Abstract
In this paper, we consider a typical continuous two dimensional \(\mathcal {P}\mathcal {T}\)-symmetric Hamiltonian and propose two different approaches to quantitatively show the difference between the η-inner products. Despite the continuity of Hamiltonian, the η-inner product is not continuous in some sense. It is shown that the difference between the η-inner products of broken and unbroken \(\mathcal {P}\mathcal {T}\)-symmetry is lower bounded. Moreover, such a property can lead to some uncertainty relation.
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Acknowledgements
This work is partially supported by the National Natural Science Foundation of China (11901526), the Postdoctoral Science Foundation of China (2020M680074) and the Science Foundation of Zhejiang Sci-Tech University (19062117-Y).
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Huang, M., Zhang, G. To Quantify the Difference of η-Inner Products in \(\mathcal {P}\mathcal {T}\)-Symmetric Theory. Int J Theor Phys 60, 2700–2708 (2021). https://doi.org/10.1007/s10773-021-04881-2
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DOI: https://doi.org/10.1007/s10773-021-04881-2