2017/02/23 by Ye Xiong, Xiong, Ye, Peiqing Tong +1
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Hermitian matrix #Mathematical physics #Mathematics #Nonlinear Schrödinger equation #Nonlinear system #Physics #Pure mathematics #Quantum #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph) #Quantum mechanics #Schrödinger equation #Statistical Mechanics (cond-mat.stat-mech) #Strongly Correlated Electrons (cond-mat.str-el) #cond-mat.stat-mech #cond-mat.str-el #quant-ph
paper · pdf · doi:10.48550/arxiv.1702.07112
published in arXiv (Cornell University) (Cornell University) · 1figure
arxiv created 2017/02/23 · openalex publication_date 2017/02/23 · arxiv updated 2017/02/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We derive a new time-dependent Schrödinger equation(TDSE) for quantum models with non-hermitian Hamiltonian. Within our theory, the TDSE is symmetric in the two Hilbert spaces spanned by the left and the right eigenstates, respectively. The physical quantities are also identical in these two spaces. Based on this TDSE, we show that exchanging two quasi-particles in a non-hermitian model can generate arbitrary geometric phase. The system can also violate the Lieb-Robinson bound in non-relativistic quantum mechanics so that an action in one place will immediately cause a change in the distance. We show that the above two surprising behaviors can also appear in anyonic model, which makes us propose that the non-hermitian single particle model may possess many common features with anyonic model.