A Bound on Chaos from Stability

2019/05/21 by Junggi Yoon, Yoon, Junggi
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #hep-th

paper · pdf · doi:10.48550/arxiv.1905.08815

5 pages plus references, 6 figures; v2: references added; v3: typos corrected, clarification added in section 3.2 and 3.3, version to appear in JHEP

arxiv created 2021/11/12 · arxiv updated 2021/11/15

Abstract

We explore the quantum chaos of the coadjoint orbit action. We study quantum fluctuation around a saddle point to evaluate the soft mode contribution to the out-of-time-ordered correlator. We show that the stability condition of the semi-classical analysis of the coadjoint orbit found by Witten (1988) leads to the upper bound on the Lyapunov exponent which is identical to the bound on chaos proven in arXiv:1503.01409. The bound is saturated by the coadjoint orbit Diff(S¹)/SL(2) while the other stable orbit Diff(S¹)/U(1) where the SL(2,ℝ) is broken to U(1) has non-maximal Lyapunov exponent.

Citations

• A bound on chaos

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