Operator growth in open quantum systems: lessons from the dissipative SYK

• DOI: 10.1007/jhep03(2023)054
• Publication Date: 2023-03-10T08:02:54Z
• Authors: Budhaditya Bhatta...; Xiangyu Cao; Pratik Nandy; Tanay Pathak
• Keywords: Dephasing; Operator (biology); Dissipative operator

We study the operator growth in open quantum systems with dephasing dissipation terms, extending Krylov complexity formalism of Phys. Rev. X 9, 041017. Our results are based on dissipative $q$-body Sachdev-Ye-Kitaev (SYK$_q$) model, governed by Markovian dynamics. introduce a notion ''operator size concentration'' which allows diagrammatic and combinatorial proof asymptotic linear behavior two sets Lanczos coefficients ($a_n$ $b_n$) large $q$ limit. corroborate semi-analytics finite $N$ limit, numerical Arnoldi iteration As result, exhibits exponential following saturation at time that grows logarithmically inverse strength. The is suppressed compared to closed system results, yet it upper bounds normalized out-of-time-ordered correlator (OTOC). provide plausible explanation from dual gravitational side.