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arXiv:1111.6686 · Scientific Reports

Average quantum dynamics of closed systems over stochastic Hamiltonians

Yu Li, Daniel F. V. James

Published Aug 23, 2025• 4 citations
arXivHTMLPDF

Abstract

We develop a formally exact master equation to describe the evolution of the average density matrix of a closed quantum system driven by a stochastic Hamiltonian. The average over stochastic processes generally results in decoherence effects in closed system dynamics, in addition to the unitary evolution. We then show that, for an important class of problems in which the Hamiltonian is proportional to a Gaussian random process, the 2nd-order master equation yields exact dynamics. The general formalism is applied to study the examples of a two-level system, two atoms in a stochastic magnetic field and the heating of a trapped ion, where we find phenomena such as decoherence-induced disentanglement.

DOI
10.1038/s41598-025-14825-z

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We develop a technique for finding the dynamical evolution in time of an averaged density matrix. The result is an equation of evolution that includes an effective Hamiltonian, as well as decoherence terms in Lindblad form. Applying the general equation to harmonic Hamiltonians, we confirm a previous formula for the effective Hamiltonian together with a additional decoherence term which should, in general, be included and whose vanishing provides the criteria for validity of the effective Hamiltonian approach. Finally, we apply the theory to examples of the ac Stark shift and three-level Raman transitions, recovering a decoherence effect in the latter.
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