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Evolution and invariants of free-particle moments

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dc.contributor.authorAndrews, Mark
dc.date.accessioned2023-04-27T23:31:09Z
dc.date.issued2021
dc.date.updated2022-02-06T07:18:00Z
dc.description.abstractMoments are expectation values of products of powers of position and momentum, taken over quantum states (or averages over a set of classical particles). For free particles, the evolution in the quantumcase is closely related to that of a set of classical particles. Here we consider the evolution of symmetrized moments for free particles in one dimension, first examining the geometric properties of the evolution for moments up to the fourth order, as determined by their extrema and inflections. These properties are specified by combinations of the moments that are invariant in that they remain constant under free evolution. An inequality constrains the fourth-order moments and shows that some geometric types of evolution are possible for a quantum particle but not possible classically, and some examples are examined. Explicit expressions are found for the moments of any order in terms of their initial values, for the invariant combinations, and for the moments in terms of these invariants.en_AU
dc.format.mimetypeapplication/pdfen_AU
dc.identifier.issn1751-8113en_AU
dc.identifier.urihttp://hdl.handle.net/1885/289751
dc.language.isoen_AUen_AU
dc.publisherIOP Electronic Journalsen_AU
dc.rights© 2021 IOP Publishing Ltd Printed in the UKen_AU
dc.sourceJournal of Physics A: Mathematical and Theoreticalen_AU
dc.subjectmomentsen_AU
dc.subjectfree-particlesen_AU
dc.subjectevolutionen_AU
dc.subjectinvariantsen_AU
dc.titleEvolution and invariants of free-particle momentsen_AU
dc.typeJournal articleen_AU
local.bibliographicCitation.issue20en_AU
local.bibliographicCitation.lastpage16en_AU
local.bibliographicCitation.startpage1en_AU
local.contributor.affiliationAndrews, Mark, College of Science, ANUen_AU
local.contributor.authoruidAndrews, Mark, u3493929en_AU
local.description.embargo2099-12-31
local.description.notesImported from ARIESen_AU
local.identifier.absfor510804 - Quantum optics and quantum optomechanicsen_AU
local.identifier.absseo280120 - Expanding knowledge in the physical sciencesen_AU
local.identifier.ariespublicationa383154xPUB19254en_AU
local.identifier.citationvolume54en_AU
local.identifier.doi10.1088/1751-8121/abf27cen_AU
local.identifier.scopusID2-s2.0-85105059121
local.publisher.urlhttps://iopscience.iop.org/en_AU
local.type.statusPublished Versionen_AU

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