On Z -Invariant Self-Adjoint Extensions of the Laplacian on Quantum Circuits Articles uri icon

publication date

  • August 2019

start page

  • 1

end page

  • 21

issue

  • 8

volume

  • 11

abstract

  • An analysis of the invariance properties of self-adjoint extensions of symmetric operators under the action of a group of symmetries is presented. For a given group G, criteria for the existence of G-invariant self-adjoint extensions of the Laplace&-Beltrami operator over a Riemannian manifold are illustrated and critically revisited. These criteria are employed for characterising self-adjoint extensions of the Laplace&-Beltrami operator on an infinite set of intervals, &;937# , constituting a quantum circuit, which are invariant under a given action of the group Z . A study of the different unitary representations of the group Z on the space of square integrable functions on Omega is performed and the corresponding Z -invariant self-adjoint extensions of the Laplace&-Beltrami operator are introduced. The study and characterisation of the invariance properties allows for the determination of the spectrum and generalised eigenfunctions in particular examples. View Full-Text

keywords

  • groups of symmetry; self-adjoint extensions; quantum circuits