Non-stochastic matrix Schrödinger equation for open systems

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 $\hat{\rho }=\mathbf{m}{\mathbf{m}}^{†}$. 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.

5 pages, 2 figures

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Cited by in corpus (6)

• Nonadiabatic Quantum Dynamics with Frozen-Width Gaussians
• Problem-free time-dependent variational principle for open quantum systems
• Adaptive variational low-rank dynamics for open quantum systems
• The wave operator representation of quantum and classical dynamics
• Positivity Preserving Density Matrix Minimization at Finite Temperatures via Square Root
• Low-rank optimal control of quantum devices