Path-Integral Formulation of Truncated Wigner Approximation for Bosonic Markovian Open Quantum Systems

The truncated Wigner approximation (TWA) enables us to calculate bosonic quantum many-body dynamics while accounting for the effects of quantum fluctuations. In this work, we formulate the TWA for bosonic Markovian open quantum systems described by the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) equation from the coherent-state path-integral approach using the Wigner function. We derive an analytical expression for the GKSL equation in the TWA where we consider a bosonic system with an arbitrary Hamiltonian with jump operators that do not couple different states. We numerically confirm that the time evolution of physical quantities and the non-equal time correlation functions obtained in our formulation agree well with the exact ones in the numerically solvable models.