Interpretation of non-Markovian stochastic Schrodinger equations as a hidden variable theory

The non-Markovian stochastic Schrödinger equation for the position unraveling

An important and well established area of quantum optics is the theory of Markovian stochastic Schrödinger equations (or by another name quantum trajectory theory). Recently stochastic Schrödinger equations have been developed for non-Markovian systems. In this paper we extend the current known stochastic Schrödinger equations for non-Markovian systems to include the position unraveling. We als...

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...

Non-Markovian stochastic Schrodinger equations: Generalization to real- valued noise using quantum measurement theory

Non-Markovian stochastic Schrödinger equations in different temperature regimes: a study of the spin-boson model.

Stochastic Schrodinger equations are used to describe the dynamics of a quantum open system in contact with a large environment, as an alternative to the commonly used master equations. We present a study of the two main types of non-Markovian stochastic Schrodinger equations, linear and nonlinear ones. We compare them both analytically and numerically, the latter for the case of a spin-boson m...

Non-markovian process modelling with Echo State Networks

Reservoir Computing (RC) is a relatively recent architecture for using recurrent neural networks. It has shown interesting performance in a wide range of tasks despite the simple training rules. We use it here in a logistic regression (LogR) framework. Considering non-Markovian time series with a hidden variable, we show that RC can be used to estimate the transition probabilities at each time ...