General properties of the spectral form factor in open quantum systems  

作　　者：Yi-Neng Zhou Tian-Gang Zhou Pengfei Zhang 

机构地区：[1]Institute for Advanced Study,Tsinghua University,Beijing 100084,China [2]Department of Physics,Fudan University,Shanghai 200438,China

出　　处：《Frontiers of physics》2024年第3期229-237,共9页物理学前沿（英文版）

摘　　要：The spectral form factor(SFF)can probe the eigenvalue statistic at different energy scales as its time variable varies.In closed quantum chaotic systems,the SFF exhibits a universal dip-ramp-plateau behavior,which reflects the spectrum rigidity of the Hamiltonian.In this work,we explore the general properties of SFF in open quantum systems.We find that in open systems the SFF first decays exponentially,followed by a linear increase at some intermediate time scale,and finally decreases to a saturated plateau value.We derive general relations between(i)the early-time decay exponent and Lindblad operators;(ii)the long-time plateau value and the number of steady states.We also explain the effective field theory perspective of general behaviors.We verify our theoretical predictions by numerically simulating the Sachdev−Ye−Kitaev(SYK)model,random matrix theory(RMT),and the Bose−Hubbard model.

关 键 词：spectral form factor open quantum system quantum chaos 

分 类 号：O17[理学—数学]