# Research news

F. Ginot, J. Caspers, M. Krüger, C. Bechinger, Phys. Rev. Lett. 128, 028001 (2022)

**Description:**
We investigate the hopping dynamics of a colloidal particle across a potential barrier
and withina viscoelastic, i.e., non Markovian bath, and report two clearly separated time
scales in the corresponding waiting time distributions. While the longer time scale exponentially
depends on the barrier height, the shorter one is similar to the relaxation time of the fluid.
This short time scale is a signature of the storage and release of elastic energy inside the bath,
that strongly increases the hopping rate. Our results are in excellent agreement with numerical
simulations of a simple Maxwell model.
(link)

M. Lee, RLC Vink, CA Volkert, M. Krüger, Phys. Rev. B 104, 174309 (2021)

**Description:**
While obtaining theoretical predictions for dissipation during sliding motion is a difficult task,
one regime that allows for analytical results is the so-called noncontact regime, where a probe is weakly
interacting with the surface over which it moves. Studying this regime for a model crystal, we extend
previously obtained analytical results and confirm them quantitatively via particle based computer
simulations. Accessing the subtle regime of weak coupling in simulations is possible via use of Green-Kubo
relations. The analysis allows to extract and compare the two paradigmatic mechanisms that have been found
to lead to dissipation: phonon radiation, prevailing even in a purely elastic solid, and phonon damping, e.g.,
caused by viscous motion of crystal atoms. While phonon radiation is dominant at large probe-surface distances,
phonon damping dominates at small distances. Phonon radiation is furthermore a pairwise additive phenomenon so
that the dissipation due to interaction with different parts (areas) of the surface adds up. This additive
scaling results from a general one-to-one mapping between the mean probe-surface force and the friction due
to phonon radiation, irrespective of the nature of the underlying pair interaction. In contrast, phonon damping
is strongly non-additive, and no such general relation exists. We show that for certain cases, the dissipation
can even decrease with increasing surface area the probe interacts with. The above properties, which are rooted
in the spatial correlations of surface fluctuations, are expected to have important consequences when
interpreting experimental measurements, as well as scaling with system size.
(link)

R. Jain, F. Ginot, M. Krüger, Physics of Fluids 33, 103101 (2021)

**Description:**
The motion of Brownian particles in nonlinear baths, such as, e.g., viscoelastic fluids,
is of great interest. We theoretically study a simple model for such bath, where two particles
are coupled via a sinusoidal potential. This model, which is an extension of the famous Prandtl
Tomlinson model, has been found to reproduce some aspects of recent experiments, such as shear-thinning
and position oscillations [J. Chem. Phys. 154, 184904 (2021)]. Analyzing this model in detail,
we show that the predicted behavior of position oscillations agrees qualitatively with experimentally
observed trends; (i) oscillations appear only in a certain regime of velocity and trap stiffness
of the confining potential, and (ii), the amplitude and frequency of oscillations increase with driving
velocity, the latter in a linear fashion. Increasing the potential barrier height of the model yields
a rupture transition as a function of driving velocity, where the system abruptly changes from a mildly
driven state to a strongly driven state. The frequency of oscillations scales as (v0-v0∗)1=2 near the
rupture velocity v0∗, found for infinite trap stiffness. Investigating the (micro-)viscosity for different
parameter ranges, we note that position oscillations leave their signature by an additional (mild) plateau
in the flow curves, suggesting that oscillations influence the micro-viscosity. For a time-modulated
driving, the mean friction force of the driven particle shows a pronounced resonance behavior, i.e,
it changes strongly as a function of driving frequency. The model has two known limits: For infinite
trap stiffness, it can be mapped to diffusion in a tilted periodic potential. For infinite bath friction,
the original Prandtl Tomlinson model is recovered. We find that the flow curve of the model (roughly)
crosses over between these two limiting cases.
(link)

R. Jain, F. Ginot, M. Krüger, J. Phys.: Condens. Matter 33, 405101 (2021)

**Description:**
We present a comprehensive study of the linear response of interacting underdamped Brownian particles
to simple shear flow. We collect six different routes for computing the response, two of which are based
on the symmetry of the considered system and observable with respect to the shear axes. We include
the extension of the Green-Kubo relation to underdamped cases, which shows two unexpected additional
terms. These six computational methods are applied to investigate the relaxation of the response towards
the steady state for different observables, where interesting effects due to interactions and a finite
particle mass are observed. Moreover, we compare the different response relations in terms of their
statistical efficiency, identifying their relative demand on experimental measurement time or computational
resources in computer simulations. Finally, several measures of breakdown of linear response theory
for larger shear rates are discussed.
(link)

R. Jain, F. Ginot, J. Berner, C. Bechinger, M. Krüger, J. Chem. Phys. 154, 184904 (2021)

**Description:**
We perform micro-rheological experiments with a colloidal bead driven through a viscoelastic
worm-like micellar fluid and observe two distinctive shear thinning regimes, each of them displaying
a Newtonian-like plateau. The shear thinning behavior at larger velocities is in qualitative agreement
with macroscopic rheological experiments. The second process, observed at Weissenberg numbers as small
as a few percent, appears to have no analog in macro rheological findings. A simple model introduced
earlier captures the observed behavior, and implies that the two shear thinning processes correspond
to two different length scales in the fluid. This model also reproduces oscillations which have been
observed in this system previously. While the system under macro-shear seems to be near equilibrium
for shear rates in the regime of the intermediate Newtonian-like plateau, the one under micro-shear is
thus still far from it. The analysis suggests the existence of a length scale of a few micrometres,
the nature of which remains elusive.
(link)

T. Holsten and M. Krüger, Phys. Rev. E 103, 032116 (2021)

**Description:**
The fluctuation-dissipation-theorem connects equilibrium to mildly (linearly) perturbed situations
in a thermodynamic manner: It involves the observable of interest and the entropy production caused
by the perturbation. We derive a relation which connects responses of arbitrary order in perturbation
strength to correlations of entropy production of lower order, thereby extending the
fluctuation-dissipation-theorem to cases far from equilibrium in a thermodynamic way. The relation
is validated and studied for a 4-state-model.
(link)