Benno Liebchen

Clustering and Pattern Formation in Chemorepulsive Active Colloids.

We demonstrate that migration away from self-produced chemicals (chemorepulsion) generates a generic route to clustering and pattern formation among self-propelled colloids. The clustering instability can be caused either by anisotropic chemical production, or by a delayed orientational response to changes of the chemical environment. In each case, chemorepulsion creates clusters of a self-limiting area which grows linearly with self-propulsion speed. This agrees with recent observations of dynamic clusters in Janus colloids (albeit not yet known to be chemorepulsive). More generally, our results could inform design principles for the self-assembly of chemorepulsive synthetic swimmers and/or bacteria into nonequilibrium patterns.

Phoretic Interactions Generically Induce Dynamic Clusters and Wave Patterns in Active Colloids.

We introduce a representative minimal model for phoretically interacting active colloids. Combining kinetic theory, linear stability analyses, and a general relation between self-propulsion and phoretic interactions in autodiffusiophoretic and autothermophoretic Janus colloids collapses the parameter space from six to two dimensionless parameters: area fraction and Péclet number. This collapse arises when the lifetime of the self-generated phoretic fields is not too short, and leads to a universal phase diagram showing that phoretic interactions generically induce pattern formation in typical Janus colloids, even at very low density. The resulting patterns include waves and dynamic aggregates closely resembling the living clusters found in experiments on dilute suspension of Janus colloids.

Pattern formation in chemically interacting active rotors with self-propulsion

We demonstrate that active rotations in chemically signalling particles, such as autochemotactic E. coli close to walls, create a route for pattern formation based on a nonlinear yet deterministic instability mechanism. For slow rotations, we find a transient persistence of the uniform state, followed by a sudden formation of clusters contingent on locking of the average propulsion direction by chemotaxis. These clusters coarsen, which results in phase separation into a dense and a dilute region. Faster rotations arrest phase separation leading to a global travelling wave of rotors with synchronized roto-translational motion. Our results elucidate the physics resulting from the competition of two generic paradigms in active matter, chemotaxis and active rotations, and show that the latter provides a tool to design programmable self-assembly of active matter, for example to control coarsening.

Interaction-induced current-reversals in driven lattices

Long-range interactions are shown to cause, as time evolves, consecutive reversals of directed currents for dilute ensembles of particles in driven lattices. These current reversals are based on a general mechanism that leads to an interaction-induced accumulation of particles in the regular regions of the underlying single-particle phase space and to a synchronized single-particle motion as well as enhanced efficiency of Hamiltonian ratchets. Suggestions for experimental implementations using ionized mesoscopic clusters in micromechanical lattices or dipolarly interacting colloidal particles in ac-driven optical lattices are provided.

Collective Behavior of Chiral Active Matter: Pattern Formation and Enhanced Flocking

We generalize the Vicsek model to describe the collective behavior of polar circle swimmers with local alignment interactions. While the phase transition leading to collective motion in 2D (flocking) occurs at the same interaction to noise ratio as for linear swimmers, as we show, circular motion enhances the polarization in the ordered phase (enhanced flocking) and induces secondary instabilities leading to structure formation. Slow rotations promote macroscopic droplets with late time sizes proportional to the system size (indicating phase separation) whereas fast rotations generate patterns consisting of phase synchronized microflocks with a controllable characteristic size proportional to the average single-particle swimming radius. Our results defy the viewpoint that monofrequent rotations form a vapid extension of the Vicsek model and establish a generic route to pattern formation in chiral active matter with possible applications for understanding and designing rotating microflocks.We generalize the Vicsek model to describe the collective behaviour of polar circle swimmers with local alignment interactions. While the phase transition leading to collective motion in 2D (flocking) occurs at the same interaction to noise ratio as for linear swimmers, as we show, circular motion enhances the polarization in the ordered phase (enhanced flocking) and induces secondary instabilities leading to structure formation. Slow rotations promote phase separation whereas fast rotations generate patterns consisting of phase synchronized microflocks with a controllable selflimited size. Our results defy the viewpoint that monofrequent rotations form a vapid extension of the Vicsek model and establish a generic route to pattern formation in chiral active matter with possible applications to control coarsening and to design rotating microflocks.

Resonant population transfer in the time-dependent quantum elliptical billiard

We analyze the quantum dynamics of the time-dependent elliptical billiard using the example of a certain breathing mode. A numerical method for the time propagation of an arbitrary initial state is developed based on a series of transformations, thereby removing the time dependence of the boundary conditions. The time evolution of the energies of different initial states is studied. The maximal and minimal energies that are reached during the time evolution show a series of resonances as a function of the applied driving frequency. At these resonances, higher (or lower) lying states are periodically populated, leading to the observed change in energy. The resonances occur when the driving frequency or a multiple of it matches the mean energetic difference between the two involved states exactly. This picture is confirmed by a few-level Rabi-like model with periodic couplings, reproducing the key results of our numerical study.

Interaction induced directed transport in ac-driven periodic potentials

We demonstrate that repulsive power law interactions can induce directed transport of particles in dissipative, ac-driven periodic potentials, in regimes where the underlying noninteracting system exhibits localized oscillations. Contrasting the well-established single particle ratchet mechanism, this interaction induced transport is based on the collective behaviour of the interacting particles yielding a spatiotemporal nonequilibrium pattern comprising persistent travelling excitations.

Disorder induced regular dynamics in oscillating lattices.

We explore the impact of weak disorder on the dynamics of classical particles in a periodically oscillating lattice. It is demonstrated that the disorder induces a hopping process from diffusive to regular motion; i.e., we observe the counterintuitive phenomenon that disorder leads to regular behavior. If the disorder is localized in a finite-sized part of the lattice, the described hopping causes initially diffusive particles to even accumulate in regular structures of the corresponding phase space. A hallmark of this accumulation is the emergence of pronounced peaks in the velocity distribution of particles that should be detectable in state of the art experiments, e.g., with cold atoms in optical lattices.

Analysis of interface conversion processes of ballistic and diffusive motion in driven superlattices.

We explore the nonequilibrium dynamics of noninteracting classical particles in a one-dimensional driven superlattice which is composed of domains exposed to different time-dependent forces. It is shown how the combination of directed transport and conversion processes from diffusive to ballistic motion causes strong correlations between velocity and phase for particles passing through a superlattice. A detailed understanding of the underlying mechanism allows us to tune the resulting velocity distributions at distinguished points in the superlattice by means of local variations of the applied driving force. As an intriguing application we present a scheme how initially diffusive particles can be transformed into a monoenergetic pulsed particle beam whose parameters such as its energy can be varied.

Patterned deposition of particles in spatio-temporally driven lattices

We present and analyze mechanisms for the patterned deposition of particles in a spatio-temporally driven lattice. The working principle is based on the breaking of the spatio-temporal translation symmetry, which is responsible for the equivalence of all lattice sites, by applying modulated phase shifts to the lattice sites. The patterned trapping of the particles occurs in confined chaotic seas, created via the ramping of the height of the lattice potential. Complex density profiles on the length scale of the complete lattice can be obtained by a quasi-continuous, spatial deformation of the chaotic sea in a frequency modulated lattice.