Mathematical Aspects of Physics with Non-Self-Adjoint Operators: 10 Years After / Les aspects mathématiques de la physique avec les opérateurs non-auto-adjoints: 10 ans après

Collection Mathematical Aspects of Physics with Non-Self-Adjoint Operators: 10 Years After / Les aspects mathématiques de la physique avec les opérateurs non-auto-adjoints: 10 ans après

Organizer(s) Boulton, Lyonell ; Krejcirik, David ; Siegl, Petr

Date(s) 01/02/2021 - 05/02/2021

linked URL https://conferences.cirm-math.fr/2153.html

00:00:00 / 00:00:00

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Absence of eigenvalues of Schrödinger, Dirac and Pauli Hamiltonians via the method of multipliers

By Lucrezia Cossetti

absence of eigenvalues

Originally arisen to understand characterizing properties connected with dispersive phenomena, in the last decades the method of multipliers has been recognized as a useful tool in Spectral Theory, in particular in connection with proof of absence of point spectrum for both self-adjoint and non self-adjoint operators. In this seminar we will see the developments of the method reviewing some recent results concerning self-adjoint and non self-adjoint Schrödinger operators in different settings, specifically both when the configuration space is the whole Euclidean space \R^d and when we restrict to domains with boundaries. We will show how this technique allows to detect physically natural repulsive and smallness conditions on the potentials which guarantee total absence of eigenvalues. Some very recent results concerning Pauli and Dirac operators will be also presented. The talk is based on joint works with L. Fanelli and D. Krejcirik.

Information about the video

Date of recording 01/02/2021
Date of publication 26/02/2021
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19711303
Cite this video Cossetti, Lucrezia (01/02/2021). Absence of eigenvalues of Schrödinger, Dirac and Pauli Hamiltonians via the method of multipliers. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19711303
URL https://dx.doi.org/10.24350/CIRM.V.19711303

Domain(s)

Bibliography

COSSETTI, Lucrezia, FANELLI, Luca, et KREJČIŘÍK, David. Absence of eigenvalues of Dirac and Pauli Hamiltonians via the method of multipliers. Communications in Mathematical Physics, 2020, vol. 379, no 2, p. 633-691. - https://doi.org/10.1007/s00220-020-03853-7
COSSETTI, Lucrezia et KREJČIŘÍK, David. Absence of eigenvalues of non‐self‐adjoint Robin Laplacians on the half‐space. Proceedings of the London Mathematical Society, 2020, vol. 121, no 3, p. 584-616. - https://doi.org/10.1112/plms.12327
FANELLI, Luca, KREJČIŘÍK, David, et VEGA, Luis. Absence of eigenvalues of two-dimensional magnetic Schrödinger operators. Journal of Functional Analysis, 2018, vol. 275, no 9, p. 2453-2472. - https://doi.org/10.1016/j.jfa.2018.08.007
FANELLI, Luca, KREJČIŘÍK, David, VEGA Luis. Spectral stability of Schrödinger operators with subordinated complex potentials. J. Spectr. Theory, 2018, vol.8 , p.575-604. - http://dx.doi.org/10.4171/JST/208

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