Real-time quantum dynamics, path integrals and the method of thimbles

Mou, Zong-Gang; Saffin, Paul M.; Tranberg, Anders; Woodward, Simon

Abstract

Direct numerical evaluation of the real-time path integral has a well-known sign problem that makes convergence exponentially slow. One promising remedy is to use Picard-Lefschetz theory to flow the domain of the field variables into the complex plane, where the integral is better behaved. By Cauchy's theorem, the final value of the path integral is unchanged. Previous analyses have considered the case of real scalar fields in thermal equilibrium, employing a closed Schwinger-Keldysh time contour, allowing the evaluation of the full quantum correlation functions. Here we extend the analysis by not requiring a closed time path, instead allowing for an initial density matrix for out-of-equilibrium initial value problems. We are able to explicitly implement Gaussian initial conditions, and by separating the initial time and the later times into a two-step Monte-Carlo sampling, we are able to avoid the phenomenon of multiple thimbles. In fact, there exists one and only one thimble for each sample member of the initial density matrix. We demonstrate the approach through explicitly computing the real-time propagator for an interacting scalar in 0+1 dimensions, and find very good convergence allowing for comparison with perturbation theory and the classical-statistical approximation to real-time dynamics.

Citation

Mou, Z.-G., Saffin, P. M., Tranberg, A., & Woodward, S. (2019). Real-time quantum dynamics, path integrals and the method of thimbles. Journal of High Energy Physics, 2019(6), Article 94. https://doi.org/10.1007/jhep06%282019%29094

• Journal Article Type: Article
• Acceptance Date: Jun 10, 2019
• Online Publication Date: Jun 19, 2019
• Publication Date: 2019-06
• Deposit Date: Jul 8, 2019
• Publicly Available Date: Jul 11, 2019
• Journal: Journal of High Energy Physics
• Electronic ISSN: 1029-8479
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 2019
• Issue: 6
• Article Number: 94
• DOI: https://doi.org/10.1007/jhep06%282019%29094
• Keywords: Lattice quantum field theory, Nonperturbative effects, Stochastic processes
• Public URL: https://nottingham-repository.worktribe.com/output/2284127
• Publisher URL: https://link.springer.com/article/10.1007%2FJHEP06%282019%29094
• Additional Information: Received: 11 March 2019; Accepted: 10 June 2019; First Online: 19 June 2019
• Contract Date: Jul 8, 2019