Related papers: Topological spectrum of classical configurations
We introduce the topological complexity of the work map associated to a robot system. In broad terms, this measures the complexity of any algorithm controlling, not just the motion of the configuration space of the given system, but the…
A model of topological field theory is presented in which the vacuum coupling constants are topological invariants of the four-dimensional spacetime. Thus the coupling constants are theoretically computable, and they indicate the…
We introduce the notion of a topological symmetry as a quantum mechanical symmetry involving a certain topological invariant. We obtain the underlying algebraic structure of the Z_2-graded uniform topological symmetries of type (1,1) and…
Although topological band theory has been used to discover and classify a wide array of novel topological phases in insulating and semi-metal systems, it is not well-suited to identifying topological phenomena in metallic or gapless…
A central question in dynamics is whether the topology of a system determines its geometry. This is known as rigidity. Under mild topological conditions rigidity holds for many classical cases, including: Kleinian groups, circle…
A string-theoretic structure of the standard model is defined having a 4-D quantum gravity metric consistent with topological and algebraic first principles. Unique topological diagrams of string states, strong and weak interactions and…
It is increasingly common for data to possess intricate structure, necessitating new models and analytical tools. Graphs, a prominent type of structure, can encode the relationships between any two entities (nodes). However, graphs neither…
We compare classical and quantum dynamics of a particle in the de Sitter spacetimes with different topologies to show that the result of quantization strongly depends on global properties of a classical system. We present essentially…
Topological materials are quantum materials with nontrivial ground-state entanglement that are irremovable so long as certain rules, like invariance under symmetries and the existence of an energy gap, are respected. They showcase…
In classical spin systems with two largely different inherent time scales, the configuration of the fast spins almost instantaneously follows the slow-spin dynamics. We develop the emergent effective theory for the slow-spin degrees of…
The relationship between the sources of physical fields and the fields themselves is investigated with regard to the coupling of topological information between them. A class of field theories that we call topological field theories is…
Flexible mechanical metamaterials possess repeating structural motifs that imbue them with novel, exciting properties including programmability, anomalous elastic moduli and nonlinear and robust response. We address such structures via…
Duality transformations within the quantum mechanics of a finite number of degrees of freedom can be regarded as the dependence of the notion of a quantum, i.e., an elementary excitation of the vacuum, on the observer on classical phase…
This article surveys the use of configuration space integrals in the study of the topology of knot and link spaces. The main focus is the exposition of how these integrals produce finite type invariants of classical knots and links. More…
The structure of real-world networks is usually difficult to characterize owing to the variation of topological scales, the nondyadic complex interactions, and the fluctuations in the network. We aim to address these problems by introducing…
Covering-based rough set theory is an extension to classical rough set. The main purpose of this paper is to study covering rough sets from a topological point of view. The relationship among upper approximations based on topological spaces…
The concept of typed topological space is introduced, for which open sets in a topology on a finite set will be assigned types (from lattice). The neighborhood system of a point, the closure and the connectedness can be defined according to…
In recent work, the authors developed a simple method of constructing topological spaces from certain well-behaved partially ordered sets -- those coming from sequences of relations between finite sets. This method associates a given poset…
Topology, a mathematical concept, has recently become a popular and truly transdisciplinary topic encompassing condensed matter physics, solid state chemistry, and materials science. Since there is a direct connection between real space,…
We briefly review the most relevant aspects of complete integrability for classical systems and identify those aspects which should be present in a definition of quantum integrability. We show that a naive extension of classical concepts to…