2021/01/31 by Balázs Gulácsi, Balázs Dóra · 4 citations
Mathematics · Physics and Astronomy · #Adiabatic process #Algebraic number #Coupling (piping) #Critical point (mathematics) #Hamiltonian (control theory) #Hermitian matrix #Master equation #Materials science #Mathematical analysis #Mathematical physics #Mathematics #Perturbation (astronomy) #Physics #Quantum #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Quantum many-body systems #Quantum mechanics #Scaling #Statistical physics #Time evolution #cond-mat.quant-gas #cond-mat.str-el #quant-ph
paper · pdf · doi:10.1103/physrevb.103.205153
published in Physical review. B./Physical review. B 103(20) (American Physical Society) · 10 pages, 6 figures
openalex created_date 2021/02/01 · openalex publication_date 2021/05/27 · arxiv created 2021/06/01 · arxiv updated 2021/06/04 · openalex updated_date 2026/08/05
Recently, defect production was investigated during nonunitary dynamics due to non-Hermitian Hamiltonian. By ramping up the non-Hermitian coupling linearly in time through an exceptional point, defects are produced in much the same way as approaching a Hermitian critical point. A generalized Kibble-Zurek scaling accounted for the ensuing scaling of the defect density in terms of the speed of the drive and the corresponding critical exponents. Here we extend this setting by adding the recycling term and considering the full Lindbladian time evolution of the problem with quantum jumps. We find that by linearly ramping up the environmental coupling in time, and going beyond the steady-state solution of the Liouvillian, the defect density scales linearly with the speed of the drive for all cases. This scaling is unaffected by the presence of exceptional points of the Liouvillian, which can show up in the transient states. By using a variant of the adiabatic perturbation theory, the scaling of the defect density is determined exactly from a set of algebraic equations. Our study indicates the distinct sensitivity of the Lindbladian time evolution to exceptional points corresponding to steady states and transient states.