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dc.contributor.author
Sohinger, Vedran
dc.contributor.author
Staffilani, Gigliola
dc.date.accessioned
2022-08-02T07:20:30Z
dc.date.available
2017-06-11T18:15:14Z
dc.date.available
2022-08-02T07:20:30Z
dc.date.issued
2015-10
dc.identifier.issn
0003-9527
dc.identifier.issn
1432-0673
dc.identifier.other
10.1007/s00205-015-0863-0
en_US
dc.identifier.uri
http://hdl.handle.net/20.500.11850/102369
dc.identifier.doi
10.3929/ethz-b-000102369
dc.description.abstract
We study the Gross–Pitaevskii hierarchy on the spatial domain 𝕋�3 . By using an appropriate randomization of the Fourier coefficients in the collision operator, we prove an averaged form of the main estimate which is used in order to contract the Duhamel terms that occur in the study of the hierarchy. In the averaged estimate, we do not need to integrate in the time variable. An averaged spacetime estimate for this range of regularity exponents then follows as a direct corollary. The range of regularity exponents that we obtain is 𝛼�>34 . It was shown in our previous joint work with Gressman (J Funct Anal 266(7):4705–4764, 2014) that the range 𝛼�>1 is sharp in the corresponding deterministic spacetime estimate. This is in contrast to the non-periodic setting, which was studied by Klainerman and Machedon (Commun Math Phys 279(1):169–185, 2008), where the spacetime estimate is known to hold whenever 𝛼�≥1 . The goal of our paper is to extend the range of α in this class of estimates in a probabilistic sense. We use the new estimate and the ideas from its proof in order to study randomized forms of the Gross–Pitaevskii hierarchy. More precisely, we consider hierarchies similar to the Gross–Pitaevskii hierarchy, but in which the collision operator has been randomized. For these hierarchies, we show convergence to zero in low regularity Sobolev spaces of Duhamel expansions of fixed deterministic density matrices. We believe that the study of the randomized collision operators could be the first step in the understanding of a nonlinear form of randomization.
en_US
dc.format
application/pdf
en_US
dc.language.iso
en
en_US
dc.publisher
Springer
en_US
dc.rights.uri
http://rightsstatements.org/page/InC-NC/1.0/
dc.title
Randomization and the Gross-Pitaevskii Hierarchy
en_US
dc.type
Journal Article
dc.rights.license
In Copyright - Non-Commercial Use Permitted
dc.date.published
2015-04-04
ethz.journal.title
Archive for Rational Mechanics and Analysis
ethz.journal.volume
218
en_US
ethz.journal.issue
1
en_US
ethz.journal.abbreviated
Arch. ration. mech. anal.
ethz.pages.start
417
en_US
ethz.pages.end
485
en_US
ethz.version.deposit
publishedVersion
en_US
ethz.notes
It was possible to publish this article open access thanks to a Swiss National Licence with the publisher.
en_US
ethz.identifier.wos
ethz.identifier.nebis
000042742
ethz.publication.place
Berlin
en_US
ethz.publication.status
published
en_US
ethz.date.deposited
2017-06-11T18:15:23Z
ethz.source
ECIT
ethz.identifier.importid
imp5936534eac05989951
ethz.ecitpid
pub:160501
ethz.eth
yes
en_US
ethz.availability
Open access
en_US
ethz.rosetta.installDate
2017-07-19T01:28:20Z
ethz.rosetta.lastUpdated
2021-02-14T13:06:42Z
ethz.rosetta.exportRequired
true
ethz.rosetta.versionExported
true
ethz.COinS
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