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/content/aip/journal/jcp/142/5/10.1063/1.4906942
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/content/aip/journal/jcp/142/5/10.1063/1.4906942
2015-02-02
2016-09-27

Abstract

For an open, time-dependent quantum system, Lindblad derived the most general modification of the quantum Liouville equation in the Markovian approximation that models environmental effects while preserving the non-negativity of the system’s density matrix. While Lindblad’s modification is correct for -electron density matrices, solution of the Liouville equation with a Lindblad operator causes the one-electron reduced density matrix (1-RDM) to violate the Pauli exclusion principle. Consequently, after a short time, the 1-RDM is not representable by an ensemble -electron density matrix (not ensemble -representable). In this communication, we derive the necessary and sufficient constraints on the Lindbladian matrix within the Lindblad operator to ensure that the 1-RDM remains -representable for all time. The theory is illustrated by considering the relaxation of an excitation in several molecules F, N, CO, and BeH subject to environmental noise.

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