Complex stochastic diffusion or stochastic Schrödinger equation

Kundeti Muralidhar

Kai Song, Linze Song, Qiang Shi

Based on the path integral approach, we derive a new realization of the exact non-Markovian stochastic Schrödinger equation (SSE). The main difference from the previous non-Markovian quantum state diffusion (NMQSD) method is that the complex Gaussian stochastic process used for the forward propagation of the wave function is correlated, which may be used to reduce the amplitude of the non-Markovian memory term at high temperatures. The new SSE is then written into the recently developed hierarchy of pure states scheme, in a form that is more closely related to the hierarchical equation of motion approach. Numerical simulations are then performed to demonstrate the efficiency of the new method.

Wilfried Grecksch, Hannelore Lisei

Crispin W. Gardiner, P. Zoller

John E. Gough

We show that the quantum state diffusion equation of Gisin and Percival, driven by complex Wiener noise, is equivalent up to a global stochastic phase to quantum trajectory models. With an appropriate feedback scheme, we set up an analog continuous measurement model which exactly simulates the Gisin-Percival quantum state diffusion.

Alberto Barchielli, Matteo Gregoratti