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|
|Data di pubblicazione:||2019|
|Digital Object Identifier (DOI):||http://dx.doi.org/10.4310/ATMP.2019.V23.N8.A4|
|Appare nelle tipologie:||1.1 Articolo in rivista|