Condensed Matter Theory

Abstract:

We investigate the self-diffusiophoretic motion of a catalytically active spherical particle confined within a wedge-shaped domain. Using the Fourier-Kontorovich-Lebedev transform, we solve the Laplace equation for the concentration field in the diffusion-dominated regime. The method of images is employed to obtain the first and second reflections of the concentration field, accounting for both monopole and dipole contributions of the particle's surface activity. Based on these results, we derive leading-order expressions for the self-induced phoretic velocity in the far-field limit and examine how it varies with the wedge opening angle and the particle's position within the domain. We focus on the contributions to the phoretic velocities arising from phoretic interactions, without accounting for hydrodynamic effects. Our findings reveal that the wedge geometry significantly affects both the magnitude and direction of particle motion. Our study provides a systematic framework for calculating the contributions to the phoretic velocity arising from concentration disturbances near corners, with implications for microfluidic design and control of autophoretic particles in confined geometries.

Abstract:

Active matter—for example, bacteria, cells, tissues, and microtubule-motor suspensions—internally generates stresses and flows. How these are communicated to their environments remains an open question central to interpreting experimental observations and emergent dynamics. To investigate the impact of active systems on their surroundings, we introduce a model that couples an active nematic fluid to an isotropic substrate fluid via friction. We numerically show that as the active layer develops turbulence, the substrate inherits the chaotic behavior, exhibiting a novel form of turbulence driven by locally generated stochastic forcing from the active layer. In particular, the short-length-scale flow structures in the active layer are filtered out, so the system behaves as a de facto low-pass filter. We derive the transfer function between the two layers analytically and use it to predict the large-q decay of the substrate energy spectrum and to investigate how tensorial quantities, such as the strain rate and the active stresses, are transmitted between the active layer and the substrate. Our analysis agrees with recent experiments measuring velocity-velocity correlations in mixtures of active and passive microtubules, and it may have implications for traction force microscopy measurements in cellular layers.

Abstract:

We develop a Monte Carlo sampling algorithm to numerically evaluate the Lehmann representation for the finite temperature single-particle Green's function in the repulsive Lieb-Liniger model. This allows us to determine the spectral function in the full range of temperatures and interactions, as well as in generalized Gibbs ensembles. We test our results against known results for dynamics at infinite interaction strength and static correlators, and find excellent agreement.

Abstract:

We compute the degeneracy of energy levels in the Kitaev quantum double model for any discrete group $G$ on any planar graph forming the skeleton of a closed orientable surface of arbitrary genus. The derivation is based on the fusion rules of the properly identified vertex and plaquette excitations, which are selected among the anyons, i.e., the simple objects of the Drinfeld center $\mathcal{Z}(\mathrm{Vec}_G)$. These degeneracies are given in terms of the quantum dimensions of the anyons and allow one to obtain the exact finite-temperature partition function of the model, valid for any finite-size system.