2018/01/05 by Ruili Zhang, Zhang, Ruili, Hong Qin +5
Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Mechanical and Optical Resonators #Orbital Angular Momentum in Optics #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.1801.01676
openalex publication_date 2018/01/05 · openalex created_date 2018/03/29 · openalex updated_date 2026/07/28
It is generally believed that Parity-Time (PT)-symmetry breaking occurs when eigenvalues or both eigenvalues and eigenvectors coincide. However, we show that this well-accepted picture of PT-symmetry breaking is incorrect. Instead, we demonstrate that the physical mechanism of PT-symmetry breaking is the resonance between positive- and negative-action modes. It is proved that PT-symmetry breaking occurs when and only when this resonance condition is satisfied, and this mechanism applies to all known PT-symmetry breakings observed in different branches of physics. The result is achieved by proving a remarkable fact that in finite dimensions, a PT-symmetric Hamiltonian is necessarily pseudo-Hermitian, regardless whether it is diagonalizable or not.