Sobolev, AV;
(2017)
Quasi-classical asymptotics for functions of Wiener-Hopf operators: smooth vs non-smooth symbols.
Geometric and Functional Analysis
, 27
(3)
pp. 676-725.
10.1007/s00039-017-0408-9.
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Abstract
We consider functions of Wiener–Hopf type operators on the Hilbert space L2(Rd). It has been known for a long time that the quasi-classical asymptotics for traces of resulting operators strongly depend on the smoothness of the symbol: for smooth symbols the expansion is power-like, whereas discontinuous symbols (e.g. indicator functions) produce an extra logarithmic factor. We investigate the transition regime by studying symbols depending on an extra parameter T≥0 in such a way that the symbol tends to a discontinuous one as T→0. The main result is two-parameter asymptotics (in the quasi-classical parameter and in T), describing a transition from the smooth case to the discontinuous one. The obtained asymptotic formulas are used to analyse the low-temperature scaling limit of the spatially bipartite entanglement entropy of thermal equilibrium states of non-interacting fermions.
| Type: | Article |
|---|---|
| Title: | Quasi-classical asymptotics for functions of Wiener-Hopf operators: smooth vs non-smooth symbols |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/s00039-017-0408-9 |
| Publisher version: | http://dx.doi.org/10.1007/s00039-017-0408-9 |
| Language: | English |
| Additional information: | This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. |
| Keywords: | Primary 47G30; 35S05; Secondary 45M05; 47B10; 47B35; Non-smooth functions of Wiener–Hopf operators; Asymptotic trace formulas; Entanglement entropy |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/1542361 |
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