title: Communication: satisfying fermionic statistics in the modeling of open time-dependent quantum systems with one-electron reduced density matrices.
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 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 F2, N2, CO, and BeH2 subject to environmental noise.
authors: Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA.
authors: Kade
authors: K
authors: Head-Marsden
authors: Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA.
authors: David A
authors: DA
authors: Mazziotti
mesh_terms: D002248:Carbon Monoxide / Q000737:chemistry; D004583:Electrons; D005461:Fluorine / Q000737:chemistry; D008958:Models, Molecular; D009584:Nitrogen / Q000737:chemistry; D011789:Quantum Theory
chemical_list: D005461:Fluorine; D002248:Carbon Monoxide; D009584:Nitrogen