Exceptional points of the Lindblad operator of a two-level system

Abstract

The Lindblad equation for a two-level system under an electric field is analyzed by mapping to a linear equation with a non-Hermitian matrix. Exceptional points of the matrix are found to be extensive; the second-order ones are located on lines in a two-dimensional parameter space, while the third-order one is at a point.

GRAPHICAL ABSTRACT

Keywords:

• Non-Hermitian quantum mechanics
• Lindblad operator
• exceptional point

Acknowledgments

The present study was carried out in an exceptionally pleasant collaboration with Prof. Nimrod Moiseyev when he invited the present author for a splendid stay at his group in Technion. In the normal situation, he would be on the list of the authors, but it is obviously awkward to have him as a co-author of the paper that the present author dedicates to him.

Disclosure statement

No potential conflict of interest was reported by the author.

ORCID

Naomichi Hatano http://orcid.org/0000-0003-0277-1856

Additional information

Funding

The present author is also grateful to the generous financial support from Technion.