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<p>We discuss aspects of the quantum Lyapunov exponent <i>λ</i><sub><i>L</i></sub> in theories with an exactly marginal SYK-like random interaction, where <i>λ</i><sub><i>L</i></sub> can be computed as a continuous function of the interaction strength <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">J</mi> </math></EquationSource> <EquationSource Format="TEX">\( \mathcal{J} \)</EquationSource> </InlineEquation>. In 1<i>d</i>, we prove a conjecture from [<CitationRef CitationID="CR1">1</CitationRef>] which states that at small <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">J</mi> </math></EquationSource> <EquationSource Format="TEX">\( \mathcal{J} \)</EquationSource> </InlineEquation>, <i>λ</i><sub><i>L</i></sub> can be found by considering a specific limit of the four-point function in the decoupled theory. We then provide additional evidence for the 2<i>d</i> version of this conjecture by discussing new examples of Lyapunov exponents which can be computed at weak coupling.</p>

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More on chaos at weak coupling

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年7月11日

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  • Rohit R. Kalloor,
  • Adar Sharon

摘要

We discuss aspects of the quantum Lyapunov exponent λL in theories with an exactly marginal SYK-like random interaction, where λL can be computed as a continuous function of the interaction strength J \( \mathcal{J} \) . In 1d, we prove a conjecture from [1] which states that at small J \( \mathcal{J} \) , λL can be found by considering a specific limit of the four-point function in the decoupled theory. We then provide additional evidence for the 2d version of this conjecture by discussing new examples of Lyapunov exponents which can be computed at weak coupling.