Low-temperature correlation functions via forward-backward quantum dynamics

We present an extension of forward-backward quantum dynamics suitable for evaluating finite-temperature time correlation functions for one-dimensional systems at low temperatures. The procedure relies on the cooling action of the Boltzmann operator, which produces a state similar to the lowest energy eigenstate with the given symmetry. As we have shown earlier, the quantum trajectories of near-eigenstates can be integrated by a numerical procedure based on a generalization of Hamilton's principle of stationary action. Evaluation of the trace may be performed in a generic basis set, obviating the need to calculate eigenstates. Numerical applications illustrate the method.