arXiv subjects

Matthias Krüger

Publications and source records attributed to Matthias Krüger.

At least 73 records · Page 4Linked to original sources

arXiv2018

Non-equilibrium forces following quenches in active and thermal matter

Non-equilibrium systems are known to exhibit long-ranged correlations due to conservation of quantities like density or momentum. This, in turn, leads to long-ranged fluctuation-induced (Casimir) forces, predicted to arise in a variety of non-equilibrium settings. Here, we study such forces, which arise transiently between parallel plates or compact inclusions in a gas of particles, following a change ("quench") in temperature or activity of the medium. Analytical calculations, as well as numerical simulations of passive or active Brownian particles, indicate two distinct forces: (i) The immediate effect of the quench is adsorption or desorption of particles of the medium to the immersed objects, which in turn initiates a front of relaxing (mean) density. This leads to time-dependent {\it density-induced forces}. (ii) A long-term effect of the quench is that density fluctuations are modified, manifested as transient (long-ranged) (pair-)correlations that relax diffusively to their (short-ranged) steady-state limit. As a result, transient {\it fluctuation-induced forces} emerge. We discuss the properties of fluctuation-induced and density-induced forces as regards universality, relaxation as a function of time, and scaling with distance between objects. Their distinct signatures allow us to distinguish the two types of forces in simulation data. Finally, we propose several scenarios for their experimental observation.

cond-mat.stat-mech↗

arXiv2018

Oscillating Modes of Driven Colloids in Overdamped Systems

Microscopic particles suspended in liquids are the prime example of an overdamped system because viscous forces dominate over inertial effects. Apart from their use as model systems, they receive considerable attention as sensitive probes from which forces on molecular scales can be inferred. The interpretation of such experiments rests on the assumption, that, even if the particles are driven, the liquid remains in equilibrium, and all modes are overdamped. Here, we experimentally demonstrate that this is no longer valid when a particle is forced through a viscoelastic fluid. Even at small driving velocities where Stokes law remains valid, we observe particle oscillations with periods up to several tens of seconds. We attribute these to non-equilibrium fluctuations of the fluid, which are excited by the particle's motion. The observed oscillatory dynamics is in quantitative agreement with an overdamped Langevin equation with negative friction-memory term and which is equivalent to the motion of a stochastically driven underdamped oscillator. This fundamentally new oscillatory mode will largely expand the variety of model systems but has also considerable implications on how molecular forces are determined by colloidal probe particles under natural viscoelastic conditions.

cond-mat.soft↗

arXiv2017

Fluctuational electrodynamics for nonlinear materials in and out of thermal equilibrium

We develop fluctuational electrodynamics for media with nonlinear optical response in and out of thermal equilibrium. Starting from the stochastic nonlinear Helmholtz equation and using the fluctuation dissipation theorem, we obtain perturbatively a deterministic nonlinear Helmholtz equation for the average field, the physical linear response, as well as the fluctuations and Rytov currents. We show that the effects of nonlinear optics, in or out of thermal equilibrium, can be taken into account with an effective, system-aware dielectric function. We discuss the heat radiation of a planar, nonlinear surface, showing that Kirchhoff's must be applied carefully. We find that the spectral emissivity of a nonlinear nanosphere can in principle be negative, implying the possibility of heat flow reversal for specific frequencies.

quant-ph↗

arXiv2017

Heat radiation and transfer for point particles in arbitrary geometries

We study heat radiation and heat transfer for pointlike particles in a system of other objects. Starting from exact many-body expressions found from scattering theory and fluctuational electrodynamics, we find that transfer and radiation for point particles are given in terms of the Green's function of the system in the absence of the point particles. These general expressions contain no approximation for the surrounding objects. As an application, we compute the heat transfer between two point particles in the presence of a sphere of arbitrary size and show that the transfer is enhanced by several orders of magnitude through the presence of the sphere, depending on the materials. Furthermore, we compute the heat emission of a point particle in front of a planar mirror. Finally, we show that a particle placed inside a spherical mirror cavity does not radiate energy.

quant-ph↗

arXiv2017

Viscosity of a sheared correlated (near-critical) model fluid in confinement

Second-order phase transitions are characterized by a divergence of the spatial correlation length of the order parameter fluctuations. For confined systems, this is known to lead to remarkable equilibrium physical phenomena, including finite-size effects and critical Casimir forces. We explore here some non-equilibrium aspects of these effects in the stationary state resulting from the action of external forces: by analyzing a model of a correlated fluid under shear, spatially confined by two parallel plates, we study the resulting viscosity within the setting of (Gaussian) Landau-Ginzburg theory. Specifically, we introduce a model in which the hydrodynamic velocity field (obeying the Stokes equation) is coupled to an order parameter with dissipative dynamics. The well-known Green-Kubo relation for bulk systems is generalized for confined systems. This is shown to result in a non-local Stokes equation for the fluid flow, due to the correlated fluctuations. The resulting effective shear viscosity shows universal as well as non-universal contributions, which we study in detail. In particular, the deviation from the bulk behavior is universal, depending on the ratio of the correlation length and the film thickness $L$. In addition, at the critical point the viscosity is proportional to $\ell/L$, where $\ell$ is a dynamic length scale. These findings are expected to be experimentally observable, especially for systems where the bulk viscosity is affected by critical fluctuations.

