Title: Attractor-driven matter Show Chinese title

Title: 吸引子驱动物质

Abstract: The state of a classical point-particle system may often be specified by giving the position and momentum for each constituent particle. For non-pointlike particles, the center-of-mass position may be augmented by an additional coordinate that specifies the internal state of each particle. The internal state space is typically topologically simple, in the sense that the particle's internal coordinate belongs to a suitable symmetry group. In this paper we explore the idea of giving internal complexity to the particles, by attributing to each particle an internal state space that is represented by a point on a strange (or otherwise) attracting set. It is of course very well known that strange attractors arise in a variety of nonlinear dynamical systems. However, rather than considering strange attractors as emerging from complex dynamics, we may employ strange attractors to {\em drive} such dynamics. In particular, by using an attractor (strange or otherwise) to model each particle's internal state space, we present a class of matter coined ``attractor-driven matter''. We outline the general formalism for attractor-driven matter and explore several specific examples, some of which are reminiscent of active matter. Beyond the examples studied in this paper, our formalism for attractor-driven dynamics may be applicable more broadly, to model complex dynamical and emergent behaviors in a variety of contexts. Show Chinese abstract

Abstract: 经典点粒子系统的状态通常可以通过给出每个组成粒子的位置和动量来指定。 对于非点状粒子，质心位置可以附加一个额外的坐标，该坐标指定每个粒子的内部状态。 内部状态空间通常是拓扑简单的，即粒子的内部坐标属于一个合适的对称群。 在本文中，我们探讨了为粒子赋予内部复杂性的想法，即为每个粒子分配一个由奇异（或其它）吸引子上的点表示的内部状态空间。 众所周知，奇异吸引子出现在各种非线性动力系统中。 然而，与其将奇异吸引子视为复杂动力学的产物，我们可能利用奇异吸引子来{\em 驱动}这样的动力学。 具体而言，通过使用一个吸引子（奇异或其它）来建模每个粒子的内部状态空间，我们提出了一类被称为 “吸引子驱动物质”的物质类型。 我们概述了吸引子驱动物质的一般形式主义，并探讨了几个具体的例子，其中一些类似于活性物质。 除了本文研究的例子外，我们对吸引子驱动动力学的形式主义可能更广泛地适用，以在各种情境中建模复杂动力学和涌现行为。