Quantum Chaos Accelerates Beyond the Limit ⚡ экспресс
Operator growth in conformal field theories with large central charge and W3 symmetry is studied. Extending the Liouvillian to $$\mathcal{L} = \kappa_1 (L_1+L_{-1}) + \kappa_2 (W_2+W_{-2})$$, Lanczos coefficients are computed in the module of descendants of a heavy primary field. Sectors with asymptotically quadratic growth $$b_N \sim N^2$$ are found, which violate the universal hypothesis on operator growth and lead to a divergence of Krylov complexity. The quadratic asymptotic behavior is already reproduced in the global subalgebra $$SL(3,\mathbb{R})$$, indicating that the violation arises from the extended higher-rank symmetry. These results show that W-symmetries qualitatively alter operator growth and allow one to bypass the usual constraints on information scrambling.
Usually, in quantum systems, information mixes gradually, like a rumor in a crowd: one person passes it to another, and that person to the next. The growth of entropy (a measure of disorder) is linear here – and was long considered a universal limit. But when additional symmetries come into play, a different picture emerges. In such systems, the influence of a single particle instantly spreads to many others – as if 'super-spreaders' appear, whispering the news to everyone at once. The entanglement speed skyrockets, and information covers the entire system almost instantly.
The discovery not only deepens the theory of quantum chaos but also promises ultra-fast quantum devices.
🎯 Black holes were considered champions of scrambling information: they reach the limit of chaos in a fraction of a second. The new discovery shows that some quantum systems can be even faster.
🎬 In Liu Cixin's 'The Three-Body Problem,' aliens instantly comprehend everything about humanity – just like information behaves in systems where speed limits are removed.