Pablo Martínez-Azcona (University of Luxemburg)
The study of chaotic behavior in the quantum realm is now at an exciting crossroads, connecting in a unique way quantum information, high energy physics, statistical mechanics and even pure math. We will begin this seminar with a broad introduction to the field of Quantum Chaos, giving particular weight to the quantities that we can use to characterize it, and how these are affected by dissipation and decoherence, focusing in particular on the Out of Time Ordered Correlator (OTOC) that defines a quantum Lyapunov exponent.
Then we will introduce a stochastic Hamiltonian, to model the effect of noise in certain physical parameters, as would happen in any realistic Noisy Intermediate Scale Quantum (NISQ) device. In this setting the evolution of quantities averaged over the noise yields the well known results from the theory of Open Quantum Systems, like Lindblad master equation. We propose to go beyond the average and study fluctuations in these systems through the Stochastic Operator Variance (SOV), which we show to be related to an OTOC, thus connecting with the theory of Quantum Chaos. We illustrate our results in a stochastic Lipkin Meshkov Glick (sLMG) model, in which we study the evolution of the SOV, showing that it behaves in a similar way to an OTOC, and then we take the classical limit where we compare the results obtained from the SOV with other methods to find the Lyapunov exponent. We will end with a perspective on future work.