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Non-Markovian Extension

G.J.Y. DESVAUX

Published Mar 19, 2026• 0 citations
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Abstract

Non-Markovian Quantum Processes with Memory Kernels Extension of the Lindblad Formalism via the Generalized Nakajima-Zwanzig EquationLast & I think for a bit of time, formalized conclusion https://zenodo.org/records/19517607 Description This repository contains the complete theoretical foundations of a (futur) rigorous extension to the Lindblad master equation for describing non-Markovian quantum processes. The work introduces a general mathematical framework based on memory kernels $K(t,s)$ to capture the effects of a structured environment with finite memory, going beyond the Markovian approximation. It is accompanied by an interactive, web-based version of this work, featuring a fully functional simulator, dynamic graphs, a 3D Bloch sphere visualization, and unit tests, available at: ((...)) Core Contributions 1. Axiomatic Definition of $\mathcal{K}_{CP}$ A rigorous definition of the space of memory kernels that preserve the fundamental properties of quantum states: complete positivity and trace conservation. Necessary and sufficient conditions for a kernel to be admissible are established and proven. Axiom A1 (Hermiticity): $K(t,s) = K^*(s,t)$ Axiom A2 ($L^2$-integrability): $\int_0^\infty\!\!\int_0^\infty |K(t,s)|^2\,ds\,dt < \infty$ Axiom A3 (Complete Positivity): $\sigma_{\min}(\hat{K}(\omega)) \geq 0,\ \forall \omega$ 2. Characterization of the Instantaneous Generator $L(t)$ A formal link between the memory kernel $K(t,s)$ and the instantaneous generator $L(t)$ is established, with explicit formulas for different kernel types: $$L(t) = \mathcal{L} + \int_0^t K(\tau)\,d\tau - K(0)$$ 3. Exactly Solvable Examples Detailed analysis of four canonical memory kernels: Exponential (Ornstein-Uhlenbeck process): $\rho_{11}(t) = \rho_{11}(\infty) + [\rho_{11}(0) - \rho_{11}(\infty)]e^{-\gamma t}$ Oscillatory (Cavity QED, damped Rabi oscillations): $K(t,s) = \Omega_R^2\cos[\Omega_R(t-s)]e^{-\kappa|t-s|}$ Compact Support (finite memory) Power-Law ($1/f$ noise, non-ergodicity): $K(t) \sim 1/t^{1-\alpha}$ 4. Quantitative Measures of Non-Markovianity Definition of three new, operationally significant measures to quantify the degree of memory in a quantum process: Measure Definition Interpretation $\mathcal{M}_L$ $\frac{1}{T}\int_0^T |\dot{L}(t)|\,dt$ Based on the temporal variation of $L(t)$. $\mathcal{M}_L = 0$ iff Markovian. $\mathcal{M}_K$ $\inf_{\{K_i\}} \| \mathcal{K} - \sum_i K_i \otimes K_i^* \|$ Distance to a simple Kraus representation. $\Deg(K)$ $\lim_{t\to\infty} \frac{\ln|K(t)|}{\ln(1/t)}$ Asymptotic exponent classifying the memory length (0 for Markovian, 1 for strongly non-Markovian). 5. Comprehensive Validation Comparison with experimental data from NMR, superconducting cavities, and the FMO complex. Proof-of-concept numerical simulations using an adaptive step-size Runge-Kutta 4 (RK45) integrator, integrated into the interactive version. Interactive Simulator (Online Version) The interactive version of this work, located at ((...)), includes a powerful falsification toolbox: Real-time RK45 Simulator with 5 selectable kernel types. Dynamic 2D plots for population $\rho_{11}(t)$, information flow $\sigma(t)$, and comparison with Lindblad. 3D Bloch sphere visualization of the qubit state. Integrated unit tests for trace conservation and complete positivity. Metrics display ($\mathcal{M}_L$, $\mathcal{M}_K$, $\Deg(K)$, $\tau_{\text{mem}}$, RK4 error). Comparison with experimental datasets (NMR, FMO, etc.). Export options for PDF, LaTeX, Markdown, and JSON data. Repository Contents CORE-IMMUABLE - extension-non-markovienne.md (8.6 MB): The comprehensive, publication-ready manuscript in Markdown format. It contains all theoretical derivations, proofs, and references. This is the permanent, citable record of the work.Online interactive version Citation If you use this work, please cite it as: DESVAUX, G. J. Y. (2023). Non-Markovian Extension. Zenodo. https://doi.org/10.5281/zenodo.19102132 Keywords Open quantum systems, Non-Markovianity, Memory kernels, Lindblad equation, Nakajima-Zwanzig equation, Complete positivity, Kraus representation, Quantum simulator, Runge-Kutta, $1/f$ noise Additional Information Languages: The core manuscript is in English. Titles are also available in French ("Extension non-markovienne") and Chinese ("非马尔可夫扩展"). NON-DISCLOSURE AGREEMENT Academic Collaboration Disclosing Party Receiving Party Legal Name: Hope 'n Mind SASU Name: Representative: Guillaume Desvaux Title / Position: Role: President-Founder Institution / Affiliation: Registration: RCS Brest, SIREN 938 261 310 Institutional Address: Address: 10 Rue Amiral Vallon, 29200 Brest, France Contact Information: This Non-Disclosure Agreement (the “Agreement”) is effective as of the date of the last signature below. 