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Title: Communication: Satisfying fermionic statistics in the modeling of open time-dependent quantum systems with one-electron reduced density matrices

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 N-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 N-electron density matrix (not ensemble N-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 N-representable for all time. The theory is illustrated by considering the relaxation of an excitation in several molecules F{sub 2}, N{sub 2}, CO, and BeH{sub 2} subject to environmental noise.
Authors:
;  [1]
  1. Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637 (United States)
Publication Date:
OSTI Identifier:
22416061
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Chemical Physics; Journal Volume: 142; Journal Issue: 5; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; APPROXIMATIONS; BERYLLIUM HYDRIDES; BOLTZMANN-VLASOV EQUATION; CARBON MONOXIDE; DENSITY MATRIX; ELECTRON DENSITY; ELECTRONS; EXCITATION; MARKOV PROCESS; MODIFICATIONS; MOLECULES; PAULI PRINCIPLE; QUANTUM SYSTEMS; RELAXATION; STATISTICS; TIME DEPENDENCE