Holographic models link critical dynamics to quantum scrambling timescales

Critical Dynamics Meet Quantum Scrambling

Researchers Mozib Bin Awal and Prabwal Phukon from Dibrugarh University have used holographic models to explore how a system’s relaxation toward equilibrium behaves near critical points and how this relates to the speed at which quantum information spreads—known as scrambling. Their analysis uncovers a universal power‑law divergence in the autocorrelation time, \(\tau\sim|\varepsilon|^{-\Delta}\) with \(\Delta\approx2/3\), that holds across variations in temperature and the conformal‑field‑theory (CFT) central charge.

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Universal Critical Exponent in Holographic CFTs

The team examined Reissner‑Nordström anti‑de Sitter (RN‑AdS) black holes and their dual CFTs, treating the cosmological constant as a thermodynamic pressure. By applying Langevin and Fokker‑Planck formalisms to the stochastic evolution of the horizon radius, they extracted the smallest non‑zero eigenvalue of the Fokker‑Planck operator, which governs the slowest relaxation mode. Across a two‑dimensional parameter space of temperature (\(T\)) and central charge (\(C\)), the relaxation dynamics consistently displayed the same dynamical critical exponent \(\Delta\approx2/3\). This robustness suggests a deep, model‑independent feature of strongly coupled holographic systems.

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From Thermodynamic Relaxation to Fast Scrambling

Beyond confirming the exponent, the authors compared the relaxation timescale to the fast‑scrambling time, \(t_{*}\sim\frac{\beta}{2\pi}\log C\), where \(\beta\) is the inverse temperature. They identified a crossover point where the relaxation time overtakes the scrambling time. In the large‑central‑charge limit this crossover scales as \(\varepsilon\sim(C\log C)^{-3/2}\), indicating that as the CFT becomes more complex the window where thermodynamic relaxation is slower than scrambling shrinks dramatically.

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Implications for Black‑Hole Information and Quantum Gravity

The work provides a concrete bridge between two traditionally separate topics: critical slowing down in statistical physics and quantum information spreading in black‑hole horizons. By showing that the same exponent governs both relaxation and scrambling near criticality, the study offers a fresh perspective on the black‑hole information paradox and on how strongly coupled quantum systems process information.

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Outlook

The authors validated their analytical predictions with full nonlinear numerical simulations of the free‑energy landscape, confirming the predicted collapse of relaxation times across different parameter trajectories. Future work could extend these methods to other holographic setups, explore experimental analogues in cold‑atom or condensed‑matter platforms, and test the predicted crossover in systems where scrambling can be measured directly.

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The study is available as an arXiv preprint (https://arxiv.org/html/2611.11889v1).