Related papers: Characterizing order in amorphous systems
Topologically-ordered phases of matter at non-zero temperature are conjectured to exhibit universal patterns of long-range entanglement which may be detected by a mixed-state entanglement measure known as entanglement negativity. We show…
A unified expression for topological invariants has been proposed recently to describe the topological order in Dirac models belonging to any dimension and symmetry class. We uncover a correspondence between the curvature function that…
We present a method to characterize the distribution of length-scales of finite, disordered patterns with, on average, radial symmetry. This method makes it possible to quantify the distribution of characteristic length scales in cases…
Some fluids are known to behave anomalously. The so-called structural anomaly which means that the fluid becomes less structures under isothermal compression is among the most frequently discussed ones. Several methods for quantifying the…
We discuss the use of symmetries for analysing the structural identifiability and observability of control systems. Special emphasis is put on the role of discrete symmetries, in contrast to the more commonly studied continuous or Lie…
In this paper we propose numerical measures for evaluating the aesthetic interest of simple patterns. The patterns consist of elements (symbols, pixels, etc.) in regular square arrays. The measures depend on two characteristics of the…
In this paper, we provide an overview of the research conducted in the context of structural systems since the latest survey by Dion et al. in 2003. We systematically consider all the papers that cite this survey as well as the seminal work…
We discuss how to characterize the behavior of a chaotic dynamical system depending on a parameter that varies periodically in time. In particular, we study the predictability time, the correlations and the mean responses, by defining a…
In the present work we investigate phase correlations by recourse to the Shannon entropy. Using theoretical arguments we show that the entropy provides an accurate measure of phase correlations in any dynamical system, in particular when…
We present a quantitative measure of physical complexity, based on the amount of information required to build a given physical structure through self-assembly. Our procedure can be adapted to any given geometry, and thus to any given type…
Complexity is a multi-faceted phenomenon, involving a variety of features including disorder, nonlinearity, and self-organisation. We use a recently developed rigorous framework for complexity to understand measures of complexity. We…
One-dimensional gapped systems are often characterized by a 'hidden' non-local order parameter, the so-called string order. Due to the gap, thermodynamic properties are robust against a weak higher-dimensional coupling between such chains…
We propose a measure of shape which is appropriate for the study of a complicated geometric structure, defined using the topology of neighborhoods of the structure. One aspect of this measure gives a new notion of fractal dimension. We…
We use a quantitative topological characterization of complex dynamics to measure geometric structures. This approach is used to analyze the weakly turbulent state of spiral defect chaos in experiments on Rayleigh-Benard convection.…
Compositionality in language refers to how much the meaning of some phrase can be decomposed into the meaning of its constituents and the way these constituents are combined. Based on the premise that substitution by synonyms is…
Connectedness, path connectedness, and uniform connectedness are well-known concepts. In the traditional presentation of these concepts there is a substantial difference between connectedness and the other two notions, namely connectedness…
Quantification of brain morphology has become an important cornerstone in understanding brain structure. Measures of cortical morphology such as thickness and surface area are frequently used to compare groups of subjects or characterise…
Topological order has become a new paradigm to distinguish ground states of interacting many-body systems without conventional long-range order. Here we discuss possible extensions of this concept to density matrices describing statistical…
We propose a diagnostic for finite temperature topological order using `topological entanglement negativity', the long-range component of a mixed-state entanglement measure. As a demonstration, we study the toric code model in $d$ spatial…
Candidates for random network media include, e.g., systems consisting of long, flexible macromolecules cross-linked (i.e., permanently bonded) together at random to form the network. Owing to the random architecture, the characteristics of…