Condensed Matter Theory

Abstract:

Spontaneous symmetry breaking in colloidal systems increasingly fascinates scientists due to the promise of new, emergent functionalities and unique properties. Here, we introduce a chemically active system where symmetry is spontaneously broken in the particle motion rather than being encoded into their structure. Using symmetric MnO2 microrods without any apparent structural features or chirality, we observe the emergence of a combination of rotational and translational motion near a substrate that resembles rolling. This motion is further enhanced if a chemically active substrate is present. To explain the occurrence of highly active motion, we investigate the flows that lead to propulsion. The results are rationalized by a theoretical model showing spontaneous symmetry breaking with a bifurcation above a critical Péclet number. To identify the chemical reactions leading to the occurrence of flow, we confirm the species involved using electron paramagnetic resonance (EPR) and X-ray photoelectron spectroscopy (XPS). Overall, the results demonstrate the potential of spontaneous symmetry breaking to accomplish active rolling motion of symmetric chemically active microparticles.

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>

Abstract:

We derive exact strong zero mode (ESZM) operators for integrable spin- S <math display="inline"> <mi>S</mi> </math> chains with open boundary conditions and a boundary field. Their locality properties are generally weaker than in the previously known cases, but they still imply infinite coherence times in the vicinity of the edges. We explain how such integrable chains possess multiple ground states describing a first-order quantum phase transition, and that the odd number of such states for integer S <math display="inline"> <mi>S</mi> </math> makes the weaker locality properties necessary. We make contact with more traditional approaches by showing how the ESZM for S=\tfrac12 <math display="inline"> <mrow> <mi>S</mi> <mo>=</mo> <mstyle displaystyle="false"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mstyle> </mrow> </math> acts on energy eigenstates given by solutions of the Bethe equations.