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

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Fournais, Søren
Søren Mikkelsen

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.

Original language	English
Journal	Letters in Mathematical Physics
Volume	110
Issue number	12
Pages (from-to)	3343-3373
ISSN	0377-9017
DOIs	https://doi.org/10.1007/s11005-020-01328-3
Publication status	Published - Dec 2020
Externally published	Yes

Bibliographical note

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.

Research areas

Commutator estimates, Optimal semiclassics, Weyl law

ID: 373181342