Solvable dilation model of $\cal PT$-symmetric systems

• URL: http://arxiv.org/abs/2104.05039v3
• Date: Fri, 17 Jun 2022 12:35:57 GMT
• Title: Solvable dilation model of $\cal PT$-symmetric systems
• Authors: Minyi Huang, Ray-Kuang Lee, Qing-hai Wang, Guo-Qiang Zhang, Junde Wu
• Abstract summary: The dilation method is a practical way to experimentally simulate non-Hermitian, especially $cal PT$-symmetric quantum systems. We present a simple yet non-trivial exactly solvable dilation problem with two dimensional time-dependent PT$-symmetric Hamiltonian.
• Score: 5.562460678645834
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The dilation method is a practical way to experimentally simulate non-Hermitian, especially $\cal PT$-symmetric quantum systems. However, the time-dependent dilation problem cannot be explicitly solved in general. In this paper, we present a simple yet non-trivial exactly solvable dilation problem with two dimensional time-dependent $\cal PT$-symmetric Hamiltonian. Our system is initially set in the unbroken $\cal PT$-symmetric phase and later goes across the so-called exceptional point and enters the broken $\cal PT$-symmetric phase. For this system, the dilated Hamiltonian and the evolution of $\cal PT$-symmetric system are analytically worked out. Our result clearly showed that the exceptional points do not have much physical relevance in a \textit{time-dependent} system.

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