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Generation and Coherent Control of Pulsed Quantum Frequency Combs
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On the discretization error of the discrete generalized quantum master equation
Ruojing Peng1, Lachlan P Lindoy2, Joonho Lee1
1Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts 02138, USA.
The Journal of Chemical Physics
|October 1, 2025
Summary
The transfer tensor method (TTM) offers a consistent discrete-time approach for quantum dynamics, clarifying initial-time corrections. Numerical validation confirms its accuracy and convergence, though alternative methods also exist.
Area of Science:
- Quantum Dynamics
- Theoretical Chemistry
- Computational Physics
Background:
- The transfer tensor method (TTM) is a discrete-time formulation of the Nakajima-Zwanzig quantum master equation (NZ-QME).
- Concerns have been raised about the consistency of TTM discretization, specifically regarding initial-time terms.
Purpose of the Study:
- To analyze the discretization structure of the TTM.
- To clarify the origin of the initial-time correction in TTM.
- To establish a consistent relationship between TTM memory kernels and NZ-QME kernels.
Main Methods:
- Detailed analysis of the TTM discretization structure.
- Numerical validation using the spin-boson model.
- Comparison with alternative discretization schemes.
Main Results:
- The origin of the initial-time correction in TTM has been clarified.
- A consistent relationship between discrete-time TTM memory kernels (KN) and continuous-time NZ-QME kernels (K(NΔt)) was established.
- Numerical results demonstrate convergence and accurate dynamics as the time step (Δt) approaches zero.
Conclusions:
- The TTM provides a consistent discretization for modeling non-Markovian quantum dynamics.
- Alternative discretization schemes, like the midpoint method, are also viable.
- Further research is needed to compare the performance of different schemes for kernel computation and dynamics simulation.
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