Related papers: Geometry- and topology-controlled synchronization …
The Kuramoto model is a classical nonlinear ODE system designed to study synchronization phenomena. Each equation represents the phase of an oscillator and the coupling between them is determined by a graph. There is an increasing interest…
Simplicial synchronization reveals the role that topology and geometry have in determining the dynamical properties of simplicial complexes. Simplicial network geometry and topology are naturally encoded in the spectral properties of the…
We report upon the numerical computation of the Euler characteristic \chi (a topologic invariant) of the equipotential hypersurfaces \Sigma_v of the configuration space of the two-dimensional lattice $\phi^4$ model. The pattern…
We study topological transitions in one dimensional superconductors that can harbor multiple edge Majorana bound states protected by chiral symmetry. The chiral symmetry arises due to the structure of the internal spin degrees of freedom of…
The influence of topological defects on phase synchronization and phase coherence in two-dimensional arrays of locally-coupled, nonidentical, chaotic oscillators is investigated. The motion of topological defects leads to a breakdown of…
The relation between thermodynamic phase transitions in classical systems and topological changes in their configuration space is discussed for two physical models and contains the first exact analytic computation of a topologic invariant…
We show that topology can protect exponentially localized, zero energy edge modes at critical points between one-dimensional symmetry protected topological phases. This is possible even without gapped degrees of freedom in the bulk ---in…
The phase transition in the mean-field XY model is shown analytically to be related to a topological change in its configuration space. Such a topology change is completely described by means of Morse theory allowing a computation of the…
Topological phase transitions track changes in topological properties of a system and occur in real materials as well as quantum engineered systems, all of which differ greatly in terms of dimensionality, symmetries, interactions, and…
The emergence of synchrony essentially underlies the functionality of many systems across physics, biology and engineering. In all established synchronization phase transitions so far, a stable synchronous state is connected to a stable…
Certain geometric properties of submanifolds of configuration space are numerically investigated for classical lattice phi^4 models in one and two dimensions. Peculiar behaviors of the computed geometric quantities are found only in the…
Study of symmetry, topology and geometric phase can reveal many new and interesting results on the topological states of matter. Here we present a completely new and interesting result of symmetry, topology and quantization of geometric…
The discovery of topological features of quantum states plays an important role in modern condensed matter physics and various artificial systems. Due to the absence of local order parameters, the detection of topological quantum phase…
Recent advancements in topological metamaterials have unveiled fruitful physics and numerous applications. Whereas initial efforts focus on achieving topologically protected edge states through principles of structural symmetry, the…
One of the important characteristics of topological phases of matter is the topology of the underlying manifold on which they are defined. In this paper, we present the sensitivity of such phases of matter to the underlying topology, by…
The Kuramoto model is a classical mathematical model in the field of non-linear dynamical systems that describes the evolution of coupled oscillators in a network that may reach a synchronous state. The relationship between the network's…
In this first paper, we demonstrate a theorem that establishes a first step toward proving a necessary topological condition for the occurrence of first or second order phase transitions: we prove that the topology of certain submanifolds…
Topological holography is a holographic principle that describes the generalized global symmetry of a local quantum system in terms of a topological order in one higher dimension. This framework separates the topological data from the local…
The tenfold classification provides a powerful framework for organizing topological phases of matter based on symmetry and spatial dimension. However, it does not offer a systematic method for transitioning between classes or engineering…
In this paper, we aim to investigate the synchronization problem of dynamical systems, which can be of generic linear or Lipschitz nonlinear type, communicating over directed switching network topologies. A mild connectivity assumption on…