Related papers: The geometry of the Double Gyroid wire network: Qu…
We review applications of noncommutative geometry in canonical quantum gravity. First, we show that the framework of loop quantum gravity includes natural noncommutative structures which have, hitherto, not been explored. Next, we present…
This PhD thesis aims at describing the applications of noncommutative geometry to particle physics and quantum field theory. It includes a brief survey of the basic principles and definitions of noncommutative geometry such as spectral…
The non commutative geometry is a possible framework to regularize Quantum Field Theory in a nonperturbative way. This idea is an extension of the lattice approximation by non commutativity that allows to preserve symmetries. The…
The possible role of gravity in a noncommutative geometry is investigated. Due to the Moyal *-product of fields in noncommutative geometry, it is necessary to complexify the metric tensor of gravity. We first consider the possibility of a…
Quantum wire networks (``quantum crossbars'', QCB) represent a 2D grid formed by superimposed crossing arrays of parallel conducting quantum wires, molecular chains or metallic single-wall carbon nanotubes. QCB coupled only by capacitive…
A general definition has been proposed recently of a linear connection and a metric in noncommutative geometry. It is shown that to within normalization there is a unique linear connection on the quantum plane and there is no metric.
The geometry of a physical system is intimately related to its spectral properties, a concept colloquially referred to as "hearing the shape of a drum". Three-dimensional topological insulator nanowires in a strong magnetic field $B$…
A quantum wire is fabricated on (001)-GaAs at the intersection of two overgrown cleaves. The wire is contacted at each end to n+ GaAs layers via two-dimensional (2D) leads. A sidegate controls the density of the wire revealing conductance…
We have investigated the weakly non-linear quantum transport properties of a two-dimensional quantum conductor. We have developed a numerical scheme which is very general for this purpose. The nonlinear conductance is computed by explicitly…
In this paper we use considerations of non-commutative geometry to deduce a model for QCD interactions. The model also explains within the same theoretical framework hitherto purely phenomenological characteristics of the quarks like their…
Quantum geometry of the electron wave function plays a significant role in the linear and non-linear responses of crystalline materials. Here, we study quantum geometry induced second harmonic generation. We identify non-linear responses…
Networks are topological and geometric structures used to describe systems as different as the Internet, the brain or the quantum structure of space-time. Here we define complex quantum network geometries, describing the underlying…
A classical Wilson line is a cooresponedce between closed paths and elemets of a gauge group. However the noncommutative geometry does not have closed paths. But noncommutative geometry have good generalizations of both: the covering…
A pedagogical and self-contained introduction to noncommutative quantum field theory is presented, with emphasis on those properties that are intimately tied to string theory and gravity. Topics covered include the Weyl-Wigner…
The geometry of Quantum Mechanics in the context of uncertainty and complementarity, and probability is explored. We extend the discussion of geometry of uncertainty relations in wider perspective. Also, we discuss the geometry of…
We briefly describe our application of a version of noncommutative differential geometry to the 3-dim quantum space covariant under the quantum group of rotations $SO_q(3)$ and sketch how this might be used to determine the correct physical…
These notes comprise the second part of two articles devoted to the construction of exact solutions of noncommutative gauge theory in two spacetime dimensions. Here we shall deal with the quantum field theory. Topics covered include an…
A detailed study is made of the noncommutative geometry of $R^3_q$, the quantum space covariant under the quantum group $SO_q(3)$. For each of its two $SO_q(3)$-covariant differential calculi we find its metric, the corresponding frame and…
We investigate the conductance of a quantum wire with two embedded quantum dots using a T-matrix approach based on the Lippmann-Schwinger formalism. The quantum dots are represented by a quantum well with Gaussian shape and the wire is…
We discuss noncommutative gauge theory from the generalized geometry point of view. We argue that the equivalence between the commutative and semiclassically noncommutative DBI actions is naturally encoded in the generalized geometry of…