Operator-Growth Obstruction to Annealed Hilbert-Schmidt Mixing in Dissipative SYK
Year: 2026
Type: article
Abstract: We prove an annealed Hilbert-Schmidt mixing obstruction in Gaussian dissipative q=4 Sachdev-Ye-Kitaev dynamics. Exact finite-N parity-size conjugacy and a frame-integrated-size identity are combined with a nonperturbative Rademacher-SYK operator-growth theorem and a fourth-order Gaussian-Rademacher Lindeberg replacement to obtain x_{Delta,N} >= C(mu/J) log log N - O(1) for every fixed disorder-averaged O(1) traceless-frame threshold. In the weak-dissipation regime where the large-N replica transition exists, its O(1) scaled time is parametrically earlier. The stronger Omega(log N) statement is conditional on uniform finite-q operator-size localization.
Institution: Ministry of Education
Language: English
Topic: Quantum many-body systems
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214460510
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