1. Purpose The Receiving Party is being provided with certain Confidential Information solely for the following purpose: Permitted Purpose: Any use of the Confidential Information outside the Permitted Purpose is strictly prohibited unless the Disclosing Party gives prior written consent. 2. Confidential Information “Confidential Information” means any non-public information disclosed by the Disclosing Party to the Receiving Party, whether in oral, written, electronic, visual, or any other form, including but not limited to: data, materials, know-how, trade secrets, source code, technical specifications, research results, business plans, financial data, client lists, and proprietary methods; information marked as confidential; oral disclosures identified as confidential at the time of disclosure and confirmed in writing within five business days. Confidential Information does not include information that: becomes publicly available through no breach of this Agreement; was already lawfully known to the Receiving Party before disclosure, as shown by written records; is independently developed without reference to the Confidential Information; is lawfully received from a third party without restriction. 3. Receiving Party Obligations The Receiving Party shall: keep all Confidential Information strictly confidential; not disclose it to any third party without prior written consent; use it only for the Permitted Purpose; protect it with at least the same degree of care used for its own confidential information, and never less than reasonable care; restrict access to personnel who need to know for the Permitted Purpose; apply appropriate physical and digital security measures, including passwords and encryption where appropriate; require any employee, contractor, or affiliate with access to be bound by confidentiality obligations at least as protective as this Agreement. 4. Prohibited Conduct The Receiving Party shall not: decompile, disassemble, or reverse engineer any source code, algorithm, product, or process; attempt to derive underlying ideas, structure, composition, or technical principles; use the Confidential Information to compete with, bypass, or unfairly benefit from the Disclosing Party; disclose the Confidential Information to any person who is not authorized under this Agreement. 5. Legal Disclosure If disclosure is required by law, court order, or competent governmental authority, the Receiving Party may disclose only the minimum required information, provided that it notifies the Disclosing Party within 48 hours, unless prohibited by law. 6. Breach Notification The Receiving Party shall notify the Disclosing Party immediately, and in any event within 48 hours, after becoming aware of any unauthorized use, access, or disclosure of the Confidential Information, and shall cooperate fully in any remedial action or legal proceeding. 7. Term The confidentiality obligations under this Agreement shall continue for five years from the Effective Date. If any Confidential Information qualifies as a trade secret under applicable law, protection shall continue for as long as that information remains a trade secret. 8. Return or Destruction Upon written request by the Disclosing Party, or immediately upon termination of the Permitted Purpose, the Receiving Party shall: return all materials containing Confidential Information; destroy all copies, notes, extracts, and derivative materials; certify in writing within thirty days that the destruction has been completed, except for one retained legal archive copy if required by law. 9. No License No license or other rights are granted under this Agreement, except the limited right to use the Confidential Information for the Permitted Purpose. All intellectual property rights remain the exclusive property of the Disclosing Party. 10. Remedies The Receiving Party acknowledges that any breach may cause irreparable harm. The Disclosing Party shall be entitled to seek: injunctive relief; monetary damages; consequential losses, where permitted by law; recovery of legal costs and attorney fees, where permitted by law; any other remedy available under applicable law. 11. Academic Collaboration The Receiving Party may publish independent research results only if such publication does not disclose Confidential Information. Before publication, the Receiving Party shall provide the Disclosing Party with a 60-day review period to identify sensitive information or potential patent issues. If applicable, published results shall acknowledge the Disclosing Party’s contribution, subject to the Disclosing Party’s prior written approval of any wording that refers to its Confidential Information. 12. Multi-Party Work If this collaboration involves more than two parties, each party shall ensure that any pers

