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.Comment: revised version, 7 pages, 2 figure

Statistics of reversible bond dynamics observed in force-clamp spectroscopy

We present a detailed analysis of two-state trajectories obtained from force-clamp spectroscopy (FCS) of reversibly bonded systems. FCS offers the unique possibility to vary the equilibrium constant in two-state kinetics, for instance the unfolding and refolding of biomolecules, over many orders of magnitude due to the force dependency of the respective rates. We discuss two different kinds of counting statistics, the event-counting usually employed in the statistical analysis of two-state kinetics and additionally the so-called cycle-counting. While in the former case all transitions are counted, cycle-counting means that we focus on one type of transitions. This might be advantageous in particular if the equilibrium constant is much larger or much smaller than unity because in these situations the temporal resolution of the experimental setup might not allow to capture all transitions of an event-counting analysis. We discuss how an analysis of FCS data for complex systems exhibiting dynamic disorder might be performed yielding information about the detailed force-dependence of the transition rates and about the time scale of the dynamic disorder. In addition, the question as to which extent the kinetic scheme can be viewed as a Markovian two-state model is discussed.Comment: 25 pages, 10 figures, Phys. Rev. E, in pres

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.Comment: 16 pages, 8 figure

Rotational Correlation Functions of Single Molecules

Single molecule rotational correlation functions are analyzed for several reorientation geometries. Even for the simplest model of isotropic rotational diffusion our findings predict non-exponential correlation functions to be observed by polarization sensitive single molecule fluorescence microscopy. This may have a deep impact on interpreting the results of molecular reorientation measurements in heterogeneous environments.Comment: 5 pages, 4 figure

Non-Arrhenius Behavior of Secondary Relaxation in Supercooled Liquids

Dielectric relaxation spectroscopy (1 Hz - 20 GHz) has been performed on supercooled glass-formers from the temperature of glass transition (T_g) up to that of melting. Precise measurements particularly in the frequencies of MHz-order have revealed that the temperature dependences of secondary beta-relaxation times deviate from the Arrhenius relation in well above T_g. Consequently, our results indicate that the beta-process merges into the primary alpha-mode around the melting temperature, and not at the dynamical transition point T which is approximately equal to 1.2 T_g.Comment: 4 pages, 4 figures, revtex

Nonequilibrium Linear Response for Markov Dynamics, II: Inertial Dynamics

We continue our study of the linear response of a nonequilibrium system. This Part II concentrates on models of open and driven inertial dynamics but the structure and the interpretation of the result remain unchanged: the response can be expressed as a sum of two temporal correlations in the unperturbed system, one entropic, the other frenetic. The decomposition arises from the (anti)symmetry under time-reversal on the level of the nonequilibrium action. The response formula involves a statistical averaging over explicitly known observables but, in contrast with the equilibrium situation, they depend on the model dynamics in terms of an excess in dynamical activity. As an example, the Einstein relation between mobility and diffusion constant is modified by a correlation term between the position and the momentum of the particle

Non-equilibrium dynamics of spin facilitated glass models

We consider the dynamics of spin facilitated models of glasses in the non-equilibrium aging regime following a sudden quench from high to low temperatures. We briefly review known results obtained for the broad class of kinetically constrained models, and then present new results for the behaviour of the one-spin facilitated Fredrickson-Andersen and East models in various spatial dimensions. The time evolution of one-time quantities, such as the energy density, and the detailed properties of two-time correlation and response functions are studied using a combination of theoretical approaches, including exact mappings of master operators and reductions to integrable quantum spin chains, field theory and renormalization group, and independent interval and timescale separation methods. The resulting analytical predictions are confirmed by means of detailed numerical simulations. The models we consider are characterized by trivial static properties, with no finite temperature singularities, but they nevertheless display a surprising variety of dynamic behaviour during aging, which can be directly related to the existence and growth in time of dynamic lengthscales. Well-behaved fluctuation-dissipation ratios can be defined for these models, and we study their properties in detail. We confirm in particular the existence of negative fluctuation-dissipation ratios for a large number of observables. Our results suggest that well-defined violations of fluctuation-dissipation relations, of a purely dynamic origin and unrelated to the thermodynamic concept of effective temperatures, could in general be present in non-equilibrium glassy materials.Comment: 72 pages, invited contribution to special issue of JSTAT on "Principles of Dynamics of Nonequilibrium Systems" (Programme at Newton Institute Cambridge). v2: New data added to Figs. 11, 23, 24, new Fig. 26 on East model in d=3, minor improvements to tex

Harmonic Vibrational Excitations in Disordered Solids and the "Boson Peak"

We consider a system of coupled classical harmonic oscillators with spatially fluctuating nearest-neighbor force constants on a simple cubic lattice. The model is solved both by numerically diagonalizing the Hamiltonian and by applying the single-bond coherent potential approximation. The results for the density of states $g(\omega)$ are in excellent agreement with each other. As the degree of disorder is increased the system becomes unstable due to the presence of negative force constants. If the system is near the borderline of stability a low-frequency peak appears in the reduced density of states $g(\omega)/\omega^2$ as a precursor of the instability. We argue that this peak is the analogon of the "boson peak", observed in structural glasses. By means of the level distance statistics we show that the peak is not associated with localized states

Two refreshing views of Fluctuation Theorems through Kinematics Elements and Exponential Martingale

In the context of Markov evolution, we present two original approaches to obtain Generalized Fluctuation-Dissipation Theorems (GFDT), by using the language of stochastic derivatives and by using a family of exponential martingales functionals. We show that GFDT are perturbative versions of relations verified by these exponential martingales. Along the way, we prove GFDT and Fluctuation Relations (FR) for general Markov processes, beyond the usual proof for diffusion and pure jump processes. Finally, we relate the FR to a family of backward and forward exponential martingales.Comment: 41 pages, 7 figures; version2: 45 pages, 7 figures, minor revisions, new results in Section

Biografische Materialien als Bildungsgelegenheit in erziehungswissenschaftlichen Studiengängen. Oder: Warum ein Seminar zu Vätern in Elternzeit? Materials biográficos como fonte de pesquisa em programas de ciência de educação. Ou: por que en seminário de pesquisa sobre pais em licença-paternidade?

Demmer C. Biografische Materialien als Bildungsgelegenheit in erziehungswissenschaftlichen Studiengängen. Oder: Warum ein Seminar zu Vätern in Elternzeit? Materials biográficos como fonte de pesquisa em programas de ciência de educação. Ou: por que en seminário de pesquisa sobre pais em licença-paternidade? In: Diezemann E, Moura RA, eds. Biosphere of Educational Studies. Aspects of a Brazilian - German cooperation between two universities. Campinas, BRA: Edições Leitura Crítica; 2016