I. Semina | Searcharxiv

arXiv2018

Stochastic wave-function unravelling of the generalized Lindblad equation

We investigate generalized non-Markovian stochastic Schroeodinger equations (SSEs), driven by a multidimensional counting process and multidimensional Brownian motion introduced by A. Barchielli and C. Pellegrini [J. Math. Phys. 51, 112104 (2010)]. We show, that these SSEs can be translated in a non-linear form, which can be efficiently simulated. The simulation is illustrated by the model of a two-level system in a structured bath and the results of the simulations are compared with the exact solution of the generalized master equation.

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arXiv2013

Stochastic Schrödinger Equations for Markovian and non-Markovian cases

Firstly, the Markovian stochastic Schrödinger equations are presented, together with their connections with the theory of measurements in continuous time. Moreover, the stochastic evolution equations are translated into a simulation algorithm, which is illustrated by two concrete examples - the damped harmonic oscillator and a two-level atom with homodyne photodetection. Then, we consider how to introduce memory effects in the stochastic Schrödinger equation via coloured noise. Specifically, the approach by using the Ornstein-Uhlenbeck process is illustrated and a simulation for the non-Markovian process proposed. Finally, an analytical approximation technique is tested with the help of the stochastic simulation in a model of a dissipative qubit.

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