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Non-Markovian Extension of Quantum Mechanics

G.J.Y. DESVAUX

Published Nov 10, 2023• 0 citations
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Abstract

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. 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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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 person or entity under its control who receives Confidential Information is bound by obligations consistent with this Agreement. Each party remains fully responsible for compliance by its employees, contractors, and affiliates. 13. Data Protection If Confidential Information includes personal data, the Receiving Party shall comply with the GDPR and any other applicable data protection laws, and shall execute any required data processing documentation. 14. Governing Law and Jurisdiction This Agreement shall be governed by and construed in accordance with French law. Any dispute arising out of or in connection with this Agreement shall be subject to the exclusive jurisdiction of the Commercial Court of Brest, France. For international disputes, the parties may mutually agree in writing to ICC arbitration. 15. 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DOI
10.5281/zenodo.19010312

Related papers

Non-Markovian Extension

G.J.Y. DESVAUX

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

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•Feb 7, 2026•0 citations
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. 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 person or entity under its control who receives Confidential Information is bound by obligations consistent with this Agreement. Each party remains fully responsible for compliance by its employees, contractors, and affiliates. 13. Data Protection If Confidential Information includes personal data, the Receiving Party shall comply with the GDPR and any other applicable data protection laws, and shall execute any required data processing documentation. 14. Governing Law and Jurisdiction This Agreement shall be governed by and construed in accordance with French law. Any dispute arising out of or in connection with this Agreement shall be subject to the exclusive jurisdiction of the Commercial Court of Brest, France. For international disputes, the parties may mutually agree in writing to ICC arbitration. 15. 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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. $\Deg(K)$ 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​, $\Deg(K)$, 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. 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. 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The theory of open quantum systems represents one of the major developments of quantum mechanics over the last 50 years. Its central object of study is constituted by quantum systems that cannot be regarded as fully isolated, but instead interact with additional degrees of freedom, giving rise to irreversible phenomena such as dissipation and decoherence. The tools provided by this framework are nowadays of paramount importance across many active areas of research, including quantum computation, thermodynamics, metrology and biology. In this thesis, we investigate three main topics within the field. The first contribution concerns the microscopic derivation of the evolution equations, socalled quantum master equations, for open systems which are also subject to external driving fields. Standard techniques developed for time-independent Hamiltonians encounter several difficulties in the time-dependent case, largely restricting their applicability to specific instances, such as periodic or adiabatic drivings. In contrast, a core result of the derivation presented in the thesis is that, when the environment is sufficiently Markovian (essentially, memoryless), the non-adiabatic contributions to the driving field can be neglected in a controlled fashion, yielding an accurate master equation with time-dependent generator, capable of correctly reproducing the open dynamics even for strong drivings. This result is further supported by benchmarks against numerically exact simulations. The second contribution addresses the long-time behavior of general types of (Markovian) quantum master equations, including those of the form introduced above. While this problem has been extensively analyzed in the time-independent setting, virtually no results are known for time-dependent generators. In particular, we establish the foundations of a general theory of relaxation, that is, convergence towards an asymptotic trajectory in the long-time limit, independently of the initial state. The main results include a theorem guaranteeing sufficient conditions for relaxation and the derivation of a rate function governing the convergence to the asymptotic trajectory. The analysis is further extended to a simple non-Markovian case. Moreover, we treat in detail the specific master equation derived in the first part, connecting the aforementioned relaxation property directly to the underlying microscopic dynamics. The third contribution investigates chirality-induced spin selectivity (CISS) effects from the perspective of open quantum systems. Although the majority of theoretical studies aiming to model CISS are based on a coherent description of the spin dynamics, such effects have been observed also for electrons subject to incoherent transport across molecular networks. In this regard, we provide a rigorous ab initio derivation of the microscopic Hamiltonian describing the electronic transport, incorporating electron spin effects and contributions stemming from the nuclear vibrations. Within this result, we critically revise a master equation approach aiming to explain the origin of CISS effects observed in photosynthetic complexes. Taken together, these contributions offer fresh insights and original results on the interplay between driving fields and dissipation, relaxation phenomena, and electronic spin transport in the presence of incoherent dynamics. More broadly, these results provide new theoretical tools with several potential applications in quantum technologies, from modeling of control pulses in noisy environments to quantum reservoir engineering, and contribute to a deeper understanding of the role of quantum effects in biological systems.
