The characterization of positivity properties of Weyl operators is a notoriously difficult problem, and not much progress has been made since the pioneering work of Kastler, Loupias, and Miracle- Sole (KLM). In this paper we begin by reviewing and giving simpler proofs of some known results for trace-class Weyl operators; the latter play an essential role in quantum mechanics. We then apply time-frequency analysis techniques to prove a phase space version of the KLM condition; the main tools are Gabor frames and the Wigner formalism. Finally, discrete approximations of the KLM condition, which are tractable numerically, are provided.
On the positivity of trace class operators / Cordero, Elena; De Gosson, Maurice; Nicola, Fabio. - In: ADVANCES IN THEORETICAL AND MATHEMATICAL PHYSICS. - ISSN 1095-0761. - STAMPA. - 23:8(2019), pp. 2061-2091.
Titolo: | On the positivity of trace class operators |
Autori: | |
Data di pubblicazione: | 2019 |
Rivista: | |
Digital Object Identifier (DOI): | http://dx.doi.org/10.4310/ATMP.2019.V23.N8.A4 |
Appare nelle tipologie: | 1.1 Articolo in rivista |
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4-Cordero.pdf | Postprint | 2. Post-print / Author's Accepted Manuscript | PUBBLICO - Tutti i diritti riservati | Visibile a tuttiVisualizza/Apri |
ATMP_23_08_A04.pdf | 2a Post-print versione editoriale / Version of Record | Non Pubblico - Accesso privato/ristretto | Administrator Richiedi una copia |
http://hdl.handle.net/11583/2843963