Stefano Negro, Deterministic chaos and Integrable Systems

ITMP seminar, Mar 22, 2023
Speaker: Dr. Stefano Negro, New York University
Title: Deterministic chaos and Integrable Systems
Abstract: Integrability and chaos are commonly assumed to be incompatible concepts. There are important reasons for this. Prime amongst these is that integrable systems are not expected to thermalise since their phase space is entirely foliated by invariant tori thanks to the presence of a large amount of symmetries. On the other hand, a deep relation exists between thermalisation and chaotic behaviour, so much so that these concepts are commonly conflated. In this talk, starting from a definition of chaos as the property of the dynamics to map small intervals to unboundedly large ones, I will present some evidence that certain integrable systems, notably integrable field theories, present this behaviour. These results suggest the need for a more careful and deep understanding of the relationship between the concepts of chaos, thermalisation and integrability, in particular when the dimension of the systems’ phase spaces is infinite.