The non-Markovian quantum behavior of open systems: An exact Monte Carlo method employing stochastic product states

Abstract

It is shown that the exact dynamics of a composite quantum system can be represented through a pair of product states which evolve according to a Markovian random jump process. This representation is used to design a general Monte Carlo wave function method that enables the stochastic treatment of the full non-Markovian behavior of open quantum systems. Numerical simulations are carried out which demonstrate that the method is applicable to open systems strongly coupled to a bosonic reservoir, as well as to the interaction with a spin bath. Full details of the simulation algorithms are given, together with an investigation of the dynamics of fluctuations. Several potential generalizations of the method are outlined.

14 pages, 5 figures

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• Genuine quantum trajectories for non-Markovian processes
• Finding the Kraus decomposition from a master equation and vice versa
• An alternative non-Markovianity measure by divisibility of dynamical map
• Stochastic quantum dynamics beyond mean-field
• Quantum Monte-Carlo method applied to Non-Markovian barrier transmission
• Exact description of non-Markovian effect in open quantum system: the discretized environment method
• Exact stochastic simulation of dissipation and non-Markovian effects in open quantum systems
• Optimizing stochastic trajectories in exact quantum jump approaches of interacting systems
• A new approach for open quantum systems based on a phonon number representation of a harmonic oscillator bath
• Wave-particle Duality in Complex Quantum Systems
• Stochastic analysis and simulation of spin star systems
• Non-Markovian effects on non-locality of a qubit-oscillator system
• Open quantum dynamics with singularities: Master equations and degree of non-Markovianity