Title: Krylov complexity, quantum chaos, and holography

Speaker: Zhuo-Yu Xian (Free Univeristy of Berlin)

  冼卓宇，现为柏林自由大学博士后。2013年于华南理工大学获得学士学位，2018年于中国科学院高能物理研究所获得博士学位，先后在中国科学院理论物理研究所、维尔兹堡大学和柏林自由大学从事博士后研究。主要从事引力物理强耦合多体物理及其全息对应的研究。在PRL、JHEP、PRD等期刊发表论文31篇，引用1100余次。

Abstract:

We review the Krylov approach to quantum systems and its connectionsto quantum chaos and holography. The Krylov method provides anefficient framework for describing quantum evolution, particularly in lowdimensional systems, and is equivalent to the tridiagonalization of theevolution operator. Krylov complexity quantifies the average number otevolution steps required to transform an initial state into a target stateThus, it a sensitive probe of ergodicity and quantum chaos in Hilbertspace.In the double-scaling limit of the Sachdev-Ye-Kitaev model, theKrylov basis spans the bulk Hilbert space of the dual Jackiw-Teitelboimgravity. In the triple-scaling limit, the Krylov complexity of the thermofielddouble state corresponds to the volume of the eternal black hole.

腾讯会议

2025.3.5