Geometric Confinement and Dynamical Transmission of a Quantum Particle in Grushin Cylinder

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dc.contributor.authorGallone, Matteo
dc.contributor.authorMichelangeli, Alessandro
dc.contributor.authorPozzoli, Eugenio
dc.date.accessioned2020-03-20T06:50:50Z
dc.date.available2020-03-20T06:50:50Z
dc.date.issued2019
dc.description69 p.en_US
dc.description.abstractWe classify the self-adjoint realisations of the Laplace-Beltrami operator minimally defined on an infinite cylinder equipped with an incom-plete Riemannian metric of Grushin type, in the non-trivial class of metrics yielding an infinite deficiency index. Such realisations are naturally interpreted as Hamiltonians governing the geometric confinement of a Schr¨odinger quan-tum particle away from the singularity, or the dynamical transmission across the singularity. In particular, we characterise all physically meaningful exten-sions qualified by explicit local boundary conditions at the singularity. Within our general classification we retrieve those distinguished extensions previously identified in the recent literature, namely the most confining and the most transmitting one.en_US
dc.identifier.urihttps://openscience.sissa.it/handle/1963/35346
dc.language.isoenen_US
dc.publisherSISSAen_US
dc.relation.ispartofseriesSISSA;26/2019/MATE
dc.subjectGeometry and Mathematical Physicsen_US
dc.titleGeometric Confinement and Dynamical Transmission of a Quantum Particle in Grushin Cylinderen_US
dc.typePreprinten_US
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