Stochastic Classical Trajectories Successfully Equilibrate Open Quantum Systems to Thermal States

A new preprint posted to arXiv reports that stochastic classical trajectories evolving in path-integral phase space are capable of equilibrating to the exact quantum thermal state of continuous-variable open quantum systems, even in the strong-coupling regime where the system and bath become highly entangled. The equilibrium state in this regime takes the form of an imaginary-time phase-space path integral, featuring direct entanglement between system positions and the bath, as well as a phase term encoding imaginary momentum-position correlations. The authors employ a Matsubara generalized Langevin equation, a recently derived framework that achieves these imaginary correlations by evolving stochastic variables into the complex plane. While this approach introduces numerical instability, the researchers demonstrate proof-of-concept equilibration for a quartic oscillator coupled to a white-noise bath. The authors describe the finding as surprising, since classical trajectory methods are not generally expected to capture exact quantum correlations of this kind. The work is presented as a potential foundation for new approximate methodologies targeting continuous-variable open quantum systems, a class of problems relevant to chemical physics and quantum information. The preprint has not yet undergone formal peer review.