论文标题
固定的Athermal网络中的远程相关性
Long-range correlations in pinned athermal networks
论文作者
论文摘要
我们得出了作为对外部固定力在二维Athermal网络中发展为响应外部固定力的位移场的确切结果。对于通过软电位相互作用的颗粒的三角晶格布置，我们开发了绿色的功能形式主义，我们用来为局部外力产生的位移场提供精确的结果。我们表明，在连续体中，位移场的衰减限制为$ 1/r $，距离力偶极子$ r $。最后，我们将公式扩展到研究外部固定力产生的位移场中的相关性。我们表明，在每个顶点上无关的固定力会产生Athermal系统中位移的远距离相关性，具有非平凡的系统尺寸依赖性。我们通过在两个维度上对Athermal网络的数值模拟来验证我们的预测。
We derive exact results for displacement fields that develop as a response to external pinning forces in two dimensional athermal networks. For a triangular lattice arrangement of particles interacting through soft potentials, we develop a Green's function formalism which we use to derive exact results for displacement fields produced by localized external forces. We show that in the continuum limit the displacement fields decay as $1/r$ at large distances $r$ away from a force dipole. Finally, we extend our formulation to study correlations in the displacement fields produced by the external pinning forces. We show that uncorrelated pinned forces at each vertex give rise to long-range correlations in displacements in athermal systems, with a non-trivial system size dependence. We verify our predictions with numerical simulations of athermal networks in two dimensions.
