RT Journal Article
T1 On Z -Invariant Self-Adjoint Extensions of the Laplacian on Quantum Circuits
A1 Balmaseda Martín, Ángel Aitor
A1 Di Cosmo, Fabio
A1 Pérez Pardo, Juan Manuel
AB 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
PB MDPI
YR 2019
FD 2019-08-14
LK https://hdl.handle.net/10016/32031
UL https://hdl.handle.net/10016/32031
LA eng
NO The authors acknowledge partial support provided by the Ministerio de Economía, Industria y Competitividad" research project MTM2017-84098-P and QUITEMAD proyect P2018/TCS-4342 funded by \Comunidad Autónoma de Madrid". A.B. acknowledges financial support by \Universidad Carlos III de Madrid" through Ph.D. program grant PIPF UC3M 01-1819. F.dC. acknowledges financial support by QUITEMAD proyect P2018/TCS-4342 .
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RD 1 sept. 2024