51�������

Abstract:

The occurrence of new textures of liquid crystals is an important factor in tuning their optical and photonics properties. Here, we show, both experimentally and by numerical computation, that under an electric field chitin tactoids (i.e. nematic droplets) can stretch to aspect ratios of more than 15, leading to a transition from a spindle-like to a cigar-like shape. We argue that the large extensions occur because the elastic contribution to the free energy is dominated by the anchoring. We demonstrate that the elongation involves hydrodynamic flow and is reversible, the tactoids return to their original shapes upon removing the field.

Abstract:

Reducing the contact time between bouncing droplets and an underlying solid surface is relevant to a broad range of industrial applications, such as anti-icing and self-cleaning. Previous work has found that placing cylindrical obstacles on the substrate leads to a reduction in contact time. For obstacles large compared to the drop, this is a result of hydrodynamic coupling between the azimuthal and axial spreading directions. For obstacles small compared to the drop, the reduction in contact time is interpreted as being due to fast retraction along the cylindrical ridge, followed by drop breakup. Here we use simulations to discuss in greater detail the effect of varying the obstacle size on the dynamics of the drop bouncing. We investigate the crossover between the two regimes and explain why the contact time is minimized when the radii of the drop and the cylindrical obstacle are comparable.

Abstract:

Characterizing how entanglement grows with time in a many-body system, for example, after a quantum quench, is a key problem in nonequilibrium quantum physics. We study this problem for the case of random unitary dynamics, representing either Hamiltonian evolution with time-dependent noise or evolution by a random quantum circuit. Our results reveal a universal structure behind noisy entanglement growth, and also provide simple new heuristics for the “entanglement tsunami” in Hamiltonian systems without noise. In 1D, we show that noise causes the entanglement entropy across a cut to grow according to the celebrated Kardar-Parisi-Zhang (KPZ) equation. The mean entanglement grows linearly in time, while fluctuations grow like ðtimeÞ 1 = 3 and are spatially correlated over a distance ∝ ðtimeÞ 2 = 3 . We derive KPZ universal behavior in three complementary ways, by mapping random entanglement growth to (i) a stochastic model of a growing surface, (ii) a “minimal cut” picture, reminiscent of the Ryu-Takayanagi formula in holography, and (iii) a hydrodynamic problem involving the dynamical spreading of operators. We demonstrate KPZ universality in 1D numerically using simulations of random unitary circuits. Importantly, the leading-order time dependence of the entropy is deterministic even in the presence of noise, allowing us to propose a simple coarse grained minimal cut picture for the entanglement growth of generic Hamiltonians, even without noise, in arbitrary dimensionality. We clarify the meaning of the “velocity” of entanglement growth in the 1D entanglement tsunami. We show that in higher dimensions, noisy entanglement evolution maps to the well-studied problem of pinning of a membrane or domain wall by disorder.