Condensed Matter Theory

Abstract:

While studies of active nematics in two dimensions have shed light on various aspects of the flow regimes and topology of active matter, three-dimensional properties of topological defects and chaotic flows remain unexplored. By confining a film of active nematics between two parallel plates, we use continuum simulations and analytical arguments to demonstrate that the crossover from quasi-two-dimensional (quasi-2D) to three-dimensional (3D) chaotic flows is controlled by the morphology of the disclination lines. For small plate separations, the active nematic behaves as a quasi-2D material, with straight topological disclination lines spanning the height of the channel and exhibiting effectively 2D active turbulence. Upon increasing channel height, we find a crossover to 3D chaotic flows due to the contortion of disclinations above a critical activity. Above this critical activity highly contorted disclination lines and disclination loops are formed. We further show that these contortions are engendered by twist perturbations producing a sharp change in the curvature of disclinations.

Abstract:

We use full nematohydrodynamic simulations to study the statics and dynamics of monolayers of cholesteric liquid crystals. Using chirality and temperature as control parameters, we show that we can recover the two-dimensional blue phases recently observed in chiral nematics, where hexagonal lattices of half-skyrmion topological excitations are interleaved by lattices of trefoil topological defects. Furthermore, we characterise the transient dynamics during the quench from isotropic to blue phase. We then proceed by confining cholesteric stripes and blue phases within finite-sized tactoids and show that it is possible to access a wealth of reconfigurable droplet shapes including disk-like, elongated and star-shaped morphologies. Our results demonstrate a potential for constructing controllable, stable structures of liquid crystals by constraining 2D blue phases and varying the chirality, surface tension and elastic constants.

Abstract:

We review recent developments in the study of out-of-equilibrium topological states of matter in isolated systems. The phenomenon of many-body localization, exhibited by some isolated systems usually in the presence of quenched disorder, prevents systems from equilibrating to a thermal state where the delicate quantum correlations necessary for topological order are often washed out. Instead, many-body localized systems can exhibit a type of eigenstate phase structure wherein their entire many-body spectrum is characterized by various types of quantum order, usually restricted to quantum ground states. After introducing many-body localization and explaining how it can protect quantum order, we then explore how the interplay of symmetry and dimensionality with many-body localization constrains its role in stabilizing topological phases out of equilibrium.

Abstract:

Real-time deformability (RT-DC) is a method for high-throughput mechanical and morphological phenotyping of cells in suspension. While analysis rates exceeding 1000 cells per second allow for a label-free characterization of complex biological samples, e.g., whole blood, data evaluation has so far been limited to a few geometrical and material parameters such as cell size, deformation, and elastic Young's modulus. But as a microscopy-based technology, RT-DC actually generates and yields multidimensional datasets that require automated and unbiased tools to obtain morphological and rheological cell information. Here, we present a statistical framework to shed light on this complex parameter space and to extract quantitative results under various experimental conditions. As model systems, we apply cell lines as well as primary cells and highlight more than 11 parameters that can be obtained from RT-DC data. These parameters are used to identify sub-populations in heterogeneous samples using Gaussian mixture models, to perform a dimensionality reduction using principal component analysis, and to quantify the statistical significance applying linear mixed models to datasets of multiple replicates.

Abstract:

We consider the full probability distribution for the transverse magnetization of a finite subsystem in the transverse field Ising chain. We derive a determinant representation of the corresponding characteristic function for general Gaussian states. We consider applications to the full counting statistics in the ground state, finite temperature equilibrium states, non-equilibrium steady states and time evolution after global quantum quenches. We derive an analytical expression for the time and subsystem size dependence of the characteristic function at sufficiently late times after a quantum quench. This expression features an interesting multiple light-cone structure.