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

Quantum Physics 2021-07-21 v2

Abstract

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

Keywords

Cite

@article{arxiv.2105.09278,
  title  = {To quantify the difference of $\eta$-inner products in $\cal PT$-symmetric theory},
  author = {Minyi Huang and Guijun Zhang},
  journal= {arXiv preprint arXiv:2105.09278},
  year   = {2021}
}

Comments

Minor corrections