Stochastic Classical Trajectories Successfully Equilibrate Open Quantum Systems to Thermal States
Researchers demonstrated that stochastic classical trajectories in path-integral phase space can equilibrate continuous-variable open quantum systems to exact quantum thermal states, even beyond the weak-coupling limit. The method uses a Matsubara generalized Langevin equation that evolves variables into the complex plane to recover quantum correlations. This finding could enable new computational approaches for simulating open quantum systems that were previously difficult to model.
A new theoretical study shows that stochastic classical trajectories propagated in path-integral phase space can reach the exact quantum equilibrium state for continuous-variable open quantum systems. The thermal state in this framework is expressed as an imaginary-time phase-space path integral where positions are entangled with the bath and momenta are correlated with positions through a phase term. The researchers used a Matsubara generalized Langevin equation to generate trajectories that evolve into the complex plane, producing the required imaginary correlations. Although the dynamics introduce numerical instability, the team successfully demonstrated equilibration for a quartic oscillator coupled to a white-noise bath. These findings are unexpected because classical stochastic methods typically cannot capture quantum correlations, yet here they recover the exact quantum state. The work suggests potential new approximate methodologies for simulating open quantum systems beyond weak-coupling regimes.
What's missing
The study acknowledges numerical instability in the complex-plane evolution but does not detail the specific computational challenges or error bounds encountered. The practical scalability of the method to higher-dimensional systems or more complex bath models is not discussed. The relationship between this approach and existing numerical methods for open quantum systems (e.g., quantum jump methods, influence functional approaches) is not explicitly addressed.
What different sources said
- arXiv physicsCenter
Equilibrating continuous-variable open quantum systems using stochastic classical trajectories in path-integral space
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