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dc.contributor.authorColbrook, Matthewen
dc.contributor.authorRoman, Bogdanen
dc.contributor.authorHansen, Andersen
dc.date.accessioned2019-08-14T23:30:18Z
dc.date.available2019-08-14T23:30:18Z
dc.date.issued2019-06-28en
dc.identifier.issn1079-7114
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/295873
dc.description.abstractComputing the spectra of operators is a fundamental problem in the sciences, with wide-ranging applications in condensed-matter physics, quantum mechanics and chemistry, statistical mechanics, etc. While there are algorithms that in certain cases converge to the spectrum, no general procedure is known that (a) always converges, (b) provides bounds on the errors of approximation, and (c) provides approximate eigenvectors. This may lead to incorrect simulations. It has been an open problem since the 1950s to decide whether such reliable methods exist at all. We affirmatively resolve this question, and the algorithms provided are optimal, realizing the boundary of what digital computers can achieve. Moreover, they are easy to implement and parallelize, offer fundamental speed-ups, and allow problems that before, regardless of computing power, were out of reach. Results are demonstrated on difficult problems such as the spectra of quasicrystals and non-Hermitian phase transitions in optics.
dc.description.sponsorshipThis work was supported by Engineering and Physical Sciences Research Council Grants No. EP/L016516/1, No. EP/R008272/1, No. EP/N014588/1, and No. EP/ L003457/1, as well as a Royal Society University Research Fellowship.
dc.languageengen
dc.publisherAmerican Physical Society
dc.rightsAll rights reserved
dc.rights.uri
dc.titleHow to Compute Spectra with Error Control.en
dc.typeArticle
prism.number250201en
prism.publicationDate2019en
prism.publicationNamePhysical Review Lettersen
prism.volume122en
dc.identifier.doi10.17863/CAM.42920
dcterms.dateAccepted2019-05-13en
rioxxterms.versionofrecord10.1103/PhysRevLett.122.250201en
rioxxterms.versionVoR
rioxxterms.licenseref.urihttp://www.rioxx.net/licenses/all-rights-reserveden
rioxxterms.licenseref.startdate2019-06-28en
dc.contributor.orcidColbrook, Matthew [0000-0003-4964-9575]
dc.identifier.eissn1079-7114
rioxxterms.typeJournal Article/Reviewen
pubs.funder-project-idEPSRC (1804238)
pubs.funder-project-idEPSRC (EP/N014588/1)
pubs.funder-project-idEPSRC (EP/L003457/1)
pubs.funder-project-idEPSRC (EP/L016516/1)
pubs.funder-project-idEPSRC (EP/R008272/1)


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