Constructing Fermionic Dynamics with Closed Moment Hierarchies
Year: 2026
Type: article
Abstract: We construct a broad class of completely positive maps and Gorini–Kossakowski–Sudarshan–Lindblad generators for fermionic systems induced by linear transformations of system and environment modes. For these maps, we derive explicit Heisenberg-picture formulas for arbitrary normally ordered monomials in terms of minors of the underlying mode-transformation matrices and environment correlation tensors. We show that for even environment states, the linear span of monomials up to any fixed order is invariant, which yields closed equations for low-order moments and makes their computation efficient. We also discuss the relation of this construction to the second quantization of non-Hermitian one-particle contractions and extend the formalism to completely positive maps arising from post-selection.
Author: A. E. Teretenkov
Institutions: Russian Academy of Sciences, Steklov Mathematical Institute
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7148982722