On the Discretization Error of the Discrete Generalized Quantum Master Equation
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912506841137152 |
|---|---|
| author | Peng, Ruojing Lindoy, Lachlan P. Lee, Joonho |
| author_facet | Peng, Ruojing Lindoy, Lachlan P. Lee, Joonho |
| contents | The transfer tensor method (TTM) [Cerrillo and Cao, Phys. Rev. Lett. 2014, 112, 110401] can be considered a discrete-time formulation of the Nakajima-Zwanzig quantum master equation (NZ-QME) for modeling non-Markovian quantum dynamics. A recent paper [Makri, J. Chem. Theory Comput. 2025, 21, 5037] raised concerns regarding the consistency of the TTM discretization, particularly a spurious term at the initial time \( t=0 \). This Communication presents a detailed analysis of the discretization structure of TTM, clarifying the origin of the initial-time correction and establishing a consistent relationship between the TTM discrete-time memory kernel \( K_N \), and the continuous-time NZ-QME kernel \( \mathcal{K}(NΔt) \). This relationship is validated numerically using the spin-boson model, demonstrating convergence of reconstructed memory kernels and accurate dynamical evolution as \( Δt \to 0 \). While TTM provides a consistent discretization, we note that alternative schemes are also viable, such as the midpoint derivative/midpoint integral scheme proposed in Makri's work. The relative performance of various schemes for either computing accurate \( \mathcal{K}(NΔt) \) from exact dynamics, or obtaining accurate dynamics from exact \( \mathcal{K}(NΔt) \), warrants further investigation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_19323 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Discretization Error of the Discrete Generalized Quantum Master Equation Peng, Ruojing Lindoy, Lachlan P. Lee, Joonho Quantum Physics Chemical Physics The transfer tensor method (TTM) [Cerrillo and Cao, Phys. Rev. Lett. 2014, 112, 110401] can be considered a discrete-time formulation of the Nakajima-Zwanzig quantum master equation (NZ-QME) for modeling non-Markovian quantum dynamics. A recent paper [Makri, J. Chem. Theory Comput. 2025, 21, 5037] raised concerns regarding the consistency of the TTM discretization, particularly a spurious term at the initial time \( t=0 \). This Communication presents a detailed analysis of the discretization structure of TTM, clarifying the origin of the initial-time correction and establishing a consistent relationship between the TTM discrete-time memory kernel \( K_N \), and the continuous-time NZ-QME kernel \( \mathcal{K}(NΔt) \). This relationship is validated numerically using the spin-boson model, demonstrating convergence of reconstructed memory kernels and accurate dynamical evolution as \( Δt \to 0 \). While TTM provides a consistent discretization, we note that alternative schemes are also viable, such as the midpoint derivative/midpoint integral scheme proposed in Makri's work. The relative performance of various schemes for either computing accurate \( \mathcal{K}(NΔt) \) from exact dynamics, or obtaining accurate dynamics from exact \( \mathcal{K}(NΔt) \), warrants further investigation. |
| title | On the Discretization Error of the Discrete Generalized Quantum Master Equation |
| topic | Quantum Physics Chemical Physics |
| url | https://arxiv.org/abs/2507.19323 |