# Research news

T.M. Muenker, G. Knotz, M. Krüger, T. Betz, Nat. Mat. ("in principle" accepted)

**Description:**
Understanding life is arguably among the most complex scientific problems faced in modern research. From a physics perspective, living systems are complex dynamic entities that operate far from thermo-dynamic equilibrium.1–3 This active, non-equilibrium behaviour, with its constant hunger for energy, allows life to overcome the ever dispersing forces of entropy, and hence drives cellular organisation and dynamics at the micrometer scale.4,5 Unfortunately, most analysis methods provided by the powerful toolbox of statistical mechanics cannot be used in such non-equilibrium situations, forcing researchers to use sophisticated and often invasive approaches to study the mechanistic processes inside living organisms. Here we introduce a new observable coined the mean back relaxation, that allows simple detection of broken detailed balance and full quantification of the active mechanics from passively observed particle trajectories. Based on three-point probabilities and exploiting Onsager’s regression hypothesis, the mean back relaxation extracts more information from passively measurements compared to classical observables such as the mean squared displacement. We show that it gives access to the non-equilibrium generating energy and the viscoelastic material properties of a well controlled artificial system, and, surprisingly, also of a variety of living systems. It thus acts as a new marker of non-equilibrium dynamics, a statement based on an astonishing relation between the mean back relaxation and the active mechanical energy. Combining, in a next step, passive fluctuations with the extracted active energy allows to overcome a fundamental barrier in the study of living systems; it gives access to the viscoelastic material properties from passive measurements.
(link)

M. Krüger, K. Asheichyk, M. Kardar, R. Golestanian, Phys. Rev. Lett. (in print)

**Description:**
We develop a theory for heat transport via electromagnetic waves inside media, and use it to derive a spatially nonlocal thermal conductivity tensor, in terms of the electromagnetic Green's function and potential, for any given system. While typically negligible for optically dense bulk media, the electromagnetic component of conductivity can be significant for optically dilute media, and shows regimes of Fourier transport as well as unhindered transport. Moreover, the electromagnetic contribution is relevant even for dense media, when in presence of interfaces, as exemplified for the in-plane conductivity of a nanosheet, which shows a variety of phenomena, including absence of a Fourier regime. (link)

with David Gelbwaser (Technion)

**Description:**
Our group will be funded by the Volkswagen Foundation to explore Casimir forces in non-equilibrium situations and non-reciprocal media. (See reference on propulsion forces below)
(link)

X. Cao, D. Das, N. Windbacher, F. Ginot, M. Krüger, C. Bechinger Nat. Phys. 19, 1904 (2023)

**Description:**
Spinning objects moving through air or a liquid experience a lift force—a phenomenon known as the Magnus effect. This effect is commonly exploited in ball sports but also is of considerable importance for applications in the aviation industry. Whereas Magnus forces are strong for large objects, they are weak at small scales and eventually vanish for overdamped micrometre-sized particles in simple liquids. Here we demonstrate a roughly one-million-fold enhanced Magnus force of spinning colloids in viscoelastic fluids. Such fluids are characterized by a time-delayed response to external perturbations, which causes a deformation of the fluidic network around the moving particle. When the particle also spins, the deformation field becomes misaligned relative to the particle’s moving direction, leading to a force perpendicular to the direction of travel and the spinning axis. Our uncovering of strongly enhanced memory-induced Magnus forces at microscales opens up applications for particle sorting and steering, and the creation and visualization of anomalous flows.
(link)

K. Asheichyk, M. Krüger Phys. Rev. Lett. 129, 170605 (2022)

**Description:**
Radiative heat transfer between two far-field-separated nanoparticles placed close to a perfectly conducting nanowire decays logarithmically slow with the interparticle distance. This makes a cylinder an excellent waveguide which can transfer thermal electromagnetic energy to arbitrary large distances with almost no loss. It leads to a dramatic increase of the heat transfer, so that, for almost any (large) separation, the transferred energy can be as large as for isolated particles separated by a few hundred nanometers. A phenomenologically found analytical formula accurately describes the numerical results over a wide range of parameters.
(link)

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)

D. Gelbwaser-Klimovsky, N. Graham, M. Kardar, and M. Krüger Phys. Rev. Lett. 126, 170401 (2021)

**Description:**
Arguments based on symmetry and thermodynamics may suggest the existence of a ratchetlike lateral Casimir force between two plates at different temperatures and with broken inversion symmetry. We find that this is not sufficient, and at least one plate must be made of nonreciprocal material. This setup operates as a heat engine by transforming heat radiation into mechanical force. Although the ratio of the lateral force to heat transfer in the near field regime diverges inversely with the plates separation, d, an Onsager symmetry, which we extend to nonreciprocal plates, limits the engine efficiency to the Carnot value ηc. The optimal velocity of operation in the far field is of the order of cηc, where c is the speed of light. In the near field regime, this velocity can be reduced to the order of ¯ωdηc, where ¯ω is a typical material frequency.
(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)