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

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We prove an optimal semiclassical bound on the trace norm of the following commutators [1(-,](Hħ) , x] , [1(-,](Hħ) , - iħ∇] and [1(-,](Hħ) , eit,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.

TidsskriftLetters in Mathematical Physics
Sider (fra-til)3343-3373
StatusUdgivet - dec. 2020

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