Non-Markovian quantum state diffusion Original Research Article

We derive new time-local stochastic Schrödinger equations which offer a fully non-Markovian extension of conventional quantum state diffusion (QSD). The Feynman–Vernon influence functional of a linear heat bath is constructed as the stochastic mean value of time-local action terms, defining a linear stochastic Schrödinger equation. As a test, conventional QSD is recovered in limiting cases allowing the Born–Markov approximation. We further transform the dynamics to obtain a non-linear, norm-conserving Schrödinger equation with appealing properties: It is suitable for numerical simulations, and it has a well-defined classical limit even before noise averaging.