**Matthias Krüger**

(MPI Intelligent Systems, Stuttgart)

leader of Emmy-Noether Group "Statistical Physics out of Equilibrium"

**Activities in soft matter and complex fluids**

Driven suspensions far from equilibrium, microscopic approaches like density functional theories. Which are the relevant ensembles (identify control variables)?

**Recent selected publications**

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

Christian Rohwer, Andrea Gambassi, and Matthias Kruger

J. Phys.: Cond. Matt. **in press** (2017)

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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.

**Measurement of second-order response without perturbation**

Laurent Helden, Urna Basu, Matthias Krüger, and Clemens Bechinger

*Europhys. Lett. ***116** (2016) 60003

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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 demonstrate that the system's susceptibilities up to second order can be obtained from the particle's equilibrium fluctuations. The measured susceptibilities are in quantitative agreement with those obtained from the response to an external perturbation.

**Driven colloidal fluids: Construction of dynamical density functional theories from exactly solvable limits**

A. Scacchi, M. Krüger and J. M. Brader, J. Phys.: Cond. Matt. **28**, 244023 (2016)

**Theory of rheology in confinement**

A. A. Aerov and M. Krüger, Phys. Rev. E **92**, 042301 (2015)