Toeplitz Density Operators and their Separability Properties

• URL: http://arxiv.org/abs/2209.08051v2
• Date: Tue, 18 Oct 2022 16:57:20 GMT
• Title: Toeplitz Density Operators and their Separability Properties
• Authors: Maurice de Gosson
• Abstract summary: Toeplitz operators (also called localization operators) are a generalization of the well-known anti-Wick pseudodifferential operators. We study several aspects of Toeplitz operators when their symbols belong to some well-known functional spaces.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Toeplitz operators (also called localization operators) are a generalization of the well-known anti-Wick pseudodifferential operators studied by Berezin and Shubin. When a Toeplitz operator is positive semi-definite and has trace one we call it a density Toeplitz operator. Such operators represent physical states in quantum mechanics. In the present paper we study several aspects of Toeplitz operators when their symbols belong to some well-known functional spaces (e.g. the Feichtinger algebra) and discuss (tentatively) their separability properties with an emphasis on the Gaussian case.

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