Out-of-time-order correlators for the Swanson Hamiltonian with interaction terms
Phys. Rev. A 113, 062205 – Published 2 June, 2026
DOI: https://doi.org/10.1103/tbjm-b9hq
Abstract
In this work, we compute the out-of-time-ordered correlator (OTOC) for canonical position and momentum operators across a hierarchy of non-Hermitian oscillator models: the exactly solvable Swanson Hamiltonian, its Kerr-nonlinear extension, and parametrically driven variants. By employing the biorthogonal formalism required for parity-time symmetric quantum mechanics, we evaluate OTOCs both at zero and finite temperature, distinguishing behavior in the unbroken (real-spectrum) and broken (complex-spectrum) phases. Our analysis reveals how integrability, nonlinearity, driving, and parity-time symmetry breaking shape the temporal growth of operator correlations—providing a clear benchmark for OTOC dynamics in non-Hermitian quadratic and weakly anharmonic systems. We further characterize critical scaling of the OTOC near the exceptional point and discuss experimental perspectives for observing these effects in photonic, circuit-QED, and trapped-ion platforms.
