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

• URL: http://arxiv.org/abs/2105.09278v2
• Date: Wed, 26 May 2021 06:50:06 GMT
• Title: To quantify the difference of $\eta$-inner products in $\cal PT$-symmetric theory
• Authors: Minyi Huang, Guijun Zhang
• Abstract summary: 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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