Pazó Diego, Gallego Rafael
Instituto de Física de Cantabria (IFCA), Universidad de Cantabria-CSIC, 39005 Santander, Spain.
Departamento de Matemáticas, Universidad de Oviedo, Campus de Viesques, 33203 Gijón, Spain.
Phys Rev E. 2023 Jul;108(1-1):014202. doi: 10.1103/PhysRevE.108.014202.
Populations of heterogeneous phase oscillators with frustrated random interactions exhibit a quasiglassy state in which the distribution of local fields is volcanoshaped. In a recent work [Phys. Rev. Lett. 120, 264102 (2018)10.1103/PhysRevLett.120.264102], the volcano transition was replicated in a solvable model using a low-rank, random coupling matrix M. We extend here that model including tunable nonreciprocal interactions, i.e., M^{T}≠M. More specifically, we formulate two different solvable models. In both of them the volcano transition persists if matrix elements M_{jk} and M_{kj} are enough correlated. Our numerical simulations fully confirm the analytical results. To put our work in a wider context, we also investigate numerically the volcano transition in the analogous model with a full-rank random coupling matrix.
具有受挫随机相互作用的异相振荡器群体呈现出一种准玻璃态，其中局部场的分布呈火山形状。在最近的一项工作[《物理评论快报》120, 264102 (2018)10.1103/PhysRevLett.120.264102]中，使用低秩随机耦合矩阵M在一个可解模型中重现了火山转变。我们在此扩展该模型，纳入可调谐的非互易相互作用，即M^T≠M。更具体地说，我们构建了两个不同的可解模型。在这两个模型中，如果矩阵元素M_{jk}和M_{kj}具有足够的相关性，火山转变就会持续存在。我们的数值模拟充分证实了分析结果。为了将我们的工作置于更广泛的背景下，我们还对具有满秩随机耦合矩阵的类似模型中的火山转变进行了数值研究。
