Condensed Matter Theory

Abstract:

We investigate channel-confined, nematic liquid crystals using the Beris–Edwards model of nematohydrodynamics. Using strong homeotropic anchoring at the walls, we find multistability, i.e. multiple coexisting states where the uniform nematic state coexists with states having spatially varying scalar nematic order and director fields. When a pressure gradient is applied, flows develop, and the inherent multistability of the system organises a variety of complex dynamics. For low pressure gradients, steady flows are established, and the director fields that emerge from the multistable states at equilibrium correspond to Bowser and Dowser configurations similar to those reported in experiments. An increasing pressure gradient destabilises steady Bowser and Dowser flow states sequentially, leading to unsteady periodic and chaotic regimes featuring cyclical topological transitions, pulsating flows, advecting defects and spatiotemporal chaos. These findings demonstrate that modest variations in the scalar nematic order, as captured by the Beris–Edwards model, can qualitatively modify equilibrium structures and give rise to complex non-equilibrium behaviour in confined nematics – contrasting with the Ericksen–Leslie model, which assumes a constant scalar order parameter. Our key model predictions – multistability, periodically oscillating states and advecting defect-mediated turbulence – can be experimentally investigated in pressure-driven channel flows of nematic fluids.

Abstract:

Although cell monolayers typically remain confluent, they can spontaneously develop persistent holes as a result of collective cellular motion. Recent studies on MDCK monolayers cultured on soft substrates have revealed that cells can align to create regions of local nematic order, and topological defects that generate localised mechanical stresses which can spontaneously trigger hole formation. To investigate this process, we develop a continuum multi-phase field model that incorporates internal dissipation and active dipolar forces that drive cell shape anisotropy. Our simulations show that reducing substrate friction enhances cell-cell velocity correlations. In the low-friction regime, topological defects generate spiral flow patterns that concentrate stress and can trigger hole formation. By contrast, in the high-friction regime, holes do not nucleate. We further demonstrate that the number and stability of the holes—whether they close or persist—depends on both substrate friction and cellular activity, through a non-dimensional friction number. These findings highlight the importance of internal dissipation in modelling collective cell motion and the critical role of collective dynamics in maintaining tissue integrity.

Abstract:

<jats:p> Preparing the thermal density matrix <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:msub> <a:mi>ρ</a:mi> <a:mi>β</a:mi> </a:msub> <a:mo>∝</a:mo> <a:msup> <a:mi>e</a:mi> <a:mrow> <a:mo>−</a:mo> <a:mi>β</a:mi> <a:mi>H</a:mi> </a:mrow> </a:msup> </a:mrow> </a:math> corresponding to a given Hamiltonian <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mi>H</b:mi> </b:math> is a task of central interest across quantum many-body physics, and is particularly salient when attempting to study it with quantum computers. Although solved in principle by recent constructions of efficiently simulable Lindblad master equations—that provably have <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:msub> <c:mi>ρ</c:mi> <c:mi>β</c:mi> </c:msub> </c:math> as a steady state [C.-F. Chen , ]—the implementation of these “exact Gibbs samplers” requires large-scale quantum computing resources and is hence challenging in practice on current or even near-term quantum devices. Here, we propose a scheme for approximately simulating an exact Gibbs sampler up to a rigorously bounded error that only requires the (repeated) implementation of three readily available ingredients: (a) analog simulation of <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mi>H</d:mi> </d:math> ; (b) strictly local but time-dependent couplings to ancilla qubits; and (c) reset of the ancillas. We give rigorous guarantees on the difference between the fixed point reached by our protocol and the exact thermal state, which only depend on parameters of the protocol and its . The procedure is efficiently implementable on near-term devices if <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:mi>H</e:mi> </e:math> is local and the mixing time scales mildly with both system size and protocol parameters. While guaranteeing the latter for Hamiltonians of interest remains an important problem for future work, here we lay the groundwork for developing fully efficient thermal state preparation protocols on quantum simulators. </jats:p>

Abstract:

Replication through cell division is one of the fundamental processes of life and a major driver of dynamics in systems ranging from bacterial colonies to embryogenesis, tissues and tumors. While regulation also shapes self-organization, many biologically relevant behaviors arise from a limited number of physical ingredients, and particle-based models have become a popular platform to investigate these emergent dynamics. However, incorporating division into such models often produces aberrant mechanical fluctuations that hinder meaningful analysis. Here, we introduce a minimal model ensuring mechanical consistency during cell division. Cells consist of two nodes, overlapping disks which separate during division, forming transient dumbbell shapes. Internal degrees of freedom, cell-cell interactions and equations of motion guarantee force continuity at all times, including during division, both for the dividing cell and its interaction partners, while allowing arbitrary anisotropic mobilities. As a benchmark, we also translate an established model of proliferating spherocylinders with similar dynamics into our theoretical framework. Numerical simulations demonstrate force continuity of the new disk cell model, quantify the improvements, and show agreement in terms of collective behaviors such as alignment and orientational order. We also demonstrate force extraction and a Voronoi-based interpretation in a confluent-tissue context—with a three-dimensional generalization in embryonic-like confinement. A reference implementation of the model in two and three dimensions is freely available as a Julia package based on InPartS.jl. Our model provides a framework for analyzing mechanical observables such as velocities and stresses, and can be readily extended with additional biological features.

Abstract:

<jats:title>Abstract</jats:title> <jats:p> Sutherland showed that the XYZ quantum spin-chain Hamiltonian commutes with the eight-vertex model transfer matrix, so that Baxter’s subsequent <jats:italic>tour de force</jats:italic> proves the integrability of both. The proof requires parametrising the Boltzmann weights using elliptic theta functions and showing they satisfy the Yang-Baxter equation. We here give a simpler derivation of the integrability of the XYZ chain by explicitly constructing an extensive sequence of conserved charges from a matrix-product operator. We show that they commute with the XYZ Hamiltonian with periodic boundary conditions or an arbitrary boundary magnetic field. A straightforward generalisation yields impurity interactions that preserve the integrability. Placing such an impurity at the edge gives an integrable generalisation of the Kondo problem with a gapped bulk. We make contact with the traditional approach by relating our matrix-product operator to products of the eight-vertex model transfer matrix. </jats:p>