Related papers: Dynamical Systems on Spectral Metric Spaces
Anisotropic homogeneous metamaterials that are neither wholly dissipative nor wholly active at a specific frequency are permitted by classical electromagnetic theory. Well-established homogenization formalisms indicate that such a…
This article is concerned with crossed products and their applications to random operators. We study the von Neumann algebra of a dynamical system using the underlying Hilbert algebra structure. This gives a particularly easy way to…
On a discrete group G a length function may implement a spectral triple on the reduced group C*-algebra. Following A. Connes, the Dirac operator of the triple then can induce a metric on the state space of reduced group C*-algebra. Recent…
As an outgrowth of our investigation of non-regular spaces within the context of quantum gravity and non-commutative geometry, we develop a graph Hilbert space framework on arbitrary (infinite) graphs and use it to study spectral properties…
In \cite{D3}, Donaldson defines a dynamical system on the space of Fubini-Study metrics on a polarized compact K\"ahler manifold. Sano proved that if there exists a balanced metric for the polarization, then this dynamical system always…
A commuting triple of Hilbert space operators $(A,B,P)$, for which the closed tetrablock $\overline{\mathbb E}$ is a spectral set, is called a \textit{tetrablock-contraction} or simply an $\mathbb E$-\textit{contraction}, where \[ \mathbb…
Let $H$ be a separable Hilbert space, $A_c:\mathcal D_c\subset H\to H$ a densely defined unbounded operator, bounded from below, let $\mathcal D_{\min}$ be the domain of the closure of $A_c$ and $\mathcal D_{\max}$ that of the adjoint.…
Classical spectral theory gives a complete description of a single normal operator, but it fails for noncommuting operators, where no canonical joint spectrum or simultaneous diagonalization exists. Existing approaches provide only partial…
The development of a metric for structural data is a long-term problem in pattern recognition and machine learning. In this paper, we develop a general metric for comparing nonlinear dynamical systems that is defined with Perron-Frobenius…
We show that if (A,a) and (B,b) are automorphic multivariable C*-dynamical systems with isometrically isomorphic tensor algebras (or semi crossed products), then the systems are piecewise conjugate over their Jacobson spectrum. This answers…
A universal formula for an action associated with a noncommutative geometry, defined by a spectal triple $(\Ac ,\Hc ,D)$, is proposed. It is based on the spectrum of the Dirac operator and is a geometric invariant. The new symmetry…
A Hilbert bimodule is a right Hilbert module X over a C*-algebra A together with a left action of A as adjointable operators on X. We consider families X = {X_s :s\in P} of Hilbert bimodules, indexed by a semigroup P, which are endowed with…
We derive the exact form of the spectral interaction of two strings mediated by a constant scalar field using methods derived from noncommutative geometry. This is achieved by considering a non-product modification of the Connes-Lott model…
We describe a general technique to study Dirac operators on noncommutative spaces under some additional assumptions. The main idea is to capture the compact resolvent condition in a combinatorial set up. Using this, we then prove that for a…
In the noncommutative geometry approach to the standard model we discuss the possibility to derive the extra scalar field sv- initially suggested by particle physicist to stabilize the electroweak vacuum - from a "grand algebra" that…
The goal of these lectures is to present the few fundamentals of noncommutative geometry looking around its spectral approach. Strongly motivated by physics, in particular by relativity and quantum mechanics, Chamseddine and Connes have…
Let $A$ be a unital simple C*-algebra with tracial rank zero and $X$ be a compact metric space. Suppose that $h_1, h_2: C(X)\to A$ are two unital monomorphisms. We show that $h_1$ and $h_2$ are approximately unitarily equivalent if and only…
Dynamical system theory is a widely used technique in the analysis of cosmological models. Within this framework, the equations describing the dynamics of a model are recast in terms of dimensionless variables, which evolve according to a…
The Spectre is an aperiodic monotile for the Euclidean plane that is truly chiral in the sense that it tiles the plane without any need for a reflected tile. The topological and dynamical properties of the Spectre tilings are very similar…
Given a spectral triple on a unital $C^{*}$-algebra $A$ and an equicontinuous action of a discrete group $G$ on $A$, a spectral triple on the reduced crossed product $C^{*}$-algebra $A\rtimes_r G$ was constructed by Hawkins, Skalski, White…