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Quantum systems at the brink: existence of bound states, critical potentials, and dimensionality

Jex, Michal and Hundertmark, Dirk and Lange, Markus (2023) Quantum systems at the brink: existence of bound states, critical potentials, and dimensionality. Forum of Mathematics, Sigma, 11. Cambridge University Press. doi: 10.1017/fms.2023.39. ISSN 2050-5094.

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Official URL: https://doi.org/10.1017/fms.2023.39

Abstract

One of the crucial properties of a quantum system is the existence of bound states. While the existence of eigenvalues below zero, that is, below the essential spectrum, is well understood, the situation of zero energy bound states at the edge of the essential spectrum is far less understood. We present complementary sharp criteria for the existence and nonexistence of zero energy ground states. Our criteria give a straightforward explanation for the folklore that there is a spectral phase transition with critical dimension four, concerning the existence versus nonexistence of zero energy ground states.

Item URL in elib:https://elib.dlr.de/197304/
Document Type:Article
Title:Quantum systems at the brink: existence of bound states, critical potentials, and dimensionality
Authors:
AuthorsInstitution or Email of AuthorsAuthor's ORCID iDORCID Put Code
Jex, MichalUNSPECIFIEDUNSPECIFIEDUNSPECIFIED
Hundertmark, DirkUNSPECIFIEDUNSPECIFIEDUNSPECIFIED
Lange, MarkusUNSPECIFIEDhttps://orcid.org/0000-0001-7198-2871147095126
Date:17 July 2023
Journal or Publication Title:Forum of Mathematics, Sigma
Refereed publication:Yes
Open Access:Yes
Gold Open Access:Yes
In SCOPUS:Yes
In ISI Web of Science:Yes
Volume:11
DOI:10.1017/fms.2023.39
Publisher:Cambridge University Press
ISSN:2050-5094
Status:Published
Keywords:Schrödinger operator, ground states, critical potentials
HGF - Research field:other
HGF - Program:other
HGF - Program Themes:other
DLR - Research area:Digitalisation
DLR - Program:D - no assignment
DLR - Research theme (Project):D - ELEVATE
Location: Ulm
Institutes and Institutions:Institute for AI Safety and Security
Deposited By: Lange, Dr. Markus
Deposited On:21 Nov 2023 12:48
Last Modified:21 Nov 2023 12:48

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