DOI
10.5281/zenodo.19102131

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Non-Markovian Extension of Quantum Mechanics

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Purpose The Receiving Party is being provided with certain Confidential Information solely for the following purpose: Permitted Purpose: Any use of the Confidential Information outside the Permitted Purpose is strictly prohibited unless the Disclosing Party gives prior written consent. 2. Confidential Information “Confidential Information” means any non-public information disclosed by the Disclosing Party to the Receiving Party, whether in oral, written, electronic, visual, or any other form, including but not limited to: data, materials, know-how, trade secrets, source code, technical specifications, research results, business plans, financial data, client lists, and proprietary methods; information marked as confidential; oral disclosures identified as confidential at the time of disclosure and confirmed in writing within five business days. 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This includes implementations in: any programming language interpreted or compiled environments parallel or distributed computing systems programmable hardware platforms such as CPU, GPU, or FPGA fixed hardware implementations including ASIC or silicon-level architectures 4. Noncommercial Restriction Any use of this work outside the definition of noncommercial use, as defined by the PolyForm Noncommercial License 1.0.0, is not permitted under this license. 5. Commercial and Operational Use Any commercial, industrial, governmental, institutional, regulatory, or production deployment of the methods described in this work constitutes use outside the scope of the PolyForm Noncommercial License 1.0.0 and therefore requires separate authorization from the author(s). 6. Derivative Works and Functional Equivalence Reimplementation, translation, refactoring, optimization, architectural modification, or claims of functional equivalence do not remove a work from the scope of the PolyForm Noncommercial License 1.0.0. Any such implementation remains subject to the same license terms. 6.a Code Size Irrelevance (No Minimum Threshold) For the avoidance of doubt, applicability of the PolyForm Noncommercial License 1.0.0 is independent of code size, number of lines, percentage of implementation, degree of literal similarity, or partial extraction. There is no minimum threshold of code volume required for a work to fall within the scope of this license. Any use, reproduction, reimplementation, refactoring, selective reuse, architectural translation, or functional incorporation of the disclosed concepts—regardless of size or extent—is subject to the terms of the PolyForm Noncommercial License 1.0.0. 7. 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Non-Markovian Quantum Processes with Memory Kernels Extension of the Lindblad Formalism via the Generalized Nakajima-Zwanzig EquationLast & I think for a bit of time, formalized conclusion https://zenodo.org/records/19517607 Description This repository contains the complete theoretical foundations of a (futur) rigorous extension to the Lindblad master equation for describing non-Markovian quantum processes. The work introduces a general mathematical framework based on memory kernels K(t,s)K(t,s)K(t,s) to capture the effects of a structured environment with finite memory, going beyond the Markovian approximation. It is accompanied by an interactive, web-based version of this work, featuring a fully functional simulator, dynamic graphs, a 3D Bloch sphere visualization, and unit tests, available at: ((...)) Core Contributions 1. Axiomatic Definition of KCP\mathcal{K}_{CP}KCP​ A rigorous definition of the space of memory kernels that preserve the fundamental properties of quantum states: complete positivity and trace conservation. Necessary and sufficient conditions for a kernel to be admissible are established and proven. Axiom A1 (Hermiticity): K(t,s)=K∗(s,t)K(t,s) = K^*(s,t)K(t,s)=K∗(s,t) Axiom A2 (L2L^2L2-integrability): ∫0∞ ⁣ ⁣∫0∞∣K(t,s)∣2 ds dt<∞\int_0^\infty\!