Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	Dr. Ruili Zhang, Beijing Jiaotong University
Inviter:
Title:	Classical instabilities of conservative systems are the results of parity-time symmetry breaking
Time & Venue:	2019.09.11 11:05-11:50 N204
Abstract:	We show that the governing equations of the classical two-fluid interaction and the incompressible fluid system are PT-symmetric, and the well-known Kelvin-Helmholtz instability and the two-stream instability are the results of spontaneous PT-symmetry breaking. By proving the theorem that all PT-symmetric Hamiltonians are pseudo-Hermitian (G-Hamiltonian), we show that PT-symmetry breaking is actually the onset of instability of pseudo-Hermitian Hamiltonian, which has been well studied Krein et al. Specifically, it is shown that the boundaries between the stable and unstable regions are locations for Krein collisions between eigenmodes with different Krein signatures. It is anticipated that this mechanism of destabilization is valid for other collective instabilities in conservative systems in plasma physics, accelerator physics, and fluid dynamics systems.