Simulations of Bose Dynamics at Finite Temperature by Complex Langevin Sampling Coherent States on a Keldysh Contour

Efficient and scalable methods for simulating the exact dynamical evolution of finite-temperature, interacting Bosons subject to a time-dependent external potential are very challenging to develop. We previously reported a stable and efficient algorithm based on complex Langevin dynamics for sampling the equilibrium coherent states field theory of an assembly of interacting bosons, and we demonstrated its correctness by locating the Bose-Einstein condensation transition temperature in a φ⁴ theory of contact interactions. In this talk, we detail an extension of this algorithm to permit sampling configurations on a Keldysh contour. The new algorithm permits evaluation of the real-time causal Green function and all dependent dynamical properties without approximations.