46 research outputs found
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 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
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 ciĂŞncia 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 CrĂtica; 2016