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By starting from the stochastic Schrodinger equation and quantum trajectory theory, we introduce memory effects by considering stochastic adapted coefficients. As an example of a natural non-Markovian extension of the theory of white noise quantum trajectories we use an Ornstein-Uhlenbeck coloured noise as the output driving process. Under certain conditions a random Hamiltonian evolution is recovered. Moreover, we show that our non-Markovian stochastic Schrodinger equations unravel some master equations with memory kernels.
Quantum trajectories are Markov processes that describe the time-evolution of a quantum system undergoing continuous indirect measurement. Mathematically, they are defined as solutions of the so-called Stochastic Schrodinger Equations, which are nonl
In this short note, we present a construction for the log-log blow up solutions to focusing mass-critical stochastic nonlinear Schroidnger equations with multiplicative noises. The solution is understood in the sense of controlled rough path as in cite{SZ20}.
The stochastic Schrodinger equation, of classical or quantum type, allows to describe open quantum systems under measurement in continuous time. In this paper we review the link between these two descriptions and we study the properties of the output
We obtain novel nonlinear Schr{o}dinger-Pauli equations through a formal non-relativistic limit of appropriately constructed nonlinear Dirac equations. This procedure automatically provides a physical regularisation of potential singularities brought
In this paper, we prove the global existence and uniqueness of the solution of the stochastic logarithmic Schrodinger (SlogS) equation driven by additive noise or multiplicative noise. The key ingredient lies on the regularized stochastic logarithmic