Recent work has addressed the possibility of simulating the quantum dynamics of polyatomic processes without any reference to harmonic bath models. Rather than introducing uncontrolled approximations to deal with the many-body problem, our approach relies on the fact that the dynamics of an unobservable environment need to be obtained only to the extent that they affect the evolution of the probed system. Exploiting the resulting structure of the influence functional from a general nonlinear medium allows pairing of the forward and reverse time evolution operators, which largely ameliorates instabilities caused by phase cancellation.
Following these ideas, we proposed a rigorous semiclassical procedure for evaluating influence functionals which employs a coherent state initial value representation of the propagator that uses trajectories initially integrated in the forward direction, subsequently returning to zero time. The backward part of the propagation cancels the dominant contributions to the action, leading to a slowly varying phase. We have shown that the integrand of the forward-backward semiclassical influence functional is purely positive by construction in the most important limit of similar forward and backward system paths, and that severe phase cancellation occurs primarily with configurations for which the influence functional approaches zero and thus need not be obtained accurately.
Our iterative path integral methodology, combined with a forward-backward semiclassical evaluation of the influence functional, leads to a powerful quantum-semiclassical methodology for simulating the dynamics of a quantum system coupled to a general anharmonic many-body environment.
- Real time path integral methods for a system coupled to an anharmonic bath.
- Iterative evaluation of the path integral for a system coupled to an anharmonic bath.
- Semiclassical influence functionals for quantum systems in anharmonic environments.
- Influence functionals with semiclassical propagators in combined forward-backward time.