Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Chemical Physics

Nonperturbative non-Markovian quantum master equation: Validity and limitation to calculate nonlinear response functions

Akihito Ishizaki, Yoshitaka Tanimura

Published Nov 27, 2007• 112 citations
Publisher
DOI
10.1016/j.chemphys.2007.10.037

Related papers

Non-Markovian master equation for linear and nonlinear systems

Gautam Gangopadhyay, Deb Shankar Ray

Based on the standard system-heat-bath model, we have formulated a theory of the non-Markovian master equation for linear and nonlinear systems for a correlation time that is short but finite. We have applied the theory to linear systems, such as harmonic oscillators and two-level atoms and calculated the band-shape functions for transient optical absorption in the pump-probe experiments. The significant interplay of nonlinearity and non-Markovian decay has been illustrated by another application of the theory to a Morse oscillator. The theory is valid for arbitrary nonlinearity and finite temperatures but within the weak-coupling limit and has been derived without ad hoc implementation of a phenomenological memory function.

Physical Review A•Aug 1, 1992•33 citations

Selected Aspects of Markovian and Non-Markovian Quantum Master Equations

K. Lendi

Lecture notes in physics•Jan 1, 2003•3 citations

Quantum Master Equations Applicable to Non-linear Response

Tomáš Mančal, František Šanda

•Nov 16, 2010•0 citations

A non-Markovian modeling of frequency upconversion via four-wave mixing schemes

M. Gabriela Boada G., Jose Morales E, Andrea Delgado

We present a non-Markovian quantum master equation tailored for optimizing of parametric upconversion via four-wave mixing (FWM) in nonlinear optical systems. Our approach nonperturbatively embeds the device environment interaction into a structured noise model, going beyond the standard Markovian and rotating-wave approximations (RWA). By constructing an equivalent dynamical model where FWM occur within a pseudo-modal structured environment, we preserve the observable device response while naturally incorporating thermalization effects induced by coherent driving. This formulation reveals the physical origins of decoherence without compromising the functional behavior of device operations. Furthermore, we reformulate phase-matching conditions within our non-Markovian framework, providing new tools for optimizing nonlinear device performance in regimes where thermal parameter drifts and coherent driven interactions compete. This is particularly relevant for integrated photonic and superconducting quantum platforms where structured environmental modes interact with driven systems over prolonged timescales. Our results emphasize the limitations of Markovian approximations in modeling sustained nonlinear interactions and offer a practical pathway to improving conversion efficiency and coherence retention under realistic operating conditions. These findings provide theoretical guidance for engineering quantum photonic devices in temperature-sensitive regimes, where precision modeling of noise and back-action is critical to performance.

Quantum Computing, Communication, and Simulation•Mar 5, 2026•0 citations

Expansion method for nonlinear quantum master equations

Marcelo A. Despósito

Physica A Statistical Mechanics and its Applications•Aug 1, 1994•0 citations

Open system dynamics in interacting quantum field theories

Brenden Bowen, Nishant Agarwal, Archana Kamal

A quantum system that interacts with an environment generally undergoes nonunitary evolution described by a non-Markovian or Markovian master equation. In this paper, we construct the non-Markovian Redfield master equation for a quantum scalar field that interacts with a second field through a bilinear or nonlinear interaction on a Minkowski background. We use the resulting master equation to set up coupled differential equations that can be solved to obtain the equal-time two-point function of the system field. We show how the equations simplify under various approximations including the Markovian limit and argue that the Redfield equation-based solution provides a perturbative resummation to the standard second-order Dyson series result. For the bilinear interaction, we explicitly show that the Redfield solution is closer to the exact solution compared to the perturbation theory-based one. Further, the environment correlation function is oscillatory and nondecaying in this case, making the Markovian master equation a poor approximation. For the nonlinear interaction, on the other hand, the environment correlation function is sharply peaked and the Redfield solution matches that obtained using a Markovian master equation in the late-time limit.

arXiv:2403.18907•Physical Review Research•Oct 14, 2025•8 citations
Based on the standard system-heat-bath model, we have formulated a theory of the non-Markovian master equation for linear and nonlinear systems for a correlation time that is short but finite. We have applied the theory to linear systems, such as harmonic oscillators and two-level atoms and calculated the band-shape functions for transient optical absorption in the pump-probe experiments. The significant interplay of nonlinearity and non-Markovian decay has been illustrated by another application of the theory to a Morse oscillator. The theory is valid for arbitrary nonlinearity and finite temperatures but within the weak-coupling limit and has been derived without ad hoc implementation of a phenomenological memory function.
We present a non-Markovian quantum master equation tailored for optimizing of parametric upconversion via four-wave mixing (FWM) in nonlinear optical systems. Our approach nonperturbatively embeds the device environment interaction into a structured noise model, going beyond the standard Markovian and rotating-wave approximations (RWA). By constructing an equivalent dynamical model where FWM occur within a pseudo-modal structured environment, we preserve the observable device response while naturally incorporating thermalization effects induced by coherent driving. This formulation reveals the physical origins of decoherence without compromising the functional behavior of device operations. Furthermore, we reformulate phase-matching conditions within our non-Markovian framework, providing new tools for optimizing nonlinear device performance in regimes where thermal parameter drifts and coherent driven interactions compete. This is particularly relevant for integrated photonic and superconducting quantum platforms where structured environmental modes interact with driven systems over prolonged timescales. Our results emphasize the limitations of Markovian approximations in modeling sustained nonlinear interactions and offer a practical pathway to improving conversion efficiency and coherence retention under realistic operating conditions. These findings provide theoretical guidance for engineering quantum photonic devices in temperature-sensitive regimes, where precision modeling of noise and back-action is critical to performance.
A quantum system that interacts with an environment generally undergoes nonunitary evolution described by a non-Markovian or Markovian master equation. In this paper, we construct the non-Markovian Redfield master equation for a quantum scalar field that interacts with a second field through a bilinear or nonlinear interaction on a Minkowski background. We use the resulting master equation to set up coupled differential equations that can be solved to obtain the equal-time two-point function of the system field. We show how the equations simplify under various approximations including the Markovian limit and argue that the Redfield equation-based solution provides a perturbative resummation to the standard second-order Dyson series result. For the bilinear interaction, we explicitly show that the Redfield solution is closer to the exact solution compared to the perturbation theory-based one. Further, the environment correlation function is oscillatory and nondecaying in this case, making the Markovian master equation a poor approximation. For the nonlinear interaction, on the other hand, the environment correlation function is sharply peaked and the Redfield solution matches that obtained using a Markovian master equation in the late-time limit.