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We develop a stability theory for contractive local IFSs on compact metric spaces. Unlike the classical global setting, local systems may exhibit a richer symbolic and geometric structure, including code spaces that are not of finite type…
We study how dispersions of colloidal particles in a cholesteric liquid crystal behave under a time-dependent electric field. By controlling the amplitude and shape of the applied field wave, we show that the system can be reproducibly…
Topological photonic insulators pave the way toward efficient integrated photonic devices with minimized scattering losses. Optical properties of the majority of topological structures proposed to date are fixed by design such that no…
Based on static and dynamical density functional theory, a phase-field-crystal model is derived which involves both the translational density and the orientational degree of ordering as well as a local director field. The model exhibits…
We study spatially localized optical vortices created by self-trapping of partially incoherent light with a phase dislocation in a biased photorefractive crystal. In a contrast to the decay of coherent self-trapped vortex beams due to the…
We demonstrate facile optical manipulation of shape of birefringent colloidal microparticles made from liquid crystal elastomers. Using soft lithography and polymerization, we fabricate elastomeric microcylinders with weakly undulating…
The rapid progress in precisely designing the surface decoration of patchy colloidal particles offers a new, yet unexperienced freedom to create building entities for larger, more complex structures in soft matter systems. However, it is…
Polarizable particles trapped in a resonator-sustained optical-lattice potential generate strong position-dependent backaction on the intracavity field. In the quantum regime particles in different energy bands are connected to different…
We study the translational motions of homonuclear diatomic molecules prepared in their ${}^3\Sigma$ electronic states, deeply bound vibrational states, and rotational states of well-defined parity. The trapping potential arises due to the…
Understanding the drift motion and dynamical locking of crystalline clusters on patterned substrates is important for the diffusion and manipulation of nano- and micro-scale objects on surfaces. In a previous work, we studied the…
Self-organization phenomena in ensembles of self-propelled particles open pathways to the synthesis of new dynamic states not accessible by traditional equilibrium processes. The challenge is to develop a set of principles that facilitate…
We analyze the dynamics of ultracold atoms in optical lattices induced by a sudden shift of the underlying harmonic trapping potential. In order to study the effect of strong interactions, dimensionality and lattice topology on transport…
Nematic liquid-crystal devices are a powerful tool to structure light in different degrees of freedom, both in classical and quantum regimes. Most of these devices exploit either the possibility of introducing a position-dependent phase…
This paper explores a mathematical technique for deriving dynamical invariants (i.e. constants of motion) in time-dependent gravitational potentials. The method relies on the construction of a canonical transformation that removes the…
We analyze the existence and stability of bright, dark, and gap matter-wave solitons in optical superlattices. Then, using these properties, we show that (time-dependent) ``dynamical superlattices'' can be used to controllably place, guide,…
Precise control of quantum particles is required for many interesting or novel experiments. Here we consider the task of transporting an atom using an external harmonic potential from one well of an optical lattice to another without…
We report a technique to realize reconfigurable colloidal crystals by using the controlled motion of particle defects above an externally modulated magnetic substrate. The transport of particles is induced by applying a uniform rotating…
The Backlund Transform, first developed in the context of differential geometry, has been classically used to obtain multi-soliton states in completely integrable infinite dimensional dynamical systems. It has recently been used to study…
The existence of anharmonic localization of lattice vibrations in a perfect 3-D diatomic ionic crystal is established for the rigid-ion model by molecular dynamics simulations. For a realistic set of NaI potential parameters, an intrinsic…
We propose a method for achieving dynamically controllable transport of highly mobile matter-wave solitons in a driven two-dimensional optical lattice. Our numerical analysis based on the mean-field model and the theory based on the…