Real-time quantum dynamics, path integrals and the method of thimbles
arXiv:1902.09147
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.
arXiv comment34 pages, 12 figures; more references added
References in corpus (21)
- Keldysh technique and non-linear sigma-model: basic principles and applications
- High density QCD on a Lefschetz thimble?
- Analytic Continuation Of Chern-Simons Theory
- Thermalization of Quantum Fields from Time-Reversal Invariant Evolution Equations
- Lattice simulations of real-time quantum fields
- Monte Carlo simulations on the Lefschetz thimble: taming the sign problem
- Classical Fields Near Thermal Equilibrium
- Classical approximation for time dependent quantum field theory: diagrammatic analysis for hot scalar fields
- A Monte Carlo algorithm for simulating fermions on Lefschetz thimbles
- Monte Carlo study of real time dynamics
- Lefschetz-thimble analysis of the sign problem in one-site fermion model
- Finite-Density Monte Carlo Calculations on Sign-Optimized Manifolds
- Hidden topological angles and Lefschetz thimbles
- Schwinger-Keldysh on the lattice: a faster algorithm and its application to field theory
- Parallel tempering algorithm for integration over Lefschetz thimbles
- Deep Learning Beyond Lefschetz Thimbles
- Lefschetz thimbles and stochastic quantisation: Complex actions in the complex plane
- Metropolis Monte Carlo on the Lefschetz thimble: application to a one-plaquette model
- Tempered transitions between thimbles
- Finite Density Near Lefschetz Thimbles
- Real-Time Feynman Path Integral Realization of Instantons