ArticleProceedings of the National Academy of Sciences of the United States of America2023
Instantons and the quantum bound to chaos.
Article in Proceedings of the National Academy of Sciences of the United States of America, 2023. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 3 papers.
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3 citing papers in PubMed, 5 citations in OpenAlex.
- Quantum information scrambling and chemical reactions.Proceedings of the National Academy of Sciences of the United States of America · 2024Article
- Quantum scrambling across an energy barrier.Proceedings of the National Academy of Sciences of the United States of America · 2023Article
- Instantons and the quantum bound to chaos.Proceedings of the National Academy of Sciences of the United States of America · 2023Article
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4 authors at 2 institutions in 3 countries.
Funding
Abstract
The rate at which information scrambles in a quantum system can be quantified using out-of-time-ordered correlators. A remarkable prediction is that the associated Lyapunov exponent [Formula: see text] that quantifies the scrambling rate in chaotic systems obeys a universal bound [Formula: see text]. Previous numerical and analytical studies have indicated that this bound has a quantum-statistical origin. Here, we use path-integral techniques to show that a minimal theory to reproduce this bound involves adding contributions from quantum thermal fluctuations (describing quantum tunneling and zero-point energy) to classical dynamics. By propagating a model quantum-Boltzmann-conserving classical dynamics for a system with a barrier, we show that the bound is controlled by the stability of thermal fluctuations around the barrier instanton (a delocalized structure which dominates the tunneling statistics). This stability requirement appears to be general, implying that there is a close relation between the formation of instantons, or related delocalized structures, and the imposition of the quantum-chaos bound.
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