An optimal semiclassical bound on commutators of spectral projections with position and momentum operators
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An optimal semiclassical bound on commutators of spectral projections with position and momentum operators. / Fournais, Søren; Mikkelsen, Søren.
In: Letters in Mathematical Physics, Vol. 110, No. 12, 12.2020, p. 3343-3373.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - An optimal semiclassical bound on commutators of spectral projections with position and momentum operators
AU - Fournais, Søren
AU - Mikkelsen, Søren
N1 - Funding Information: The authors were partially supported by the Sapere Aude Grant DFF–4181-00221 from the Independent Research Fund Denmark. Part of this work was carried out while both authors visited the Mittag-Leffler Institute in Stockholm, Sweden. Funding Information: The authors were partially supported by the Sapere Aude Grant DFF?4181-00221 from the Independent Research Fund Denmark. Part of this work was carried out while both authors visited the Mittag-Leffler Institute in Stockholm, Sweden. Publisher Copyright: © 2020, Springer Nature B.V.
PY - 2020/12
Y1 - 2020/12
N2 - We prove an optimal semiclassical bound on the trace norm of the following commutators [1(-∞,](Hħ) , x] , [1(-∞,](Hħ) , - iħ∇] and [1(-∞,](Hħ) , ei⟨t,x⟩] , where Hħ is a Schrödinger operator with a semiclassical parameter ħ, x is the position operator, -iħ∇ is the momentum operator, and t in Rd is a parameter. These bounds are in the non-interacting setting the ones introduced as an assumption by N. Benedikter, M. Porta and B. Schlein in a study of the mean-field evolution of a fermionic system.
AB - We prove an optimal semiclassical bound on the trace norm of the following commutators [1(-∞,](Hħ) , x] , [1(-∞,](Hħ) , - iħ∇] and [1(-∞,](Hħ) , ei⟨t,x⟩] , where Hħ is a Schrödinger operator with a semiclassical parameter ħ, x is the position operator, -iħ∇ is the momentum operator, and t in Rd is a parameter. These bounds are in the non-interacting setting the ones introduced as an assumption by N. Benedikter, M. Porta and B. Schlein in a study of the mean-field evolution of a fermionic system.
KW - Commutator estimates
KW - Optimal semiclassics
KW - Weyl law
UR - http://www.scopus.com/inward/record.url?scp=85090462959&partnerID=8YFLogxK
U2 - 10.1007/s11005-020-01328-3
DO - 10.1007/s11005-020-01328-3
M3 - Journal article
AN - SCOPUS:85090462959
VL - 110
SP - 3343
EP - 3373
JO - Letters in Mathematical Physics
JF - Letters in Mathematical Physics
SN - 0377-9017
IS - 12
ER -
ID: 373181342