2018/05/31 by Josef Rammensee, Juan-Diego Urbina, Klaus Richter · 1 citation
Physics and Astronomy · #cond-mat.stat-mech #hep-th #quant-ph
paper · pdf · doi:10.1103/physrevlett.121.124101
published as Phys. Rev. Lett. 121, 124101 (2018) · 6 + 10 pages, 2 figures, small adjustments to match with the published version
arxiv created 2018/09/24 · arxiv updated 2018/09/25
Out-of-time-order correlators (OTOCs) have been proposed as sensitive probes for chaos in interacting quantum systems. They exhibit a characteristic classical exponential growth, but saturate beyond the so-called scrambling or Ehrenfest time τ\rm E in the quantum correlated regime. Here we present a path-integral approach for the entire time evolution of OTOCs for bosonic N-particle systems. We first show how the growth of OTOCs up to τ\rm E = (1/λ) log N is related to the Lyapunov exponent λ of the corresponding chaotic mean-field dynamics in the semiclassical large-N limit. Beyond τ\rm E, where simple mean-field approaches break down, we identify the underlying quantum mechanism responsible for the saturation. To this end we express OTOCs by coherent sums over contributions from different mean-field solutions and compute the dominant many-body interference term amongst them. Our method further applies to the complementary semiclassical limit ℏ → 0 for fixed N, including quantum-chaotic single- and few-particle systems.