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

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2019-08-14
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MDPI
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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
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Groups of symmetry, Self-adjoint extensions, Quantum circuits
Bibliographic citation
Balmaseda, A. Di Cosmo, F. y Pérez Pardo, J. M. (2019). On Z -Invariant Self-Adjoint Extensions of the Laplacian on Quantum Circuits. Symmetry, 11(8), 1047.