An optimal semiclassical bound on certain commutators
| Title: | An optimal semiclassical bound on certain commutators |
|---|---|
| Authors: | Fournais, Søren, Mikkelsen, Søren |
| Publication Year: | 2019 |
| Collection: | Mathematics Mathematical Physics |
| Subject Terms: | Mathematical Physics |
| More Details: | We prove an optimal semiclassical bound on the trace norm of the following commutators $[\boldsymbol{1}_{(-\infty,0]}(H_\hbar),x]$, $[\boldsymbol{1}_{(-\infty,0]}(H_\hbar),-i\hbar\nabla]$ and $[\boldsymbol{1}_{(-\infty,0]}(H_\hbar),e^{itx}]$, where $H_\hbar$ is a Schr\"odinger operator with a semiclassical parameter $\hbar$, $x$ is the position operator and $-i\hbar\nabla$ is the momentum operator. These bounds corresponds to a mean-field version of bounds introduced as an assumption by N. Benedikter, M. Porta and B. Schlein in a study of the mean-field evolution of a fermionic system. |
| Document Type: | Working Paper |
| Access URL: | http://arxiv.org/abs/1912.08467 |
| Accession Number: | edsarx.1912.08467 |
| Database: | arXiv |
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