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

Søren Fournais; Søren Mikkelsen

doi:10.1007/s11005-020-01328-3

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

Søren Fournais^*, Søren Mikkelsen

^*Corresponding author af dette arbejde

Institut for Matematik

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avis › Tidsskriftartikel › Forskning › peer review

Abstract

We prove an optimal semiclassical bound on the trace norm of the following commutators [1₍_-_∞_,_](H_ħ) , x] , [1₍_-_∞_,_](H_ħ) , - iħ∇] and [1₍_-_∞_,_](H_ħ) , eⁱ^⟨^t^,^x^⟩] , where H_ħ is a Schrödinger operator with a semiclassical parameter ħ, x is the position operator, -iħ∇ is the momentum operator, and t in R^d 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.

Originalsprog	Engelsk
Tidsskrift	Letters in Mathematical Physics
Vol/bind	110
Nummer	12
Sider (fra-til)	3343-3373
ISSN	0377-9017
DOI	https://doi.org/10.1007/s11005-020-01328-3
Status	Udgivet - dec. 2020

Adgang til dokumentet

10.1007/s11005-020-01328-3

Andre filer og links

http://www.scopus.com/inward/record.url?scp=85090462959&partnerID=8YFLogxK

Citationsformater

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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.",

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

AU - Fournais, Søren

AU - Mikkelsen, Søren

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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

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U2 - 10.1007/s11005-020-01328-3

DO - 10.1007/s11005-020-01328-3

M3 - Journal article

AN - SCOPUS:85090462959

SN - 0377-9017

VL - 110

SP - 3343

EP - 3373

JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

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