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.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Feb 02, 2015
- Source ID
- 10.1063/1.4906942
Entities
People
- David A Mazziotti
- Kade Head-Marsden
Organizations
- Air Force Office of Scientific Research
- Microsoft
- National Science Foundation
- University of Chicago
- W. M. Keck Foundation