Truncated Wigner approximation as a non-positive Kraus map

We show that the Truncated Wigner Approximation developed in the flat phase-space is mapped into a Lindblad-type evolution with an indefinite metric in the space of linear operators. As a result, the classically evolved Wigner function corresponds to a non-positive operator \(\hat{R}(t)\), which doe...

Ausführliche Beschreibung

Gespeichert in:

Bibliographische Detailangaben
Veröffentlicht in:	arXiv.org
Hauptverfasser:	Klimov, A B, Sainz, I, Romero, J L
Format:	Paper
Sprache:	Englisch
Veröffentlicht:	Ithaca Cornell University Library, arXiv.org 09.08.2021
Schlagworte:	Approximation Eigenvalues Evolution Linear operators Mathematical analysis Second harmonic generation
ISSN:	2331-8422
Online-Zugang:	Volltext
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!

Beschreibung
Zusammenfassung:	We show that the Truncated Wigner Approximation developed in the flat phase-space is mapped into a Lindblad-type evolution with an indefinite metric in the space of linear operators. As a result, the classically evolved Wigner function corresponds to a non-positive operator \(\hat{R}(t)\), which does not describe a physical state. The rate of appearance of negative eigenvalues of \(\hat{R}(t)\) can be efficiently estimated. The short-time dynamics of the Kerr and second harmonic generation Hamiltonains are discussed.
Bibliographie:	SourceType-Working Papers-1 ObjectType-Working Paper/Pre-Print-1 content type line 50
ISSN:	2331-8422
DOI:	10.48550/arxiv.2108.04189