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An optimal semiclassical bound on commutators of spectral projections with position and momentum operators
Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaper › Journal article › Research › peer-review
DOI
- https://doi.org/10.1007/s11005-020-01328-3
Final published version
- Søren Fournais ,
- Søren Mikkelsen, University of Bristol
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.
| Original language | English |
|---|---|
| Journal | Letters in Mathematical Physics |
| Volume | 110 |
| Issue | 12 |
| Pages (from-to) | 3343-3373 |
| ISSN | 0377-9017 |
| DOIs | |
| Publication status | Published - Dec 2020 |
- Commutator estimates, Optimal semiclassics, Weyl law
Research areas
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ID: 201770334