Quantum chaos has recently seen a revived wave of interest due to its potential connections with quantum thermalization, many-body localization, and black hole physics. Among the slew of the operational diagnostics of quantum chaos, the concept of operator growth, which has been studied in both single-particle and many-body quantum systems, was proposed to characterize how a "simple" operator acquires increasing complexity under the Heisenberg time evolution of a chaotic dynamics. In this talk, we will re-examine the validity of operator growth in single-particle quantum systems. Using the quantum cat map as an explicit example, we will demonstrate that the operator growth picture is basis-dependent and fails to capture the additional quantum symmetries in certain cat maps, jeopardizing its validity as a chaos criterion. We will further discuss similar issues in the context of many-body quantum systems.
This event will be held virtually, if you are interested in attending please contact Janice at jbenner@illinios.edu for the invitation link.
