Related papers: Addendum to "Superconnections and Parallel Transpo…
Superdiffusion is an anomalous transport behavior. Recently, a new mechanism, termed the ``nodal mechanism," has been proposed to induce superdiffusion in quantum models. However, existing realizations of the nodal mechanism have so far…
This article presents new colored link invariants by introducing the concepts of multi-quandles and topological multi-quandles.
The functionality of nodes in a network is often described by the structural feature of belonging to the giant component. However, when dealing with problems like transport, a more appropriate functionality criterion is for a node to belong…
In this paper we establish a one-to-one correspondence between $S^1$-gerbes with connections, on the one hand, and their holonomies, for simply connected manifolds, or their parallel transports, in the general case, on the other hand. This…
We study the charge transport properties of fields confined to a (2+1)-dimensional defect coupled to (3+1)-dimensional super-Yang-Mills at large-$\nc$ and strong coupling, using AdS/CFT techniques applied to linear response theory. The dual…
We define a notion of connection in a fibre bundle that is compatible with a singular foliation of the base. Fibre bundles equipped with such connections are in plentiful supply, arising naturally for any Lie groupoid-equivariant bundle,…
This paper defines a notion of parallel transport in a lattice of quantum particles, such that the transformation associated with each link of the lattice is determined by the quantum state of the two particles joined by that link. We focus…
Our traditional notion of a cell is changing dramatically given the increasing degree of heterogeneity in 4G and emerging 5G systems. Rather than belonging to a specific cell, a device would choose the most suitable connection from the…
We establish that the isomorphy type as an abstract algebraic variety of the complement of an ample hyperplane sub-bundle H of a projective space bundle of rank r-1 over the projective line depends only on the the r-fold self-intersection…
The (parallel) linear transports along paths in vector bundles are axiomatically described. Their general form and certain properties are found. It is shown that these transports are locally (i.e. along every fixed path) always Euclidean…
This paper is motivated by recent developments of higher gauge theory. Different from its style of using higher category theory, we try to describe the concept of higher parallel transport within setting of classical principal bundle…
Just as gauge theory describes the parallel transport of point particles using connections on bundles, higher gauge theory describes the parallel transport of 1-dimensional objects (e.g. strings) using 2-connections on 2-bundles. A 2-bundle…
The transport in complex multiple quantum well heterostructures is theoretically described. The model is focused on quantum cascade detectors, which represent an exciting challenge due to the complexity of the structure containing 7 or 8…
Any endomorphism of a finitely generated free group naturally descends to an injective endomorphism of its stable quotient. In this paper, we prove a geometric incarnation of this phenomenon: namely, that every expanding irreducible train…
We show that in a nonintegrable spin ladder system with the XX type of coupling along the legs and the XXZ type along the rungs there are invariant subspaces that support ballistic magnetization transport. In the complementary subspace the…
We investigate the implications of different forms of multi-group connectivity. Four multi-group connectivity modalities are considered: co-memberships, edge bundles, bridges, and liaison hierarchies. We propose generative models to…
Commutativity has the same inherent limitations as compatibility. Then, it is worth conceiving simple concurrency control techniques. We propose a restricted form of commutativity which increases parallelism without incurring a higher…
Unitals can be obtained as closures of affine unitals via parallelisms. The isomorphism type of the closure depends on the chosen parallelism, which need not be unique. For affine $\operatorname{SL}(2,q)$-unitals, we introduce a class of…
We present a method to extract temporal hypergraphs from sequences of 2-dimensional functions obtained as solutions to Optimal Transport problems. We investigate optimality principles exhibited by these solutions from the point of view of…
In this paper, a brief review of the history of topological insulators is given. After that,electronic transport experiments in topological insulator-superconductor hybrid structures, including experimental methods, physical properties and…