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<p>We establish an inequality restricting the evolution of states in quantum field theory with respect to the modular flow of a wedge, <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\Delta ^{is}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi mathvariant="normal">Δ</mi> <mrow> <mi mathvariant="italic">is</mi> </mrow> </msup> </math></EquationSource> </InlineEquation>, for large |<i>s</i>|. Our bound is related to the quantum null energy condition, QNEC. In one interpretation, it can be seen as providing a “chaos bound” <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\le 2\pi \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>≤</mo> <mn>2</mn> <mi>π</mi> </mrow> </math></EquationSource> </InlineEquation> on the Lyapunov exponent with respect to Rindler time, <i>s</i>. Mathematically, our inequality is a statement about half-sided modular inclusions of von Neumann algebras.</p>

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Modular time evolution and the QNEC

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月6日

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  • Stefan Hollands

摘要

We establish an inequality restricting the evolution of states in quantum field theory with respect to the modular flow of a wedge, \(\Delta ^{is}\) Δ is , for large |s|. Our bound is related to the quantum null energy condition, QNEC. In one interpretation, it can be seen as providing a “chaos bound” \(\le 2\pi \) ≤ 2 π on the Lyapunov exponent with respect to Rindler time, s. Mathematically, our inequality is a statement about half-sided modular inclusions of von Neumann algebras.