The non-Markovian stochastic Schrödinger equation for the position unraveling

The Non-Markovian stochastic Schrödinger equation for the position unravelling

A non-Markovian stochastic Schrödinger equation developed from a hidden variable interpretation

Do non-Markovian diffusive stochastic Schrödinger equations (SSEs) for open quantum systems have a physical interpretation? In a recent paper we investigated this question using the orthodox interpretation of quantum mechanics [phys. Rev. A 66, 012108 (2002)] . We found that the solution of a non-Markovian SSE at time t represents the state the system would be in at that time if a measurement w...

Ergodicity for the Weakly Damped Stochastic Non-linear Schrödinger Equations

We study a damped stochastic non-linear Schrödinger (NLS) equation driven by an additive noise. It is white in time and smooth in space. Using a coupling method, we establish convergence of the Markovian transition semi-group toward a unique invariant probability measure. This kind of method was originally developped to prove exponential mixing for strongly dissipative equations such as the Nav...

Stochastic Schrödinger equations with coloured noise

A natural non-Markovian extension of the theory of white noise quantum trajectories is presented. In order to introduce memory effects in the formalism an Ornstein-Uhlenbeck coloured noise is considered as the output driving process. Under certain conditions a random Hamiltonian evolution is recovered. Moreover, non-Markovian stochastic Schrödinger equations which unravel non-Markovian master e...

The non-Markovian stochastic Schrödinger equation for open systems

We present the non-Markovian generalization of the widely used stochastic Schrödinger equation. Our result allows to describe open quantum systems in terms of stochastic state vectors rather than density operators, without Markov approximation. Moreover, it unifies two recent independent attempts towards a stochastic description of non-Markovian open systems, based on path integrals on the one ...