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High Energy Physics - Theory
Title: Operator size growth in Lindbladian SYK
(Submitted on 11 Mar 2024 (v1), last revised 18 Mar 2024 (this version, v2))
Abstract: We investigate the growth of operator size in the Lindbladian SYK model with $q$-body interaction terms and linear jump terms at finite dissipation strength. We compute the operator size as well as its distribution numerically at finite $q$ and analytically at large $q$. With dissipative (productive) jump terms, the size converges to a value smaller (larger) than half the number of Majorana fermions. At weak dissipation, the evolution of operator size displays a quadratic-exponential-plateau behavior. The plateau value is determined by the ratios between the coupling of the interaction and the linear jump term in the large $q$ limit. The operator size distribution remains localized in the finite size region even at late times, contrasting with the unitary case. Moreover, we also derived the time-independent orthogonal basis for operator expansion which exhibits the operator size concentration at finite dissipation. Finally, we observe that the uncertainty relation for operator size growth is saturated at large $q$, leading to a classical dynamics of the operator size growth with dissipation.
Submission history
From: Zhuo-Yu Xian [view email][v1] Mon, 11 Mar 2024 19:12:50 GMT (1215kb,D)
[v2] Mon, 18 Mar 2024 22:12:41 GMT (1184kb,D)
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