method can be used for a clearcut distinction of homogeneously and heterogeneously broadened susceptibilities as they occur in the relaxation of supercooled liquids or other disordered materials. This is because only in the heterogeneous case is a frequency selective modification of the response possible.

cond-mat↗