2403.15596
Incorporating Memory into Propagation of 1-Electron Reduced Density Matrices
Harish S. Bhat, Hardeep Bassi, Karnamohit Ranka, Christine M. Isborn
correctmedium confidence
- Category
- Not specified
- Journal tier
- Specialist/Solid
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The candidate solution reproduces the paper’s Proposition 6: starting from unitary propagation of P(t) and the vec–Kronecker identity, switching to a Hermitian basis via S̃, enforcing trace and known zero entries to form M''(t) and b_ℓ(t), solving with the left pseudoinverse under full-column-rank, and reinserting fixed coordinates through an affine map A to obtain vec(Q(t+1)) = B̃ (exp(i H(t)^T Δt) ⊗ exp(−i H(t) Δt)) S̃ A(M''(t)+ b_ℓ(t)). These steps match equations (36), (38)–(41) and the surrounding discussion of constraints and rank assumptions in the paper’s Section IV.C–D, culminating in Proposition 6 .
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} specialist/solid
\textbf{Justification:}
The manuscript presents a rigorous, constraint-preserving delay-equation framework for 1RDM propagation. The derivation is internally consistent, well-motivated by physics, and carefully transitions from an unconstrained pseudoinverse-based scheme to a constrained, Hermitian-basis formulation. While the main assumption (full column rank of M''(t)) is clearly stated and partially explored, a deeper theoretical characterization of rank growth would enhance the paper. Presentation could be further improved with a compact symbol map and an illustrative worked example.