Extracting Lyapunov exponents and ergodization time of chaotic many-particle systems from Loschmidt echoes and out-of-time-order correlators

Speaker: Andrei Tarkhov, Skolkovo Institute of Science and Technology

When: November 14, 2018 (Wed), 03:00PM to 04:00PM (add to my calendar)
Location: SCI 328

This event is part of the Biophysics/Condensed Matter Seminar Series.

We suggest an experimentally feasible routine for demonstrating Lyapunov instability, testing ergodicity and estimating ergodization time in chaotic classical many-particle systems by monitoring equilibrium noise of virtually any observable before and after time reversal of dynamics (Loschmidt echo). We discuss a quantum counterpart of the method involving out-of-time-order correlators (OTOCs). The ergodization time is defined as the typical time required for extracting the largest Lyapunov exponent from a system’s dynamics. For illustration, we apply the method to a lattice of coupled Bose-Einstein condensates in the classical regime describable by the discrete Gross-Pitaevskii equation. We corroborate our theoretical analysis by direct numerical simulations demonstrating that the largest Lyapunov exponent and, if the system passes the ergodicity test, the ergodization time can indeed be extracted from Loschmidt echoes. [1] A. E. Tarkhov, B. V. Fine, arXiv:1804.09732 (2018). [2] A. E. Tarkhov, S. Wimberger, and B. V. Fine, Phys. Rev. A. 96, 023624 (2017).