\!\int_0^\infty |K(t,s)|^2\,ds\,dt < \infty∫0∞​∫0∞​∣K(t,s)∣2dsdt<∞ Axiom A3 (Complete Positivity): σmin⁡(K^(ω))≥0, ∀ω\sigma_{\min}(\hat{K}(\omega)) \geq 0,\ \forall \omegaσmin​(K^(ω))≥0, ∀ω 2. Characterization of the Instantaneous Generator L(t)L(t)L(t) A formal link between the memory kernel K(t,s)K(t,s)K(t,s) and the instantaneous generator L(t)L(t)L(t) is established, with explicit formulas for different kernel types: L(t)=L+∫0tK(τ) dτ−K(0)L(t) = \mathcal{L} + \int_0^t K(\tau)\,d\tau - K(0)L(t)=L+∫0t​K(τ)dτ−K(0) 3. Exactly Solvable Examples Detailed analysis of four canonical memory kernels: Exponential (Ornstein-Uhlenbeck process): ρ11(t)=ρ11(∞)+[ρ11(0)−ρ11(∞)]e−γt\rho_{11}(t) = \rho_{11}(\infty) + [\rho_{11}(0) - \rho_{11}(\infty)]e^{-\gamma t}ρ11​(t)=ρ11​(∞)+[ρ11​(0)−ρ11​(∞)]e−γt Oscillatory (Cavity QED, damped Rabi oscillations): K(t,s)=ΩR2cos⁡[ΩR(t−s)]e−κ∣t−s∣K(t,s) = \Omega_R^2\cos[\Omega_R(t-s)]e^{-\kappa|t-s|}K(t,s)=ΩR2​cos[ΩR​(t−s)]e−κ∣t−s∣ Compact Support (finite memory) Power-Law (1/f1/f1/f noise, non-ergodicity): K(t)∼1/t1−αK(t) \sim 1/t^{1-\alpha}K(t)∼1/t1−α 4. Quantitative Measures of Non-Markovianity Definition of three new, operationally significant measures to quantify the degree of memory in a quantum process: Measure Definition Interpretation ML\mathcal{M}_LML​ 1T∫0T∣L˙(t)∣ dt\frac{1}{T}\int_0^T |\dot{L}(t)|\,dtT1​∫0T​∣L˙(t)∣dt Based on the temporal variation of L(t)L(t)L(t). ML=0\mathcal{M}_L = 0ML​=0 iff Markovian. MK\mathcal{M}_KMK​ inf⁡{Ki}∥K−∑iKi⊗Ki∗∥\inf_{\{K_i\}} \| \mathcal{K} - \sum_i K_i \otimes K_i^* \|inf{Ki​}​∥K−∑i​Ki​⊗Ki∗​∥ Distance to a simple Kraus representation. \Deg(K)\Deg(K)\Deg(K) lim⁡t→∞ln⁡∣K(t)∣ln⁡(1/t)\lim_{t\to\infty} \frac{\ln|K(t)|}{\ln(1/t)}limt→∞​ln(1/t)ln∣K(t)∣​ Asymptotic exponent classifying the memory length (0 for Markovian, 1 for strongly non-Markovian). 5. Comprehensive Validation Comparison with experimental data from NMR, superconducting cavities, and the FMO complex. Proof-of-concept numerical simulations using an adaptive step-size Runge-Kutta 4 (RK45) integrator, integrated into the interactive version. Interactive Simulator (Online Version) The interactive version of this work, located at ((...)), includes a powerful falsification toolbox: Real-time RK45 Simulator with 5 selectable kernel types. Dynamic 2D plots for population ρ11(t)\rho_{11}(t)ρ11​(t), information flow σ(t)\sigma(t)σ(t), and comparison with Lindblad. 3D Bloch sphere visualization of the qubit state. Integrated unit tests for trace conservation and complete positivity. Metrics display (ML\mathcal{M}_LML​, MK\mathcal{M}_KMK​, \Deg(K)\Deg(K)\Deg(K), τmem\tau_{\text{mem}}τmem​, RK4 error). Comparison with experimental datasets (NMR, FMO, etc.). Export options for PDF, LaTeX, Markdown, and JSON data. Repository Contents CORE-IMMUABLE - extension-non-markovienne.md (8.6 MB): The comprehensive, publication-ready manuscript in Markdown format. It contains all theoretical derivations, proofs, and references. This is the permanent, citable record of the work.Online interactive version Citation If you use this work, please cite it as: DESVAUX, G. J. Y. (2023). Non-Markovian Extension. Zenodo. https://doi.org/10.5281/zenodo.19102132 Keywords Open quantum systems, Non-Markovianity, Memory kernels, Lindblad equation, Nakajima-Zwanzig equation, Complete positivity, Kraus representation, Quantum simulator, Runge-Kutta, 1/f1/f1/f noise Additional Information Languages: The core manuscript is in English. Titles are also available in French ("Extension non-markovienne") and Chinese ("非马尔可夫扩展"). NON-DISCLOSURE AGREEMENT Academic Collaboration Disclosing Party Receiving Party Legal Name: Hope 'n Mind SASU Name: Representative: Guillaume Desvaux Title / Position: Role: President-Founder Institution / Affiliation: Registration: RCS Brest, SIREN 938 261 310 Institutional Address: Address: 10 Rue Amiral Vallon, 29200 Brest, France Contact Information: This Non-Disclosure Agreement (the “Agreement”) is effective as of the date of the last signature below. 1. 