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arXiv:1704.04115 · Physical Review A

Parallel dynamics between non-Hermitian and Hermitian systems

P. Wang, S. Lin, L. Jin, Z. Song

Published Jun 1, 2018• 2 citations
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Abstract

We reveals a connection between non-Hermitian and Hermitian systems by studying the connection between a family of non-Hermitian and Hermitian Hamiltonians based on exact solutions. In general, for a dynamic process in a non-Hermitian system $\mathcal{H}$, there always exists a parallel dynamic process governed by the corresponding Hermitian conjugate system ${\mathcal{H}}^{\ifmmode\dagger\else\textdagger\fi{}}$. We show that a linear superposition of the two parallel dynamics is exactly equivalent to the time evolution of a state under a Hermitian Hamiltonian $H$, and we present the relations between ${H,\mathcal{H},{\mathcal{H}}^{\ifmmode\dagger\else\textdagger\fi{}}}$.

DOI
10.1103/physreva.97.062101

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