## An optimal semiclassical bound on commutators of spectral projections with position and momentum operators

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avisTidsskriftartikelForskningpeer review

### Standard

I: Letters in Mathematical Physics, Bind 110, Nr. 12, 12.2020, s. 3343-3373.

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avisTidsskriftartikelForskningpeer review

### Author

Fournais, Søren ; Mikkelsen, Søren. / An optimal semiclassical bound on commutators of spectral projections with position and momentum operators. I: Letters in Mathematical Physics. 2020 ; Bind 110, Nr. 12. s. 3343-3373.

### Bibtex

@article{c8f58e628554400f931cf8b7289ac828,
title = "An optimal semiclassical bound on commutators of spectral projections with position and momentum operators",
abstract = "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 Schr{\"o}dinger 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.",
keywords = "Commutator estimates, Optimal semiclassics, Weyl law",
author = "S{\o}ren Fournais and S{\o}ren Mikkelsen",
year = "2020",
month = dec,
doi = "10.1007/s11005-020-01328-3",
language = "English",
volume = "110",
pages = "3343--3373",
journal = "Letters in Mathematical Physics",
issn = "0377-9017",
publisher = "Springer",
number = "12",

}

### RIS

TY - JOUR

T1 - An optimal semiclassical bound on commutators of spectral projections with position and momentum operators

AU - Fournais, Søren

AU - Mikkelsen, Søren

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 -