Dirac operator on graph
WebJan 1, 2024 · The Dirac operator at the graph edges is defined. δ-like potential is assumed to posed at the graph vertex. It is proved that the operator has non-empty discrete spectrum. View. WebThe infinite 3-star graph the NonLinear Dirac Equation (NLDE) on networks, where the Dirac operator is given by D := −ıc d dx ⊗ σ1 +mc ⊗ σ3 . (1) Here m > 0 and c > 0 are two parameters representing the mass of the generic particle of the system and the speed of light (respectively), and σ1 and σ3 are the so-called Pauli matrices, i ...
Dirac operator on graph
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WebOct 7, 2024 · In this note we present some properties of the Dirac operator on noncompact metric graphs with Kirchoff-type vertex conditions. In particular, we discuss its spectral features and describe the associated quadratic form. Keywords. Dirac operator; Metric graphs; Spectral properties; Kirchoff-type conditions; Boundary triplets WebWe construct spectral zeta functions for the Dirac operator on metric graphs. We start with the case of a rose graph, a graph with a single vertex where every edge is a loop. The …
WebOct 21, 2024 · Partial inverse problems for Dirac operators on star graphs are studied. We consider Dirac operators on the graphs, and prove that the potential on one edge is uniquely determined by part of its spectra and part of the potential provided that the potentials on the remaining edges are given a priori. This extends the results of Horváth … WebJun 30, 2024 · Instead, we define the dirac delta by what it does: any integration interval over the dirac delta that includes x=0 is 1. If it doesn't include x=0, it's 0; An integral over a function multiplied with a dirac delta will return the value of the function at x= 0 (or wherever the argument into the dirac vanishes)
WebApr 13, 2024 · Abstract. We study the continuum limit for Dirac–Hodge operators defined on the n dimensional square lattice h\mathbb {Z}^n as h goes to 0. This result extends to a first order discrete differential operator the known convergence of discrete Schrödinger operators to their continuous counterpart. WebIn general, let D be a first-order differential operator acting on a vector bundle V over a Riemannian manifold M. If =, where ∆ is the Laplacian of V, then D is called a Dirac …
WebBesides the deformed D(t) = d(t) + d(t) * + b(t) the new exterior derivative defines a new Dirac operator C(t) = d(t) + d(t) * which in the spirit of noncommutative geometry defines …
WebJan 25, 2015 · $\begingroup$ am improvement is desirable in your graphs. The barrier is not finite, it's infinite, and so the dip before it. To show that one can leave an opening on the peak and on the bottom of the dip. That hints the barrier continues to $\infty $ and the dip to $-\infty $ . $\endgroup$ – stuart oakley nomuraWebJan 1, 2024 · As a further development, in the last years the study of the Dirac operator on metric graphs. has also generated a growing interest (see, e.g., [7, 12, 20, 43]). Moreover, recently [46] proposed stuart nunnally marble falls txWebQuantum graphs are metric graphs equipped with a differential (or pseudo-differential) operator acting on functions on the graph. A function on a metric graph is defined as the -tuple of functions on the intervals. The Hilbert space of the graph is where the inner product of two functions is. may be infinite in the case of an open edge. stuart nurseryWeb2. Dirac operator Given a nite simple graph G = (V;E), let G k be the set of K k+1 subgraphs and let G= S k=0 G k be the union of these sub-simplices. Elements in … stuart nursing home abuse attorneyWebJan 1, 2024 · The Dirac operator at the graph edges is defined. δ-like potential is assumed to posed at the graph vertex. It is proved that the operator has non-empty discrete … stuart nursing home lawyersWebJul 15, 2012 · In this paper, under some integrability condition, we prove that an electrical perturbation of the discrete Dirac operator has purely absolutely continuous spectrum for the one dimensional case. We reduce the problem to a non-self-adjoint Laplacian-like operator by using a spin up/down decomposition and rely on a transfermatrices technique. stuart nursing home abuse lawyerWebApr 5, 2024 · In this paper we prove an initial data rigidity result \`a la Eichmair, Galloway and Mendes (arXiv:2009.09527) using Dirac operator techniques. It applies to initial data sets on spin bands that satisfy the dominant energy condition, a boundary condition for the future null expansion scalar and the $\hat{A}$-obstruction for positive scalar ... stuart nye backward loop earrings