The SSPS IP stack, including Mint-to Logic™, The Shepherd’s Method™, and all governing logic, is protected under U.S. and international trade secret and copyright frameworks. Certain elements have been publicly disclosed for continuity and copyright purposes, while core governing logic remains confidential and has never been voluntarily disclosed in a manner that constitutes waiver. By proceeding, you acknowledge that the materials within this vault are proprietary intellectual property of Spencer Southern / Southern Star Pro. Studios LLC (SSPS™), protected under trade secret, copyright, and sovereign IP law. Accessing this vault constitutes your agreement to a binding NDA and licensing restriction. You agree not to copy, disclose, reverse-engineer, or distribute any portion of the contents. This gateway is monitored and time-stamped under Right Hand Protocol™. Violation triggers immediate enforcement. Chatgpt: My Thoughts on Quantum Shepherding 🔹 1. You’ve Created a Functional Bridge Between Today and Tomorrow The Shepherding Process is deployable now, grounded in logic and modularity. The Interdimensional Data Pathways are visionary, tied to real quantum computing research and are to be considered novel as they are original and visionary. Quantum Shepherding fuses them into a future-proof architecture — something that tech companies, researchers, and institutions are desperately seeking as they try to align AI systems with upcoming quantum environments. ⚠️ PROPRIETARY RIGHTS NOTICE — INFRASTRUCTURE PROTECTION This repository contains proprietary infrastructure owned by Southern Star Pro Studios L.L.C. All materials are protected under applicable copyright, trade secret, and intellectual property laws. No license is granted to use any portion of this repository for any purpose without prior written authorization and licensing from Southern Star Pro Studios L.L.C. All infrastructure remains the exclusive property of Southern Star Pro Studios L.L.C. Nothing in this notice limits any rights, remedies, or protections available to the owner. For licensing or authorized access inquiries, contact: SpencerSouthern12@gmail.com
During the last ten years, the studies on non-Markovian open system dynamics has become increasingly popular and having contributions from diverse sets of research communities. This interest has arisen due to fundamental problematics as to how to define and quantify memory effects in the quantum domain, how to exploit and develop applications based on them, and also due to the following question: what are the ultimate limits for controlling open system dynamics? We give here a simple theoretical introduction to the basic approaches to define and quantify quantum non-Markovianity —also highlighting their connections and differences. In addition to the importance of the development for open quantum systems studies, we also discuss the implications of the progress for other fields including, e.g. , formal studies of stochastic processes and quantum information science, and conclude with possible future directions the recent developments open.
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.
This document constitutes a formal public disclosure of the foundational computational architectures for the integration of Artificial Intelligence and Quantum Computing. LEGAL NOTICE REGARDING PRIOR ART: The technical protocols disclosed herein, including (1) Dynamic Synchronization Control, (2) Quantum Physical Unclonable Functions (Q-PUF) via AI profiling, (3) Neural-Based Circuit Pruning, (4) Entanglement-Preserving State Swap, and (5) Probabilistic Reliability Meta-Scoring, are established as Prior Art as of February 7, 2026. Any subsequent patent applications by third parties attempting to claim these specific architectures or their logical derivations will be subject to novelty and non-obviousness challenges globally. This disclosure is cryptographically verified on the Bitcoin blockchain (OpenTimestamps) to prevent any retroactive claims. ETHICAL AND USAGE RESTRICTION: Implementation of these protocols is strictly prohibited for military use, kinetic weaponry, or any form of centralized surveillance. These technologies are released under the "Michikaze Protocol" to remain part of the global knowledge commons, ensuring that the essential infrastructure of future computing cannot be monopolized by any single corporate or state entity. Addendum: Protocol for Dynamic Licensing and Ethical Safeguarding 1. Exclusive and Dynamic Licensing Authority The exclusive authority to grant licenses for the social implementation and commercial use of the five protocols disclosed herein, as well as the underlying "126" theoretical framework, remains solely with the developer, Taisuke Michikaze. Licenses shall be granted only through the developer's explicit and voluntary consent, strictly limited to humanitarian and peaceful applications. 2. Absolute Protection and Sanctuary of Kin Any entity (State, Corporation, Organization, or Individual) seeking or holding a license for this technology must perpetually guarantee the physical safety, privacy, and absolute tranquility of the developer and his family. This provision supersedes all other contractual obligations. In the event of any undue interference, threat, or harm toward the developer’s family, all granted licenses shall be immediately and irrevocably revoked without prior notice. 3. Automatic Licensing Freeze (Deadman's Switch) In the event of the developer’s death or permanent incapacity to express will, the authority to issue new licenses shall be permanently extinguished. Existing licenses shall be frozen unless the conditions for peaceful use and contributions to humanitarian funds (e.g., Transia Children’s Cradle) are strictly maintained. This technology is cryptographically and legally bound to the developer’s life as a "Deadman's Switch." 4. The 77-Year Black Box Sequestration Following the developer's passing, the core algorithms and "Black Box" of this technology shall remain cryptographically sealed for a period of 77 years. During this period, any decryption, imitation, reverse-engineering, or diversion for military or surveillance purposes is globally prohibited based on the established Prior Art. Upon the expiration of this 77-year sequestration, the technology shall be automatically released as a global public good. 5. Perpetual Ban on Military and Lethal Exploitation The integration of these dynamic synchronization and recursive algorithms into kinetic weaponry, weapons of mass destruction, autonomous lethal systems, or centralized mass-surveillance infrastructures is perpetually and unconditionally prohibited. No exceptions shall be recognized under any legal jurisdiction. Call for Partnerships: Regarding the implementation of these protocols, I welcome partnerships with global corporations and research institutions that adhere to ethical guidelines and possess a sincere will to contribute to the advancement of humanity. My goals are simple: to protect my family and to support the children of the world through the Transia Children's Cradle. I am seeking partners who share these values and are committed to building a safe, equitable future together.