cond-mat.stat-mech↗

arXiv2017

A Gaussian theory for fluctuations in simple liquids

Assuming an effective quadratic Hamiltonian, we derive an approximate, linear stochastic equation of motion for the density-fluctuations in liquids, composed of overdamped Brownian particles. From this approach, time dependent two point correlation functions (such as the intermediate scattering function) are derived. We show that this correlation function is exact at short times, for any interaction and, in particular, for arbitrary external potentials so that it applies to confined systems. Furthermore, we discuss the relation of this approach to previous ones, such as dynamical density functional theory as well as the formally exact treatment. This approach, inspired by the well known Landau-Ginzburg Hamiltonians, and the corresponding "Model B" equation of motion, may be seen as its microscopic version, containing information about the details on the particle level.

cond-mat.soft↗

arXiv2016

Anharmonic particles: suppressing van der Waals forces by an external field

We study the classical thermal component of Casimir, or van der Waals, forces between point particles with highly anharmonic dipole Hamiltonians when they are subjected to an external electric field. Using a model for which the individual dipole moments saturate in a strong field (a model that mimics the charges in a neutral, perfectly conducting sphere), we find that the resulting Casimir force depends strongly on the strength of the field, as demonstrated by analytical results. For a certain angle between external field and center to center axis, the fluctuation force can be tuned and suppressed to arbitrarily small values. We compare the forces between these anharmonic particles to those between harmonic ones, and also provide a simple formula for asymptotically large external fields, which we expect to be generally valid for the case of saturating dipole moments.

cond-mat.mes-hall↗

arXiv2016

Many body heat radiation and heat transfer in the presence of a non-absorbing background medium

Heat radiation and near-field radiative heat transfer can be strongly manipulated by adjusting geometrical shapes, optical properties, or the relative positions of the objects involved. Typically these objects are considered as embedded in vacuum. By applying the methods of fluctuational electrodynamics, we derive general closed-form expressions for heat radiation and heat transfer in a system of $N$ arbitrary objects embedded in a passive non-absorbing background medium. Taking into account the principle of reciprocity, we explicitly prove the symmetry and positivity of transfer in any such system. Regarding applications, we find that the heat radiation of a sphere as well as the heat transfer between two parallel plates is strongly enhanced by the presence of a background medium. Regarding near- and far-field transfer through a gas like air, we show that a microscopic model (based on gas particles) and a macroscopic model (using a dielectric contrast) yield identical results. We also compare the radiative transfer through a medium like air and the energy transfer found from kinetic gas theory.

physics.class-ph↗

arXiv2016

Transient Casimir forces from quenches in thermal and active matter

We compute fluctuation-induced (Casimir) forces for classical systems after a temperature quench. Using a generic coarse-grained model for fluctuations of a conserved density, we find that transient forces arise even if the initial and final states are force-free. In setups reminiscent of Casimir (planar walls) and van der Waals (small inclusions) interactions, we find comparable exact universal expressions for the force. Dynamical details only scale the time axis of transient force curves. We propose that such quenches can be achieved, for instance, in experiments on active matter, employing tunable activity or interaction protocols.

cond-mat.stat-mech↗

arXiv2016

Measurement of second-order response without perturbation

We study the second order response functions of a colloidal particle being subjected to an anharmonic potential. Contrary to typical response measurements which require an external perturbation, here we experimentally confirm a recently developed approach where the system's susceptibilities up to second order are obtained from the particle's equilibrium trajectory [PCCP $\mathrm{\bf 17}$, 6653 (2015)]. The measured susceptibilities are in quantitative agreement with those obtained from the response to an external perturbation.

cond-mat.soft↗

arXiv2016

The modified Langevin description for probes in a nonlinear medium

When the motion of a probe strongly disturbs the thermal equilibrium of the solvent or bath, the nonlinear response of the latter must enter the probe's effective evolution equation. We derive that induced stochastic dynamics using second order response around the bath thermal equilibrium. We discuss the nature of the new term in the evolution equation which is not longer purely dissipative, and the appearance of a novel time-scale for the probe related to changes in the dynamical activity of the bath. A major application for the obtained nonlinear generalized Langevin equation is in the study of colloid motion in a visco-elastic medium.

