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arXiv · 2105.09278

To quantify the difference of $\eta$-inner products in $\cal PT$-symmetric theory

Minyi Huang·Guijun Zhang
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Abstract

In this paper, we consider a typical continuous two dimensional $\cal PT$-symmetric Hamiltonian and propose two different approaches to quantitatively show the difference between the $\eta$-inner products. Despite the continuity of Hamiltonian, the $\eta$-inner product is not continuous in some sense. It is shown that the difference between the $\eta$-inner products of broken and unbroken $\cal PT$-symmetry is lower bounded. Moreover, such a property can lead to an uncertainty relation.

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Minyi Huang, Guijun Zhang. 2021-05-19. To quantify the difference of $\eta$-inner products in $\cal PT$-symmetric theory. https://doi.org/10.1007/s10773-021-04881-2

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