-Invariant Self-Adjoint Extensions of the Laplacian on Quantum Circuits
Depto. de Matemáticas, Univ. Carlos III de Madrid, Avda. de la Universidad 30, Leganés, 28911 Madrid, Spain
Instituto de Ciencias Matemáticas (CSIC - UAM - UC3M - UCM) ICMAT, C/ Nicolás Cabrera 13-15, 28049 Madrid, Spain
Author to whom correspondence should be addressed.
Received: 16 July 2019 / Revised: 6 August 2019 / Accepted: 10 August 2019 / Published: 14 August 2019
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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,
, constituting a quantum circuit, which are invariant under a given action of the group
. A study of the different unitary representations of the group
on the space of square integrable functions on
is performed and the corresponding
-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.
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MDPI and ACS Style
Balmaseda, A.; Di Cosmo, F.; Pérez-Pardo, J.M. On
-Invariant Self-Adjoint Extensions of the Laplacian on Quantum Circuits. Symmetry 2019, 11, 1047.
Balmaseda A, Di Cosmo F, Pérez-Pardo JM. On
-Invariant Self-Adjoint Extensions of the Laplacian on Quantum Circuits. Symmetry. 2019; 11(8):1047.
Balmaseda, Aitor; Di Cosmo, Fabio; Pérez-Pardo, Juan M. 2019. "On
-Invariant Self-Adjoint Extensions of the Laplacian on Quantum Circuits." Symmetry 11, no. 8: 1047.
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