Non-Markovian quantum state diffusion

We derive new time-local stochastic Schrodinger equations which offer a ful ly non-Markovian extension of conventional quantum state diffusion (QSD). T he 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 Schrodinger equation. As a test, conventional QSD is recovered in limiting cases allowing the Born-Markov approximation. We further transf orm the dynamics to obtain a non-linear, norm-conserving Schrodinger equati on with appealing properties: It is suitable for numerical simulations, and it has a well-defined classical limit even before noise averaging. (C) 200 1 Elsevier Science B.V. All rights reserved.