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Riccardo Borsato

Last modified by Ricardo Julio Rodríguez Fernández on 2026/06/16 12:51

Measures of complexity and chaos in quantum systems

Titor: Riccardo Borsato

Supervisor: Riccardo Borsato

Quantum systems can exhibit a wide range of dynamical behaviours, from fully integrable and exactly solvable regimes to strongly chaotic dynamics. A key challenge is to quantify the degree of chaos present in a quantum system. Recently, the notion of "Krylov complexity" (or "spread complexity") has emerged as a promising measure of this.
The student will study the relevant literature, with particular emphasis on arXiv:2202.06957, to understand this concept and its theoretical foundations. They will learn the algorithmic procedure to evaluate Krylov complexity and apply it to specific solvable models for which analytical results are possible. If time permits, more complicated systems will be analysed with numerical and computational techniques.