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arXiv · 1408.6624

Non-stochastic matrix Schrödinger equation for open systems

Loïc Joubert-Doriol·Ilya G. Ryabinkin·Artur F. Izmaylov
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Abstract

We propose an extension of the Schrödinger equation for a quantum system interacting with environment. This equation describes dynamics of auxiliary wave-functions $\mathbf{m}$, from which the system density matrix can be reconstructed as $\hatρ = \mathbf{m} \mathbf{m}^\dagger$. We formulate a compatibility condition, which ensures that the reconstructed density satisfies a given quantum master equation for the system density. The resulting non-stochastic evolution equation preserves positive-definiteness of the system density and is applicable to both Markovian and non-Markovian system-bath treatments. Our formalism also resolves a long-standing problem of energy non-conservation in the time-dependent variational principle applied to mixed states of closed systems.

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Loïc Joubert-Doriol, Ilya G. Ryabinkin, Artur F. Izmaylov. 2014-11-29. Non-stochastic matrix Schrödinger equation for open systems. https://doi.org/10.1063/1.4903829

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