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The resistance R of a high density network of 6 nm diameter Bi wires in porous Vycor glass is studied in order to observe its expected semiconductor behavior. R increases from 300 K down to 0.3 K. Below 4 K, where R varies approximately as…
We investigate electronic quantum transport through nano-wires with one-sided surface roughness. A magnetic field perpendicular to the scattering region is shown to lead to exponentially diverging localization lengths in the…
A link between canonical quantum gravity and fermionic quantum field theory is established in this paper. From a spectral triple construction which encodes the kinematics of quantum gravity semi-classical states are constructed which, in a…
With the rapid development of quantum information and technology in recent years, the construction of quantum internet for interconnecting all kinds of quantum devices, such as quantum processors and sensors, will be the next trend for…
We explore the experimental observation that complex networks of porous media exhibit the property that the porous coordination number is proportional to its size. Based in this geometry-topology duality we developed an analytical approach…
It is shown that a $d$-dimensional classical SU(N) Yang-Mills theory can be formulated in a $d+2$-dimensional space, with the extra two dimensions forming a surface with non-commutative geometry.
Carbon nanotubes are a feverishly-studied topic in the scientific community as of late. Mathematically, they can be modeled with a quantum graph. Here we consider a structure somewhat similar to carbon nanotubes, another quantum graph that…
We clarify relations between the higher dimensional quantum Hall effect and A-class topological insulator. In particular, we elucidate physical implications of the higher dimensional non-commutative geometry in the context of A-class…
Spin networks are at the core of quantum gravity. Our aim is to plug the mathematical community at large into the procedures turn to create a finite quantum theory of general relativity. For this, because of the different cultural…
Geometric quantum mechanics aims to express the physical properties of quantum systems in terms of geometrical features preferentially selected in the space of pure states. Geometric characterisations are given here for systems of one, two,…
Topological quantum materials have emerged as a frontier in condensed matter physics as well as in materials science, with intriguing electronic states that are robust to perturbations. Among the diverse structural motifs, kagome, chiral,…
We give a general and nontechnical review of some aspects of noncommutative geometry as a tool to understand the structure of spacetime. We discuss the motivations for the constructions of a noncommutative geometry, and the passage from…
Using the formalism of noncommutative geometric gauge theory based on the superconnection concept, we construct a new type of vector gauge theory possessing a shift-like symmetry and the usual gauge symmetry. The new shift-like symmetry is…
We discuss various aspects of noncommutative geometry of a smooth subalgebra of the Toeplitz algebra. In particular, we study the structure of derivations on this subalgebra.
Quantum descriptions of many complex systems are formulated most naturally in bases of states that are not mutually orthogonal. We introduce a general and powerful yet simple approach that facilitates solving such models exactly by…
We propose a novel mechanism for creating a qubit based on a tight knot, that is a nano-quantum wire system so small and so cold as to be quantum coherent with respect to curvature-induced effects. To establish tight knots as legitimate…
Data describing the three-dimensional structure of physical networks is increasingly available, leading to a surge of interest in network science to explore the relationship between the shape and connectivity of physical networks. We…
We formulate a mathematical setup for computational neural networks using noncommutative algebras and near-rings, in motivation of quantum automata. We study the moduli space of the corresponding framed quiver representations, and find…
Research in two-dimensional (2D) materials has experienced rapid growth in the past few years. In particular, various layered compounds exhibiting quantum phenomena, such as superconductivity and magnetism, have been isolated in atomically…
Geometrization of physical theories have always played an important role in their analysis and development. In this contribution we discuss various aspects concerning the geometrization of physical theories: from classical mechanics to…