Exact stochastic simulation of dissipation and non-Markovian effects in open quantum systems

Abstract

The exact dynamics of a system coupled to an environment can be described by an integro-differential stochastic equation of its reduced density. The influence of the environment is incorporated through a mean-field which is both stochastic and non-local in time and where the standard two-times correlation functions of the environment appear naturally. Since no approximation is made, the presented theory incorporates exactly dissipative and non-Markovian effects. Applications to the spin-boson model coupled to a heat-bath with various coupling regimes and temperature show that the presented stochastic theory can be a valuable tool to simulate exactly the dynamics of open quantum systems. Links with stochastic Schroedinger equation method and possible extensions to "imaginary time" propagation are discussed.

accepted for publication in Physical Review E

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• Quantum Monte-Carlo method applied to Non-Markovian barrier transmission
• Approach to solving spin-boson dynamics via non-Markovian quantum trajectories
• Exact description of non-Markovian effect in open quantum system: the discretized environment method
• Linear-algebraic bath transformation for simulating complex open quantum systems
• Derivation of exact master equation with stochastic description: Dissipative harmonic oscillator
• Realization of hierarchical equations of motion from stochastic perspectives
• Non-Markovian dynamics in a spin star system: The failure of thermalization
• Effective description of the short-time dynamics in open quantum systems
• A new approach for open quantum systems based on a phonon number representation of a harmonic oscillator bath
• Stochastic decoupling approach to the quantum dissipative dynamics: Perturbative and non-perturbative treatments
• Entropy and Its Quantum Thermodynamical Implication for Anomalous Spectral Systems