cond-mat.soft↗

arXiv2016

Flight of a heavy particle nonlinearly coupled to a quantum bath

Fluctuation and dissipation are by-products of coupling to the `environment.' The Caldeira-Leggett model, a successful paradigm of quantum Brownian motion, views the environment as a collection of harmonic oscillators linearly coupled to the system. However, symmetry considerations may forbid a linear coupling, e.g. for a neutral particle in quantum electrodynamics. We argue that nonlinear couplings can lead to a fundamentally different behavior. Specifically, we consider a heavy particle quadratically coupled to quantum fluctuations of the bath. In one dimension the particle undergoes anomalous diffusion, unfolding as a power-law distribution in space, reminiscent of Lévy flights. We suggest condensed matter analogs where similar effects may arise.

quant-ph↗

arXiv2016

Fluctuational electrodynamics for nonlinear media

We develop fluctuational electrodynamics for media with nonlinear optical response. In a perturbative manner, we amend the stochastic Helmholtz equation to describe fluctuations in a nonlinear setting, in agreement with the fluctuation dissipation theorem, and identify the local (Rytov) current fluctuations. We show how the linear response (the solution of the scattering problem) of a collection of objects is found from the individual responses, as measured in isolation. As an example, we compute the Casimir force acting between nonlinear objects which approaches the result for linear optics for large separations, and deviates for small distances.

quant-ph↗

arXiv2015

Anisotropic particles near surfaces: Self-propulsion and friction

We theoretically study the phenomenon of self-propulsion through Casimir forces in thermal non-equilibrium. Using fluctuational electrodynamics, we derive a formula for the self-propulsion force for an arbitrary small object in two scenarios, i) for the object being isolated, and ii) for the object being close to a planar surface. In the latter case, the self-propulsion force (i.e., the force parallel to the surface) increases with decreasing distance, i.e., it couples to the near-field. We numerically calculate the lateral force acting on a hot spheroid near a surface and show that it can be as large as the gravitational force, thus being potentially measurable in fly-by experiments. We close by linking our results to well-known relations of linear response theory in fluctuational electrodynamics: Looking at the friction of the anisotropic object for constant velocity, we identify a correction term that is additional to the typically used approach.

quant-ph↗

arXiv2015

Theory of rheology in confinement

The viscosity of fluids is generally understood in terms of kinetic mechanisms, i.e., particle collisions, or thermodynamic ones as imposed through structural distortions upon e.g. applying shear. Often the former is less relevant, and (damped) Brownian particles are considered good fluid model systems. We formulate a general theoretical approach for rheology in confinement, based on the many particle diffusion equation, evaluated via classical density functional theory. We discuss the viscosity for the situation of two parallel walls in relative motion as a function of wall-to-wall distance.

cond-mat.soft↗

arXiv2015

Frenetic aspects of second order response

Starting from second order around thermal equilibrium, the response of a statistical mechanical system to an external stimulus is not only governed by dissipation and depends explicitly on dynamical details of the system. The so called frenetic contribution in second order around equilibrium is illustrated in different physical examples, such as for non-thermodynamic aspects in the coupling between system and reservoir, for the dependence on disorder in dielectric response and for the nonlinear correction to the Sutherland--Einstein relation. More generally, the way in which a system's dynamical activity changes by the pertubation is visible (only) from nonlinear response.

cond-mat.stat-mech↗

arXiv2014

Heat transfer between anisotropic nanopartricles: Enhancement and switching

We theoretically study heat transfer between two anisotropic nanoparticles in vacuum, and derive closed expressions in terms of the anisotropic dipole polarizabilities. We show that transfer between two small spheroids can be many times as large as the one for two spheres of same volumes. Such increase with anisotropy is also found for the heat emission of an isolated small spheroid. Furthermore, we observe a strong dependence of transfer on the relative orientation, yielding the interpretation as a heat transfer switch. The switch quality, given as the ratio of transfer in the ``on'' and ``off'' positions, is observed to be as large as $10^3$ in the near field and even larger in the far field.

quant-ph↗

arXiv2014

Driven colloidal suspensions in confinement and density functional theory: Microstructure and wall-slip

We theoretically investigate general properties of driven (sheared) colloidal suspensions in confinement, based on methods of classical density functional theory. In the absence of an exact closed (Smoluchowski-) equation for the one-particle density under shear, we formulate a set of general conditions for approximations, and show that a simple closure fulfills them. The exact microscopic stress tensor is identified. Exemplifying the situation near a wall (oriented parallel to the direction of shear), we note that the microscopic shear stress is not necessarily homogeneous. Formulating a second equation additional to the Smoluchowski equation, we achieve a homogeneous shear stress, and thereby compute the local flow velocity near the wall. This finally leads to a slip length of the complex fluid at the wall.

cond-mat.stat-mech↗