Linearized symmetrized quantum time correlation functions calculation via phase pre-averaging

Abstract

We recently introduced an iterative method to compute quantum time correlation functions [Bonella et al., J. Chem. Phys 133 (16), 164105 (2010)]. There, the thermal part of the correlation function is treated exactly and, similar to the linearization techniques, at zero order of iteration only classical dynamics is required. In this work, we propose a new scheme for the zero-order iteration of the method which significantly improves the efficiency of the calculations for high dimensional model systems.

Keywords:

• approximate quantum time correlation functions
• semiclassical dynamics
• linearized methods
• Monte Carlo algorithm

Acknowledgements

This paper is dedicated to Luciano Reatto, on the occasion of his retirement, as a testimony of his tireless efforts to convince us classical statistical mechanics simulators to study quantum problems. The authors are grateful to D. Ceperley and E. Liberatore for useful discussions on the penalty method. Financial support from SFI Grant No. 08-IN.1-I1869 and from the Istituto Italiano di Tecnologia under the SEED project grant No. 259 SIMBEDD – Advanced Computational Methods for Biophysics, Drug Design and Energy Research is acknowledged.

Notes

1. If is the λth ‘bead’ along the forward/backward path, with , the change of variables is and .

2.  is a product of Gaussians that can be sampled directly using relatively standard methods such as staging [34] or the Levy flight algorithm [35].

3. Given the exponential form of the observable, the convergence of this calculation might be difficult. However, since the configurations r and are close (in the spirit of a standard Metropolis move), this should not be a problem.