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Universal Time Evolution of Holographic and Quantum Complexity.
Masamichi Miyaji1, Shan-Ming Ruan2, Shono Shibuya3
1RIKEN, RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS), 2-1 Hirosawa, Wako, Saitama 351-0198, Japan.
Physical Review Letters
|May 1, 2026
Summary
Holographic complexity in black holes shows universal growth and saturation, similar to chaotic quantum systems. This behavior stems from specific pole structures and quantum chaos principles in spectral statistics.
Area of Science:
- Theoretical Physics
- Quantum Gravity
- Black Hole Physics
Background:
- Holographic complexity is the bulk dual of quantum complexity, revealing black hole interior geometry.
- The complexity = anything proposal connects quantum complexity to geometric properties.
Purpose of the Study:
- Introduce a spectral representation for holographic complexity generating functions.
- Analyze the universal behavior of holographic complexity measures.
Main Methods:
- Utilize generating functions and their spectral representation.
- Apply the residue theorem to analyze pole structures.
- Connect to random matrix theory and spectral statistics.
Main Results:
- Generating functions exhibit a universal slope-ramp-plateau structure.
- Demonstrate that specific pole structures are necessary and sufficient for linear growth.
- Show that spectral level repulsion causes late-time saturation.
Conclusions:
- Holographic complexity exhibits universal dynamics analogous to chaotic quantum systems.
- The study provides a theoretical framework linking quantum chaos to black hole complexity.
- Confirms the origins of universal growth and saturation in holographic complexity.
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