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Abstract "Last & I think for a bit of time, formalized conclusion https://zenodo.org/records/19517607 " This "wip" presents a starting extension of quantum mechanics to non-Markovian processes, establishing a unified theoretical framework for open quantum systems with temporal memory. We develop a mathematical formalism based on temporal convolution integrals and memory operators, providing a unified description of Markovian and non-Markovian dynamics. Original contributions: Generalization of the Lindblad equation via temporal memory kernels Rigorous classification of processes by memory degree Geometric measure of non-Markovianity based on state space geometry Five explicitly falsifiable hypotheses with experimental protocols Keywords: Quantum mechanics Non-Markovian processes Master equation Open quantum systems Falsifiability 1. Introduction 1.1 Historical context and open problem Quantum mechanics, founded by Schrödinger (1926) and Heisenberg (1925), describes the deterministic evolution of isolated systems via the Schrödinger equation. However, any real physical system interacts with its environment — this is the paradigm of open quantum systems. Since the work of Caldeira and Leggett (1983) on quantum Brownian motion, and the contributions of Lindblad (1976) on quantum semigroup generators, the open systems formalism has become fundamental in quantum theory. However, a major problem remains unsolved: the complete and operationally significant characterization of quantum non-Markovianity. Central problem: Existing measures of non-Markovianity (BLP, RHP, Š) do not provide quantitative predictions on physical observables that could be experimentally tested with given precision. Our work addresses this gap by proposing a theoretical framework with numerically testable predictions.(...) 8. Conclusion This work presented a rigorous and systematically testable extension of quantum mechanics to non-Markovian processes. Unlike previous approaches that focused on qualitative measures, we provide a framework with numerically verifiable predictions. NON-DISCLOSURE AGREEMENT Academic Collaboration Disclosing Party Receiving Party Legal Name: Hope 'n Mind SASU Name: Representative: Guillaume Desvaux Title / Position: Role: President-Founder Institution / Affiliation: Registration: RCS Brest, SIREN 938 261 310 Institutional Address: Address: 10 Rue Amiral Vallon, 29200 Brest, France Contact Information: This Non-Disclosure Agreement (the “Agreement”) is effective as of the date of the last signature below. 1. 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This preprint presents a self-contained and mathematically explicit reconstruction of the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) master equation starting from exact microscopic unitary dynamics through the Nakajima-Zwanzig projection operator formalism. Beginning with the exact non-local generalized master equation, we systematically analyze the hierarchy of approximations required for the emergence of a Markovian quantum dynamical semigroup. The Born (weak-coupling), Markov (time-localization), and secular approximations are derived and interpreted as successive information-reduction steps, each associated with clearly identifiable mathematical assumptions and physical consequences. Particular attention is devoted to the role of secularization in transforming the Redfield generator into a completely positive GKSL structure. To provide a concrete worked example, the formalism is applied to a damped two-level system coupled to a bosonic thermal reservoir, where the Redfield and GKSL equations are derived explicitly and compared at the microscopic level. Beyond the derivation itself, the work develops a systematic map of validity limits and failure regimes. The breakdown of the Born, Markov, secular, factorization, and stationarity assumptions is analyzed in terms of environmental correlation times, spectral-density structure, non-Markovian memory effects, information backflow, and loss of semigroup behavior. The resulting framework clarifies the precise operational domain in which GKSL dynamics can be regarded as a physically reliable effective description and provides a rigorous foundation for applications involving entropy-production theorems, quantum thermodynamics, and open-system information theory.
A post-Markovian quantum master equation is derived, which includes bath memory effects via a phenomenologically introduced memory kernel k(t)k(t)k(t). The derivation uses as a formal tool a probabilistic single-shot bath-measurement process performed during the coupled system-bath evolution. The resulting analytically solvable master equation interpolates between the exact Nakajima-Zwanzig equation and the Markovian Lindblad equation. A necessary and sufficient condition for complete positivity in terms of properties of k(t)k(t)k(t) is presented, in addition to a prescription for the experimental determination of k(t)k(t)k(t). The formalism is illustrated with examples.
