Explicit closed-form propagators for time-dependent gain-loss master equations
Abstract
Time ordering is a central obstacle in driven open-system dynamics governed by master equations with time-dependent rates. We derive explicit closed-form factorizations of the chronological and antichronological propagators for a time-dependent generator of the form ℒ(t)=α(t)A+β(t)B, when the commutator [A,B] is a simultaneous eigenoperator of the adjoint actions of A and B, namely [A,[A,B]]=λA[A,B] and [B,[A,B]]=λB[A,B]. In contrast to the disentangling procedure known as the Wei-Norman decomposition, our construction determines the factorization coefficients directly, without solving a coupled system of nonlinear differential equations. Applying this result to the bosonic gain-loss Lindblad equation, we obtain the exact dynamical map for arbitrary time-dependent gain and loss rates. The gain-loss master equation provides a canonical description of a driven harmonic oscillator coupled to a thermal bath. We benchmark the construction by deriving the time evolution of the Wigner function of an initial Fock state and comparing it with independent phase-space results. We further apply the resulting dynamical map to evaluate the code-space survival probability of a binomial bosonic code under driven gain-loss dynamics.
Related
- A Closed-Form Master Solution for Gravitational Decoupling of a Unified Family of Isotropic Stellar Seeds
- qdmag: A Python package for simulating nonequilibrium magnetization of molecules using quantum master equations
- Quantum-Classical Neural Networks for Solving Lindblad Master Equations
- A thermodynamic analysis of nonsecular master equations, beyond strict energy conservation and Gibbs equilibrium state
- Closed-form hard-sphere thermodynamics under nanoscale confinement: from equations of state to unmixing forces
BibTeX
@misc{dupays2026explicit,
title = {{Explicit closed-form propagators for time-dependent gain-loss master equations}},
author = {Léonce Dupays},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.24617},
eprint = {2609.24617},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.24617},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Explicit closed-form propagators for time-dependent gain-loss master equations
AU - Léonce Dupays
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.24617
UR - https://arxiv.org/abs/2609.24617
AB - Time ordering is a central obstacle in driven open-system dynamics governed by master equations with time-dependent rates. We derive explicit closed-form factorizations of the chronological and antichronological propagators for a time-dependent generator of the form ℒ(t)=α(t)A+β(t)B, when the commutator [A,B] is a simultaneous eigenoperator of the adjoint actions of A and B, namely [A,[A,B]]=λ_A[A,B] and [B,[A,B]]=λ_B[A,B]. In contrast to the disentangling procedure known as the Wei-Norman decomposition, our construction determines the factorization coefficients directly, without solving a coupled system of nonlinear differential equations. Applying this result to the bosonic gain-loss Lindblad equation, we obtain the exact dynamical map for arbitrary time-dependent gain and loss rates. The gain-loss master equation provides a canonical description of a driven harmonic oscillator coupled to a thermal bath. We benchmark the construction by deriving the time evolution of the Wigner function of an initial Fock state and comparing it with independent phase-space results. We further apply the resulting dynamical map to evaluate the code-space survival probability of a binomial bosonic code under driven gain-loss dynamics.
ER -