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<p>We develop a finite-dimensional formulation of the recently introduced notion of “timelike entanglement”, defined in terms of two-point functions between operators supported on different Cauchy slices. Using a local orthonormal operator basis, we recast this construction in terms of a <i>generalized response tensor</i>. Building on this, we introduce a <i>generalized spacetime density kernel</i> (GSDK) corresponding to higher point correlation functions, including time-ordered as well as out-of-time-ordered correlators. Motivated by the structure of Haar probe averaging, we contract the (2<i>N</i>)-leg GSDK with cyclic permutation operators and thereby define a <i>kernel form factor</i>. This quantity is computable even when Haar averaging is not feasible, and it reduces to the (2<i>N</i>)-th moment of the spectral form factor, evaluated at an <i>N</i>-enhanced effective temperature. The correlation functions of the GSDK operators also yield the SFF, with an effective (1/<i>N</i>)-reduction of the physical time-scales. The GSDK places both early time scrambling diagnostics and late time spectral statistics on a similar footing and clarifies how higher-point correlators and non-trivial time ordering capture fine-grained dynamical information of a quantum system.</p>

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Temporal correlations and chaos from spacetime kernels

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年4月17日

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  • Rathindra Nath Das,
  • Arnab Kundu,
  • Matheus H. Martins Costa,
  • Nemai Chandra Sarkar

摘要

We develop a finite-dimensional formulation of the recently introduced notion of “timelike entanglement”, defined in terms of two-point functions between operators supported on different Cauchy slices. Using a local orthonormal operator basis, we recast this construction in terms of a generalized response tensor. Building on this, we introduce a generalized spacetime density kernel (GSDK) corresponding to higher point correlation functions, including time-ordered as well as out-of-time-ordered correlators. Motivated by the structure of Haar probe averaging, we contract the (2N)-leg GSDK with cyclic permutation operators and thereby define a kernel form factor. This quantity is computable even when Haar averaging is not feasible, and it reduces to the (2N)-th moment of the spectral form factor, evaluated at an N-enhanced effective temperature. The correlation functions of the GSDK operators also yield the SFF, with an effective (1/N)-reduction of the physical time-scales. The GSDK places both early time scrambling diagnostics and late time spectral statistics on a similar footing and clarifies how higher-point correlators and non-trivial time ordering capture fine-grained dynamical information of a quantum system.