Currently, there is no systematic way to describe a quantum process with memory solely in terms of experimentally accessible quantities. However, recent technological advances mean we have control over systems at scales where memory effects are non-negligible. The lack of such an operational description has hindered advances in understanding physical, chemical, and biological processes, where often unjustified theoretical assumptions are made to render a dynamical description tractable. This has led to theories plagued with unphysical results and no consensus on what a quantum Markov (memoryless) process is. Here, we develop a universal framework to characterize arbitrary non-Markovian quantum processes. We show how a multitime non-Markovian process can be reconstructed experimentally, and that it has a natural representation as a many-body quantum state, where temporal correlations are mapped to spatial ones. Moreover, this state is expected to have an efficient matrix-product-operator form in many cases. Our framework constitutes a systematic tool for the effective description of memory-bearing open-system evolutions.
Description Boson sampling, originally proposed by Scott Aaronson and Alex Arkhipov as a candidate pathway toward quantum computational advantage, requires the evaluation of matrix permanents of complex-valued submatrices drawn from Haar-random unitary transformations. Computing the permanent of a general complex matrix is a well-known #P-hard problem and represents the principal computational barrier for classical simulation of linear-optical quantum circuits. This work introduces an evolutionary approach to permanent evaluation, derived from Glynn’s ±1 enumeration formula, traversed through binary reflected Gray code, extended to complex-valued arithmetic, and organized as a shared-nothing parallel computation model. Preliminary experiments suggest that the resulting implementation exhibits unexpected performance characteristics, enabling evaluation of boson-sampling–relevant matrix sizes on low-resource commodity hardware without the use of specialized accelerators. These observations raise a natural question: How far can classical simulation of boson sampling be pushed using carefully engineered algorithms? The accompanying manuscript provides the full algorithmic formulation, validation methodology, benchmark procedures, and numerical results required to reproduce and evaluate the approach. Statement of Prior Art and License Terms (Aligned with PolyForm Noncommercial License 1.0.0) 1. Permitted Noncommercial Use Use of the concepts, algorithms, and computational methods described in this work for noncommercial purposes, including academic research, independent study, education, benchmarking, validation, reproducibility studies, and experimental evaluation, is permitted under the terms of the PolyForm Noncommercial License 1.0.0, provided that proper attribution is given. 2. Statement of Prior Art This publication constitutes a formal public disclosure establishing prior art for the algorithmic methods and computational strategies described herein, including but not limited to: parallel traversal of Glynn permanent enumeration Gray-code–driven combinatorial traversal techniques complex-valued permanent computation strategies for boson-sampling matrices multi-core implementations targeting low-resource commodity hardware environments This disclosure is intended solely to prevent third-party patent claims on the disclosed concepts and does not grant any commercial rights. 3. Scope of the License All implementations of the methods described in this work—whether in software or hardware—are governed by the PolyForm Noncommercial License 1.0.0. 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Enforcement and Remedies Any use of the methods described in this work in violation of the PolyForm Noncommercial License 1.0.0 may be addressed through remedies available under applicable international law. Nothing in this disclosure prevents the author(s), or third parties acting on their behalf, from performing technical analysis or reverse engineering of deployed systems for the purpose of determining whether the disclosed methods have been implemented following the publication date of this work. 11. Versioning This record may contain multiple versions. Updates to presentation, terminology, benchmarks, or documentation do not alter: the core methodological contributions the scope of protection the license terms The most recent license and scope documents in the repository are authoritative. 12. Knowledge Contamination Any individual or entity that has reviewed, studied, tested, or otherwise been exposed to the materials contained in this record shall be considered knowledge-contaminated with respect to the disclosed concepts. Subsequent development of substantially similar implementations may therefore be evaluated in light of this prior exposure and the timestamped archival record of this publication. AuthorAndrés Sebastián Pirolo ORCID 0009-0004-3899-1222 andrespirolo@gmail.com Legal and External Affairs📧 brisademar96@gmail.com
We construct a large class of non-Markovian master equations that describe the dynamics of open quantum systems featuring strong memory effects, which relies on a quantum generalization of the concept of classical semi-Markov processes. General conditions for the complete positivity of the corresponding quantum dynamical maps are formulated. The resulting non-Markovian quantum processes allow the treatment of a variety of physical systems, as is illustrated by means of various examples and applications, including quantum optical systems and models of quantum transport.