Condensed Matter Theory

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.

Abstract:

Proliferation and motility are ubiquitous drivers of activity in biological systems. Here, we study a dense binary mixture of motile and proliferating particles with exclusively repulsive interactions, where homeostasis in the proliferating subpopulation is maintained by pressure-induced removal. Using numerical simulations, we show that phase separation emerges naturally in this system at high density and weak enough self-propulsion. We map the full two-component system to an effective single-component active Brownian particle model that recapitulates this behavior. This allows us to identify the emergent effects of the proliferating matrix on motile particles that interact to produce phase separation: enhanced diffusion, renormalized self-propulsion, reduced persistence, and an effective attraction between motile particles. Our results establish a specific type of phase transition based on these emergent effects and pave a way to reinterpret the physics of dense cellular populations, such as bacterial colonies or tumors, as systems of mixed active matter.

Abstract:

Theories of self-organized active fluid surfaces have emerged as an important class of minimal models for the shape dynamics of biological membranes, cells, and tissues. However, due to their inherent geometric nonlinearities and the absence of general minimization principles in active systems, it remains a major challenge to systematically study the emergent shape spaces that such theories give rise to. Here, we introduce a variational approach that allows for a direct computation of stationary surface geometries and flows, which enables the classification of nonequilibrium phase transitions in shape spaces described by active surface theories. To achieve this, we construct a dissipation functional systematically from the entropy production in active surfaces and show how generic symmetries imposed by Onsager relations can be exploited to also account for reactive nondissipative terms in constitutive laws. This functional is supplemented by Lagrange multipliers that relax nonlinear geometric constraints, which leads to a tractable variational problem suitable for implicit dynamic simulations and explicit calculations of nontrivial steady state geometries and flows. We apply this framework to study the dynamics of open fluid membranes and closed active fluid surfaces, and characterize the space of stationary solutions that corresponding surfaces and flows occupy. These analyses rationalize the interplay of first-order shape transitions of internally and externally forced fluid membranes, reveal degenerate regions in stationary shape spaces of mechanochemically active surfaces, and identify a mechanism by which hydrodynamic screening controls the geometry of active surfaces undergoing cell divisionlike shape transformations.