Abstract
Recently, much attention is paid to the consideration of physical models described by $\mathcal{PT}$-symmetric Hamiltonians. In this paper, we establish a necessary and sufficient condition for existence of a stable $\mathcal{C}$-symmetry for a class of $\mathcal{PT}$-symmetric extensions of a symmetric operator $S$ with deficiency indices $(2,2)$.
Key words: PT -symmetric Hamiltonians, exact PT -symmetry, real spectrum, stable C-symmetry, extension theory of symmetric operators, boundary triplets, Krein spaces, Clifford algebra.
Full Text
Article Information
| Title | On stable $\mathcal{C}$-symmetries for a class of $\mathcal{PT}$-symmetric operators |
| Source | Methods Funct. Anal. Topology, Vol. 19 (2013), no. 1, 73-79 |
| MathSciNet |
MR3088320 |
| zbMATH |
1289.47047 |
| Milestones | Received 21/11/2012; Revised 01/12/2012 |
| Copyright | The Author(s) 2013 (CC BY-SA) |
Authors Information
O. M. Patsyuck
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs'ka, Kyiv, 01601, Ukraine
Citation Example
O. M. Patsyuck, On stable $\mathcal{C}$-symmetries for a class of $\mathcal{PT}$-symmetric operators, Methods Funct. Anal. Topology 19
(2013), no. 1, 73-79.
BibTex
@article {MFAT671,
AUTHOR = {Patsyuck, O. M.},
TITLE = {On stable $\mathcal{C}$-symmetries for a class of $\mathcal{PT}$-symmetric operators},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {19},
YEAR = {2013},
NUMBER = {1},
PAGES = {73-79},
ISSN = {1029-3531},
MRNUMBER = {MR3088320},
ZBLNUMBER = {1289.47047},
URL = {http://mfat.imath.kiev.ua/article/?id=671},
}
