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This study demonstrates that stochastic classical trajectories can successfully equilibrate continuous-variable open quantum systems to their exact thermal states, even beyond the weak-coupling limit. Although the method introduces numerical instability by evolving variables into the complex plane to capture imaginary momentum-position correlations, it successfully models a quartic oscillator coupled to a white-noise bath. These findings suggest a potential new pathway for simulating complex quantum systems where traditional approximations may fall short.
Equilibrating continuous-variable open quantum systems using stochastic classical trajectories in path-integral space
arXiv:2606.10665v1 Announce Type: new Abstract: Beyond the weak-coupling limit, open quantum systems equilibrate to a highly entangled thermal state. For continuous-variable systems, this state can be written explicitly as an imaginary-time phase-space path integral, in which the positions are directly entangled with the bath, and the momenta are correlated with the positions through a phase term. Here, we ask to what extent this state can be reached by propagating stochastic classical trajectories in path-integral phase space. Surprisingly, we find that the trajectories equilibrate to the exact quantum equilibrium state, recovering the purely imaginary momentum-position correlation in the phase term. The trajectories are generated using a recently derived Matsubara generalized Langevin equation, which produces the imaginary correlations by evolving the stochastic variables into the complex plane. This makes the dynamics numerically unstable, but we are nonetheless able to demonstrate the equilibration of a quartic oscillator coupled to a white-noise bath. These unexpected findings could lead to new approximate methodologies for simulating continuous-variable open quantum systems.
Abstract:Beyond the weak-coupling limit, open quantum systems equilibrate to a highly entangled thermal state. For continuous-variable systems, this state can be written explicitly as an imaginary-time phase-space path integral, in which the positions are directly entangled with the bath, and the momenta are correlated with the positions through a phase term. Here, we ask to what extent this state can be reached by propagating stochastic classical trajectories in path-integral phase space. Surprisingly, we find that the trajectories equilibrate to the exact quantum equilibrium state, recovering the purely imaginary momentum-position correlation in the phase term. The trajectories are generated using a recently derived Matsubara generalized Langevin equation, which produces the imaginary correlations by evolving the stochastic variables into the complex plane. This makes the dynamics numerically unstable, but we are nonetheless able to demonstrate the equilibration of a quartic oscillator coupled to a white-noise bath. These unexpected findings could lead to new approximate methodologies for simulating continuous-variable open quantum systems.
Quantum Physics (quant-ph); Chemical Physics (physics.chem-ph)
arXiv:2606.10665 [quant-ph]
(or arXiv:2606.10665v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2606.10665 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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