Related papers: Category of SET orders
Mapping an atomistic configuration to an $N$-point correlation of a field associated with the atomic positions (e.g. an atomic density) has emerged as an elegant and effective solution to represent structures as the input of…
We supply basic tools for the study of the topological order of a multiplet which is an eigenspace of a finite-dimensional normal operator with continuous parameters. We allow intrinsic degeneracies within the multiplet where a well-known…
We investigate a category of quantum posets that generalizes the category of posets and monotone functions. Up to equivalence, its objects are hereditarily atomic von Neumann algebras equipped with quantum partial orders in Weaver's sense.…
For quantum field theories with global symmetry, we can study the behavior of the partition function with the background gauge field to diagnose different quantum phases. For the case of discrete symmetries, we find that the…
Exploiting the symmetry topological field theory/topological order correspondence (SymTFT/TO), together with the higher-categorical structure of 6D N =(2,0) SCFTs, we prove that the total quantum dimension of the relative gaugeable algebra…
A self-correcting quantum memory can store and protect quantum information for a time that increases without bound with the system size and without the need for active error correction. We demonstrate that symmetry can lead to…
Systems of equations with sets of integers as unknowns are considered. It is shown that the class of sets representable by unique solutions of equations using the operations of union and addition $S+T=\makeset{m+n}{m \in S, \: n \in T}$ and…
We propose a definition of a non-invertible symmetry enriched topological order (NI-SETO), and we implement our definition for string net models. We do so in two ways, using full inclusions of unitary fusion categories (UFCs), as well as…
A new approach is suggested to the problem of quantising causal sets, or topologies, or other such models for space-time (or space). The starting point is the observation that entities of this type can be regarded as objects in a category…
Tree sets are abstract structures that can be used to model various tree-shaped objects in combinatorics. Finite tree sets can be represented by finite graph-theoretical trees. We extend this representation theory to infinite tree sets.…
We investigate the set of partial partitions of a finite set, ordered by inclusion. With this ordering the set of partial partitions can be studied as an abstract simplicial complex. We use the theory of shellable nonpure complexes to find…
Preference orderings are orderings of a set of items according to the preferences (of judges). Such orderings arise in a variety of domains, including group decision making, consumer marketing, voting and machine learning. Measuring the…
We develop a compositional framework for generalized reversible computing using copy-discard categories and resource theories. We introduce partitioned matrices between partitioned sets as subdistribution matrices which preserve the…
In this paper we have investigated enumeration orders of elements of r.e. sets enumerated by means of Turing machines. We have defined a reducibility based on enumeration orders named "Enumeration Order Reducibility" on computable functions…
We show that the symmetry topological field theory (SymTFT) construction, also known as the topological holography, provides a natural and intuitive framework for the entropic order parameter characterising phases with (partially) broken…
Classical problems of sorting and searching assume an underlying linear ordering of the objects being compared. In this paper, we study a more general setting, in which some pairs of objects are incomparable. This generalization is relevant…
Topological order has been proposed to go beyond Landau symmetry breaking theory for more than twenty years. But it is still a challenging problem to generally detect it in a generic many-body state. In this paper, we will introduce a…
This article is a fundamental study in computable measure theory. We use the framework of TTE, the representation approach, where computability on an abstract set X is defined by representing its elements with concrete "names", possibly…
Optimization problems, generalized equations, and the multitude of other variational problems invariably lead to the analysis of sets and set-valued mappings as well as their approximations. We review the central concept of set-convergence…
Sigma models effectively describe ordered phases of systems with spontaneously broken symmetries. At low energies, field configurations fall into solitonic sectors, which are homotopically distinct classes of maps. Depending on context,…